生育間隔與嬰兒死亡率的關聯性: 尼加拉瓜的實證 - 政大學術集成

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(1)國立政治大學應用經濟與社會發展英語碩士學位學程 International Master’s Program of Applied Economics and Social Development College of Social Sciences National Chengchi University. 政治大碩士論文. 立. ‧. ‧ 國. 學. Master’s Thesis. sit. y. Nat. The association between birth spacing and infant mortality: Evidence from Nicaragua. n. er. io. 生育間隔與嬰兒死亡率的關聯性: 尼加拉瓜的實證 a. iv l C n hengchi U. Student: 卡綺亞 Kiara Argentina Calero Hernandez Advisor: 連賢明 Hsien-Ming Lien. 中華民國 109 年 07 月 July 2020. DOI:10.6814/NCCU202001257.

(2) Abstract This study aims to provide evidence on the association between the length of birth spacing and infant mortality, and the mechanisms by which the interval produces deleterious effect in child survival for the Nicaraguan experience. Using pooled data from the Demographic and Health Surveys of 1998-2011, the association is evidenced by using survival analysis. The results show that there’s generalized deleterious effect of the shortest than 18 months interval for Nicaraguan mothers, while finding indication of the existence of maternal depletion syndrome and sibling competition. A larger effect prevails for teenage mothers that space their children closely, possibly due to her unreadiness for childbearing and childbirth. While, the lack of wealth of the household and the inaccessibility to public health care of which rural areas suffer from, can play a. 政治大 of any form of sibling competition. Concrete policy implications should be segmented by 立 large role in enhancing the deleterious effect of the short birth interval through the boost. age groups and respond to different capabilities of family responses to deal with the. ‧ 國. 學. potential effects of a short-spaced pregnancy and childbirth.. ‧. Keywords: Birth spacing, infant mortality, causal mechanisms, Nicaragua, survival. y. Nat. analysis. n. al. er. io. sit. 關鍵詞：生育間隔，嬰兒死亡率，因果機制，尼加拉瓜，生存分析. Ch. engchi. i Un. v. 2 DOI:10.6814/NCCU202001257.

(3) Acknowledgements Firstly, I would like express my gratitude to my thesis advisor Prof. Lien HsienMing, Professor of the Department of Public Finance at National Chengchi University. Prof. Lien was always prompt to provide his advice on all the stages of this process. He consistently guided me through this research, to gather and obtain the best and more relevant research results. I would also like to acknowledge Prof. Li Hao-Chung, Associate Professor of the Department of Economics at National Chengchi University and Prof. Yang Tzu-Ting, Research Fellow at Academia Sinica for being part of my defense committee, providing valuable insights and commentary on this thesis. Finally, I more than grateful and indebted to my parents, family and friends for. 政治大 studying abroad and the research process of writing this thesis. This accomplishment will 立. their unconditional support and continuous encouragement throughout my years of. 學. ‧ 國. not be possible without their help.. My most sincere thanks. Kiara Calero. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. 3 DOI:10.6814/NCCU202001257.

(4) Table of contents 1.1.. Problem ..................................................................................................................... 8. 1.2.. Purpose ..................................................................................................................... 8. Literature Review .............................................................................................................. 9 2.1.. Child spacing............................................................................................................. 9. 2.2.. Infant and child mortality......................................................................................... 12. 2.3.. Child spacing effects on infant and child mortality ................................................... 14. 2.3.1. a). Maternal depletion syndrome ................................................................................... 15. b). Sibling competition.................................................................................................. 16. c). Breastfeeding-pregnancy overlap ............................................................................. 16. d). Alternative mechanisms ........................................................................................... 17. 2.3.2.. 立. Data and Methods ........................................................................................................... 19 Data......................................................................................................................... 19. 3.2.. Empirical methods ................................................................................................... 23. 學. 3.1. 3.2.1.. Survival analysis .................................................................................................. 23. ‧. a). Non-parametric estimations ..................................................................................... 24. b). Semi-parametric estimation: The Cox proportional hazard model ............................. 25. c). Extended Cox proportional hazard model for time-dependent variables .................... 27. d). Parametric estimation: The Weibull model ............................................................... 27. y. Nat. io. al. v. 3.2.2.. Empirical model .................................................................................................. 28. 3.2.3.. Expected results ................................................................................................... 30. n. 4. 政治大. Empirical evidence of the mechanisms in the literature ..................................... 17. ‧ 國. 3. Causal mechanism of effects of spacing in infant mortality............................... 15. sit. 2. Introduction ...................................................................................................................... 6. er. 1. Ch. engchi. i Un. Results ............................................................................................................................ 30 4.1.. Non-parametric findings .......................................................................................... 30. 4.2.. Semi-parametric model findings .............................................................................. 33. 4.2.1.. Cox proportional hazards model ....................................................................... 33. 4.2.2.. Extended Cox proportional hazards model ....................................................... 36. 4.3.. Parametric model findings ....................................................................................... 38. 4.3.1.. Weibull distribution model ............................................................................... 38. 4.3.2.. Weibull model: By-groups definitions on predominance of causal mechanisms 41. 5. Limitations of the study ................................................................................................... 46. 6. Conclusions .................................................................................................................... 47. References .............................................................................................................................. 52 Appendix ................................................................................................................................ 55. 4 DOI:10.6814/NCCU202001257.

(5) List of tables Table 1: Nicaraguan DHS (1998-2011) general description ......................................... 20 Table 2: Description of variables used in the empirical model ..................................... 21 Table 3: Distribution of selected socioeconomic variables among Nicaraguan families, 1998-2011 ................................................................................................................... 31 Table 4: Cox proportional hazards model for determinants of infant mortality in Nicaragua.................................................................................................................... 35 Table 5: Extended Cox proportional hazard model for time-dependent variables results for determinants of infant mortality in Nicaragua ........................................................ 37. 政治大. Table 6: Weibull distribution model results for determinants of infant mortality in Nicaragua.................................................................................................................... 39. 立. Table 7: Average marginal effects for Weibull distribution model of determinants of. ‧ 國. 學. infant mortality in Nicaragua....................................................................................... 40 Table 8: Weibull distribution model results for determinants of infant mortality in. ‧. Nicaragua by-group specifications .............................................................................. 42 Table 9: Linear probability model for infant mortality in Nicaragua ............................ 56. Nat. sit er. io. List of figures. y. Table 10: Weibull distribution model results by gender of Nicaraguan children .......... 57. al. n. iv n C Figure 1: Kaplan Meier survival curves intervals.................................... 33 h efornInterbirth gchi U Figure 2: Nelson Aalen cumulative hazard for Interbirth intervals ............................... 55. 5 DOI:10.6814/NCCU202001257.

(6) 1 Introduction Around 5.3 million children died in 2018 worldwide before reaching five years of age. Even more alarming is the fact that 75% of those children didn’t even live past their first year1. Infant mortality is a health tragedy that has greatly affected the world, much more so before the current reproductive health care technological developments widely diffused. Over the past decades, the world has constantly reduced the rates of death of this young and entirely dependent group, only in the past twenty-years the infant mortality death has been cut by half, falling from 56.3 to 28.9 deaths per 1,000 live births. Nonetheless, the decrease of infant mortality has not been equal, as some regions are still falling behind in the reduction targets. Nearly 80% of the 4 million of the infant deaths of 2018 occurred in Sub-Saharan Africa or South Asia (49% and 30%, respectively).. 治政 best performance in reducing child mortality, with most 大 countries reducing at least 20% 立 of their child mortality rates, while others –including Nicaragua– had cut off the mortality. On the contrary, in the latter half of the past century Latin America has had the. ‧ 國. 學. rates among children in half from 1980-2000 (Ahmad, Lopez & Inoue, 2000). Although, in Nicaragua the greater results of the reduction of the infant mortality rate were seen. ‧. during the early 80s and from the mid-1990s throughout 2009, averaging a 5% yearly consistent decline. Nonetheless, in recent years the rate of infant mortality in the country. y. Nat. sit. has continued to decline but at a very slow rate reaching a decrease of 0.6% to 1% decline. al. er. io. yearly (World Bank, 2020).. v. n. On the other hand, the good historical performance doesn’t hold as strongly when. Ch. i Un. dissecting the comparison within the Latin American region. Nicaragua has the second. engchi. largest infant mortality rate in Central America –and the 11th among Latin American countries– with a rate of 15.7 deaths of children belong one year old per 1,000 live births, i.e. 1.5% of Nicaraguan children will not live past their first year and 1.8% will pass away before turning five years old. The target of the Sustainable Development Goals (SDGs) is to reduce by 2030 the child mortality to 25 per 1,000 live births, thus, the target has been met in Nicaragua since 2003. But the issue remains relevant because most of these deaths are preventable; under a free-public health care system and considering all the modern methods to prevent and treat diseases during early childhood the rate is still too high, even when compared to the Latin American average of 14 deaths per 1,000 live births. Among the main causes of 1. Statistics on number of infant deaths and infant mortality rates taken from the World Bank Data (2020).. 6 DOI:10.6814/NCCU202001257.

(7) infant mortality in Nicaragua, the Ministry of Health points out the following reasons: respiratory distress syndrome, sepsis, asphyxia, birth defects, pneumonia and severe diarrhea (Ministerio de Salud, 2008). Nevertheless, all of these conditions and diseases have their own set of causes and triggers. Particularly, research has identified the largest causes in developing countries to be associated with malnutrition, as the lack of nutrients make children more vulnerable to infectious diseases, as well as quantity and frequency, namely mother’s birth parity and child spacing, since those dictate how resources are spread within the household (Blau, 1986). Indeed, the World Health Organization (WHO) has expressly suggested waiting at least 24 months after a live birth to attempt another pregnancy, that is, an interbirth interval of 33 months or roughly 3 years. The recommendation pursues the objective of reducing the risk of adverse maternal, perinatal and infant outcomes (World Health Organization, 2007).. 立. 政治大. Considering the above, the Nicaraguan government has recognized in official. ‧ 國. 學. documents and large-scale health strategy planning that young mothers and short birth intervals have a deleterious effect in child health and development, increasing their risk. ‧. of death (Ministerio de Salud, 2007). Within the same document, the country-level strategy for sexual and reproductive health highlights the main pathways towards. sit. y. Nat. improving mothers and children’s health: (1) Through sexual education, that leads to. io. er. increase awareness of family planning and also increases teenage first sexual-act age; (2) through family planning and contraceptives, by actually meeting the unsatisfied demand. n. al. Ch. i Un. v. and increasing the utilization rate; and through the improvement and expansion of health. engchi. care services, such as increasing institutional births and the coverage of antenatal care. Despite these guidelines, the issue lies on the lack of objective actions proposed nor taken. Sexual education remains a weak spot on the policy actions, as schools do not approach sexuality topics as properly and in-depth as it’s needed by the Nicaraguan youth. In addition, there are many teenagers and young people that escape the policies as they are out of the educational system. There’s no evidence, despite being recognized as a potential influencing factor in infant, child and maternal mortality, that sexual education in Nicaragua addresses the importance of birth spacing as a tool to reduce the risk of exposing both mothers and children to health hazards. On top of that, there’s also little evidence that supports the WHO claims of the deleterious effects of short or long birth intervals for the Nicaraguan case, nor there’s evidence on the possible mechanism by which such association can be made. There is a 7 DOI:10.6814/NCCU202001257.

(8) lot to be said about whether advocating to promote an optimal interval provides a viable infant and child mortality reduction route. The former lies on the fact that the promotion of a healthy-recommended birth interval is a not so well understood public health intervention, consequently also heavily underutilized (Norton, 2005). The importance of proper birth spacing is widely known, but for the Nicaraguan case, is based on evidence for other countries and regions and has not been used as a policy tool. Nicaragua, thus, has an unrealized potential of tackling infant and child mortality through polices directed to increase the spacing between births and improving mothers and children health through healthier reproductive practices.. 1.1.. Problem On one hand, infant mortality remains high in Nicaragua, when compared to the. 政治大 health complications. On the other hand, a significantly large proportion of Nicaraguan 立 mothers choose to have children very shortly spaced apart (less than 18 months). At the Latin American statistics, and most of these deaths occur due to preventable diseases and. ‧ 國. 學. same time, it’s widely promoted by international organizations and backed on international research on the past century, that short child spacing does impact negatively. ‧. the risk of death of a child and has deleterious health outcomes. Despite these broadly. y. Nat. recognized propositions, there’s little evidence for the Nicaraguan experience regarding. sit. how impactful and damaging, if at all, can the short birth intervals be for child survival. n. al. er. io. outcomes; and also, what possible mechanisms would those effects be attributed to.. 1.2.. Purpose. Ch. engchi. i Un. v. This study aims to provide evidence on the association between the length of birth spacing and infant mortality, and the mechanisms by which the interval produces deleterious effect in child survival for the Nicaraguan experience based on data from the Demographic and Health Surveys of 1998-2011. Particularly, this study’s purpose is to analyze how child spacing along with a set of other possible incidence factors can increase or decrease the risk of death that a child is exposed to; and which mechanisms will these results be associated with. Ultimately, the results provided by this research also aim to serve as baseline information for the policy makers and contribute to better shape public and private interventions towards addressing the health tragedy that is infant and child mortality. By providing evidence on this matter, policy makers can better shape their strategies towards reducing infant mortality and increasing the welfare of Nicaraguan families. 8 DOI:10.6814/NCCU202001257.

(9) 2 Literature Review The study of human fertility has followed, from multidisciplinary standpoints, the main dynamics of population transitions in the world. Those transitions, whether attained as responses to economic transformations at regional, country and household levels, or to technological innovations regarding family planning mechanisms, among other possible causes, have fueled scholarly discussion for decades. The truth is that in the past six decades, family size has fallen by half –from 5 to 2.5 children per family– in a worldwide trend (Darroch, 2013); and family planning, boosted as public policy for developed and developing countries alike, is more widely used and has improved parental decision regarding number and timing of fertility (Powell, 1995). These factors introduce a new variable in the household fertility decision-making,. 治政 that deal with the same fertility time constraint but want大 fewer children. Therefore, time 立 spacing between births becomes a key issue, especially when these decisions have child spacing. The consistent decline of family size expands the possibilities for families,. ‧ 國. 學. important consequences in the life outcomes of the members of the household.. 2.1.. Child spacing. ‧. Decisions regarding child spacing are also determined by heterogeneous. sit. y. Nat. characteristics that surround human behavior. In their comprehensive cross-country comparative study, Rodriguez, et al. (1984) found that birth intervals were determined by. io. er. early behavior and socioeconomic differences that affect the reproductive process,. al. n. iv n C U age at the start of the interval, h e n gbehavior; its incidence breastfeeding and contraceptive c h i and. especially for transitional societies, i.e. developed countries, such as education, through. through aging sterility, ultimately ceasing the opportunity window for reproduction. In regards to age, for the interval between the first and second child, older women were found to be more likely to space their births closer than younger women did (Wineberg & McCarthy, 1989). These reflect the pressure due to the fertility time constraint and the uses of contraception among younger women experienced in the last decades since Morgan and Rindfuss (1999) found that the relationship between early childbearing, parents having more children in their lifetimes and the subsequent rapid pacing of the births, weakened deeply in comparison to previous studies (Bumpass, Rindfuss & Janosik, 1978; Trussell & Menken, 1978). Among other determinants for the spacing between children are the preferences regarding parental presence, specifically those in terms of breastfeeding. The prolonged 9 DOI:10.6814/NCCU202001257.

(10) breastfeeding does not only benefit child nurture and development but is also the cause of lactational amenorrhea in breastfeeding moms (Smith, 1985). Additionally, breastfeeding practices are also subject to cultural traditions and societal influence, and as Smith (1985) also finds, the median of some countries in Southeast Asia and SubSaharan Africa between 15 to 30 months of prolonged breastfeeding. Thus, whether as byproduct decision of increased education or indirectly through cultural legacy traditions, longer periods of full-breastfeeding increase the spacing between births. Returning to Rodriguez, et al. (1984), households in developed countries that have tools to highly control their fertility, evaluate the timing and spacing of early births; but the later ones may include pregnancies product of contraceptive failures. For which, the authors suggest accounting for socioeconomic variables such as housing tenure, race and religion. Nonetheless, there are also unaccounted for occurrences in the household that. 政治大. might lead to changes in child spacing. For instance, Winikoff (1987) suggests that. 立. unusual long intervals between births can be caused by disruptions to the family. ‧ 國. 學. ecosystem, e.g. divorce, death of one of the parents. Or on the other hand, biological factors mainly associated with the mothers, such as predisposition to fetal loss, death of. ‧. the previous child, abortions, and the mother’s health on itself, are all associated with the variations in the length of birth intervals (Winikoff, 1987).. Nat. sit. y. Considering the aforementioned determinants, families decide upon optimal. io. er. length intervals but this decision has consequences in life outcome for the offspring and the household on itself. It’s also argued that households may foresee these unwanted. n. al. Ch. i Un. v. outcomes and modify their selection of spacing length. On the macro level, longer interval. engchi. reduces the potential of child production when considering the fertility time constraint, thus reducing the rate of population growth. Alternatively, it can also impact the rate of growth of a population through its incidence on the average spacing between generations (Newman, 1983). At the household level, larger spacing between children serves to reduce the family size (Hanushek, 1992), which is, in turn, a key factor in increasing the family resources allocated, such as investments in human capital and parental time, namely resource-dilution hypothesis of Blake (1981). Still, on the micro-level, longer child spacing increases the cost of raising children, when assuming economies of scale, i.e. children of close ages have similar needs that can be met more efficiently when attending their needs collectively (Newman, 1981, as cited in Newman & McCulloch, 1984). On. 10 DOI:10.6814/NCCU202001257.

(11) the contrary, according to Powell (1995), longer birth intervals can favor the recovery from financial difficulties, consumption smoothing and proper spending planning. Furthermore, the spacing decision has not only consequences on how the income is allocated, but for starters, how is it made. For instance, in dynamic models of fertility, delaying the timing of first birth and closed spacing decisions reduce the effects of childbearing in the labor market, i.e. reducing the opportunity cost of having children, represented in household forgone wages, human capital investments and depreciation (Troske, 2013). When the focus is changed to spacing outcome effects in children – while building on the resource-dilution hypothesis–, longer spacing determines the number of children clustered at a particular age group which prominently determines the allocation of household resources (Powell, 1995). In this regard, the more intensive investment in. 政治大. children can be coined to higher quality, specifically reflected educational performance. 立. variables of children with longer spacing intervals.. ‧ 國. 學. Nonetheless, the more immediate results of birth spacing are those related to the health adverse perinatal and infant outcomes. Research suggests that when births are. ‧. spaced closely or too far apart, there’s an increase in the risk of adverse perinatal outcomes such as preterm birth, low weight at birth, smaller size for gestational age and. Nat. sit. io. er. et al., 2012).. y. underweight (Conde-Agudelo, Rosas-Bermúdez, & Kafury-Goeta, 2006; Conde-Agudelo,. For surviving offspring, regardless of these adverse predispositions, they are. n. al. Ch. i Un. v. more likely to suffer from short- and long-term health consequences of the short birth. engchi. spacing. Notably, most effects are associated with nutrition and weight. For instance, Rutstein and Johnson (2004) compared 24-29 months intervals to 36-41 months ones, finding a decrease in underweight of 29% for the long-spaced births. A year later, Rutstein (2005) elaborated on another outcome variable, nutrition, and found that shorter birth spacing has a clear pattern of more undernutrition. In this sense, his empirical research found that the association of chronic malnutrition with birth intervals was statistically significant in 6 out of 14 surveys that collected anthropometric measurements data, while the relationship of spacing with general malnutrition was found significant in 5 surveys. Incidences in the quality of nutrition are of particular interest when they become persistent and its cumulative effects transform into long-term impacts on a child’s health, i.e. stunting, low height-for-age parameter. When the relationship between longer spacing and lower risk of malnutrition is confirmed, it has been found that intervals of more than 11 DOI:10.6814/NCCU202001257.

(12) 36 months reduced stunting from 10% to 50% (Dewey & Cohen, 2007). This is a particularly pressing issue for the developing world, where leading risk factors are primarily related to communicable, maternal, perinatal, and nutritional conditions; in stark contrast with developed countries, where the risk is mainly associated with noncommunicable diseases (Lopez, et al., 2006). All of the above puts into perspective the deleterious effects on children either at one point in time or in the long-run of those who survive. But it is more important to consider that the persistence and worsening of these health –and other household’s– impacts as a result of the length of the spacing on children might deeply reduce the odds of survival for children past certain ages. The triggering of all possible positive consequences of the length of birth intervals and reduction of family size, described above relies on the assumption of living offspring. In the end, reduction of child mortality is a. 政治大. developmental, human and ethical priority for the world’s agenda, especially in the. 立. developing world, where the incidence of this phenomenon is still far from fully mitigated.. Infant and child mortality. ‧ 國. 學. 2.2.. Infant mortality has been a consistent historical world health tragedy. Volk and. ‧. Atkinson (2013) estimated evolutionary data for infant mortality, finding that historically up until the beginning of the last century, around 27% of children failed to survive past. y. Nat. sit. their first year of life, while 47.5% did not survive past puberty. From the 1950s through. er. io. the 1960s, child mortality rates in Africa were still similar to those depicted in the. al. iv n C of age, while in Asia one in four children to survive h e failed i U their fifth year of life (United h n c g Nations, 2019). n. evolutionary estimates, around one of three children died before they reached five years. Nonetheless, mortality rates among children below 5 years of age have constantly declined over the past 70 years, though a sharp contrast can be seen in the trends of reduction of child mortality for high- and low-income regions. Not only on this indicator but as a characteristic of the development of countries in the past decade, inequality and poverty fueled the global needs for a joint effort on improving welfare around the world. The latter resulting in early global initiatives such as the Universal Declaration of Human Rights (UDHR) or research-based policy-making of the development decade in the 1960s (Hulme, 2008). The more substantive shift towards prioritizing world problems like child and infant mortality came in the 1990s, through the human development approach that 12 DOI:10.6814/NCCU202001257.

(13) permeated into international organizations. The earliest discussion of what provides the basis of this approach is Amartya Sen’s conceptual framework on capability approach – contained in his lecture from 1979 through 1987 2 –, focusing on people as ‘ends’ of development, i.e. a developmental theory people-centric (Alkire, 2010). This prominent school of thought continued to grow and develop their approach, concepts and measures, but a premature impact is found in the publication of the 1990’s United Nations Development Programme (UNDP) first Human Development Report (HDR). The report called for global actions to enlarge people’s choices and forming human capabilities, rather than centering on traditional economic measures. HDRs also cross-over developmental topics with humanity’s pressing issues such as gender, natural resources, sustainability, climate change, democracy and inequality. Also, in 1990 the World Summit for Children took place, which was the largest-. 政治大. to-date gathering of heads of state, to adopt policies to improve children’s wellbeing. The. 立. target agreed on was to reduce the under-five child mortality rate by one third or to 70 per. ‧ 國. 學. 1,000 live births, whichever yielded a lower indicator (United Nations Children’s Fund, 1990). Meanwhile, international donors, such as USAID’s Child Survival Initiative, set. ‧. broad strategies for achieving certain targets on reduction of child mortality; mainly through better immunization coverage, oral rehydration therapy, boosting health and. Nat. sit. y. nutrition of mothers and children, and by reducing high-risk births (Ahmad, et al., 2000).. io. er. All of these steps, along with the increasing global partnership sentiment, paved the way to the world’s biggest commitment among states and multilateral agencies to. n. al. Ch. i Un. v. reduce poverty and improve multidimensional wellbeing, the Millennium Development. engchi. Goals (MDGs) in 2000. The MDGs included infant, child and maternal mortality targets as main goals, despite them being absent from preceding material “We the Peoples - The Role of the United Nations in the 21st Century” and the concerns from the Vatican and conservative Islamic states (Hulme, 2008). The goal set was to reduce by two thirds the under-five child mortality rate in the period from 1990 to 2015, but by 2015 the rate was reduced by half, dropping from 90 to 43 deaths per 1,000 live births, failing to meet the MDG (United Nations, 2015a).. Alkire (2010) highlights Sen’s 1979 lecture ‘Equality of What?, 1985’s ‘Well-being, Agency and Freedom’, and 1987’s ‘Commodities and Capabilities’ and ‘The Standard of Living’; which cover the starting point of the capability approach, more philosophical development to it, and linkages to economic development. 2. 13 DOI:10.6814/NCCU202001257.

(14) Also, by 2015, the global partnership goals evolved into the Sustainable Development Goals (SDGs), where child mortality became an indicator instead of a goal on itself. The now renewed target plans to reduce neonatal mortality to 12 per 1,000 live births and under-5 mortality to 25 per 1,000 live births by 2030 (United Nations, 2015b). In 2017, children 0 to 5 years old died in the same proportions –5.4 million– as older age groups did: 5 million of the 65-69 years old group, 5.3 million from the 70-74 years old group or the 85-89 years old group with 5.3 million deaths (Institute for Health Metrics and Evaluation, 2018). These facts along with the failure to reduce the original millennium goal, the new multiple goals reflected on the SDGs and the downgrading of child mortality from a pressing issue to yet another indicator, places more uncertainty on the effective achievement of this target in the foreseeable future.. 治政大 with infant and child The spacing of births has a long-documented association 立 mortality outcomes, in fact, the earliest studies date of almost a century ago and already Child spacing effects on infant and child mortality. 學. ‧ 國. 2.3.. present the notions of the deleterious effect of shorter birth spacing and optimal interbirth intervals (Stevenson (1923) and Hughes (1923) as cited in Hobcraft, McDonald &. ‧. Rutstein (1983)). The research on this effect has been approached from different disciplines, such as population studies, medicine, sociology and economics, to name a. y. Nat. sit. few. Nonetheless, it has moved to mainstream knowledge as a result of international. er. io. organizations endorsing this proposal as a policy recommendation.. al. iv n C waiting at least 24 months after a live to attempt h ebirth i Uanother pregnancy, that is, an h n c g interbirth interval of 33 months or roughly 3 years. The recommendation pursues the n. Particularly, the World Health Organization (WHO) has expressly suggested. objective of reducing the risk of adverse maternal, perinatal and infant outcomes (World Health Organization, 2007). Experts that participated on that 2005’s technical consultation agreed on the notion of an the deleterious effect of short intervals, and concluded the following: (1) birth-to-pregnancy intervals of six months or shorter had a higher associated risk of maternal mortality; and (2) birth-to-pregnancy intervals shorter than 18 months had a greater risk of infant, neonatal and perinatal mortality, lower weight at birth, being smaller for gestational age, and pre-term delivery (World Health Organization, 2007). Multidisciplinary studies have attempted, for almost a century, to provide evidence on this long-running seemingly strong negative relationship. Although, the 14 DOI:10.6814/NCCU202001257.

(15) exploration of formal channels or mechanism by which child spacing can have deleterious effect on maternal and child health and survival started in the mid-1960s. In spite of the multiple causal mechanism assessed over the years, the literature usually coincides in three main mechanism for the “short intervals-infant mortality” relationship: a) maternal depletion syndrome, b) sibling competition and c) insufficient breastfeeding (CondeAgudelo, et al., 2012). Most of the studies also include confounding factors, that if controlled, can isolate the effect of child spacing. Some of these factors include socioeconomic conditions and previous birth outcomes, to name a few. 2.3.1. Causal mechanism of effects of spacing in infant mortality a) Maternal depletion syndrome This mechanism was first discussed by Jelliffe and Maddocks in 1964, although,. 治政 women who are in a continuous cycle of reproduction, 大 synthesizing fetal and placental 立 protein and producing breast milk non-stop, might affect the weight of their children and their early proposal did not include child spacing. The authors introduced the notion that. ‧ 國. 學. her health status (Jelliffe & Maddocks, 1964). When including child spacing, a mother with constant pregnancies and short birth intervals does not get the chance to recover and. ‧. replenish her nutritional values, therefore increasing the odds of pregnancy losses and having low birth weight children (Hobcraft, et al., 1983).. y. Nat. sit. Among some of the representations of maternal depletion that affect mother’s and. al. er. io. child health outcomes are the exhaustion of energy and protein resulting from short. v. n. interpregnancy intervals (King, 2003) and the risk of folate insufficiency, which parallelly,. Ch. i Un. impacts their children’s hazard of neural tube defects, retarded intrauterine growth, and. engchi. preterm birth (Smits & Esseds, 2001). DaVanzo, et al. (2008) found that the survival outcome of the pregnancy amplifies the maternal depletion syndrome, that is, live births or stillbirths are more depleting than miscarriages or abortions. Additionally, live births are usually followed by periods of breastfeeding which further depletes maternal physiological and nutritional stores. Children with low weight at birth have a greater risk of mortality than those with an average normal weight and the group differences are accentuated for those with socioeconomic disadvantages (McCormick, 1985). Regardless of technological improvements and increased use of modern medical methods, the change in survival for very low birth weight –those who weighed less than 1500g at birth– had barely improved between 1990 and 2002 (Fanaroff, et al., 2007). The situation worsens for developing 15 DOI:10.6814/NCCU202001257.

(16) countries. Children severely growth-restricted and those who were born preterm are at higher risk of perinatal death, primarily of complications that in are not fatal in developed countries, but which care access is limited and difficult for developing countries (Kramer & Victora, 2001). Since women that already have inadequate food intake and are unable to adjust their energy expenditure to lower levels are the most likely to suffer from maternal depletion (Conde-Agudelo, et al., 2012), low-income mothers are more vulnerable to be affected by this mechanism. b) Sibling competition Another potential mechanism whereby a short or long interval may decrease the odds of survival is for the children in the family is sibling competition. This occurs in two instances: on one hand, when two or more children, are closely spaced, they will grow up. 政治大. close in ages which may lead them to compete for family scarce economic resources and parental care (Conde-Agudelo, et al., 2012); on the other hand, when children are spaced. 立. longer, older siblings may take precedence in taking the limited available food supplies. ‧ 國. 學. or resources of the family (Hobcraft, et al., 1983).. This mechanism is usually tested by including the survival status of the preceding. ‧. child or the index child and the preceding or subsequent interval. Nevertheless, caution is advised when assessing the survival of the preceding sibling and its impact on the length. y. Nat. sit. of the interpregnancy interval. If the precedent child dies in infancy, the interval to the. al. er. io. next birth could be shortened by an involuntary cessation of breastfeeding and temporal. n. infertility associated with lactational amenorrhea and/or the mother’s grief (Sweemer,. Ch. i Un. v. 1984) and desire to replace the deceased child (Conde-Agudelo, et al., 2012). Thus,. engchi. providing evidence on this effect has been a challenge, both theoretically and empirically, since arguably this effect is prompt to be harsher in poor families in developing countries in contrast with middle- and high- income households. c) Breastfeeding-pregnancy overlap This effect is also depicted as a type of competition among the precedent child and the new shortly spaced pregnancy. The new pregnancy induces earlier weaning on the precedent child, with consequent deleterious effects on his survival (Hobcraft, et al., 1983). Additionally, when breastfeeding–pregnancy overlap, the intakes per feeding are lower and the weight gain associated with breastfeeding nurture decreases in the corresponding for one month (Marquis, et al., 2002). Another possible effect of the overlapping breastfeeding and pregnancy is change in the composition of breast milk,. 16 DOI:10.6814/NCCU202001257.

(17) particularly affecting immunity nutrients on it, such as lysozyme concentration, lactoferrin concentration and Immunoglobulin A (Marquis, et al., 2003). Interestingly, the breastfeeding-pregnancy overlap and the short interval can be related in two ways that lead to the detrimental effect on the survival of children. For instance, the short interval can lead to early weaning and lower quality breast milk, which affects the survival odds of the preceding child; and on the other hand, the maternal decision on the length of breastfeeding also affects the birth interval through lactational amenorrhea inducing effects on mortality of both the preceding and subsequent child. d) Alternative mechanisms The mechanisms described above are among the most commonly used to support the detrimental effects of child spacing and child mortality. Nonetheless, these are far. 政治大. from being the only possible channels of impact in the odds of survival. Many studies opt for controlling for socioeconomic variables or confounding factors, such as income,. 立. which is a determinant of nutritional intake for the family; parents’ education, particularly. ‧ 國. 學. mother’s, as it represents maternal use of contraception, awareness of child care, and so forth (Sweemer, 1984; Hobcraft, et al., 1983; Boerma & Bicego, 1992; Forste, 1994;. ‧. DaVanzo, et al., 2008).. There’s a gap in the literature that should be addressed more, which is. y. Nat. sit. interpregnancy intervals and whether they change according to the outcome of the. al. er. io. preceding pregnancy, i.e. whether it resulted on live birth, stillbirth, miscarriage, or. n. induced abortion (DaVanzo, et al., 2008). These outcomes are key to properly identifying. Ch. i Un. v. the dimension of the mechanism described above. For instance, non-live outcomes should. engchi. be less depleting that a full-term live pregnancy that is followed by breastfeeding, also if the pregnancy outcome is not a live birth, there’s no immediate sibling to compete or to overlap breastfeeding and pregnancy with. Lastly, there are some more difficult to measure the mechanism of impact such as the psychological and emotional drain of mothers responsible for caring of a large family with scarce resources. These mental and emotional health effects or quality-of-life effects caused by larger families and shorter intervals are not measured nor included but maybe impacting maternal physical and psychological reserves (Winikoff, 1987). 2.3.2. Empirical evidence of the mechanisms in the literature Previously it’s been indicated research that has pioneered hypothesizing and/or proving the causal mechanism that leads short or very long intervals to result in child 17 DOI:10.6814/NCCU202001257.

(18) mortality. In this subsection, research that provides evidence or questions the existence of such mechanisms is summarized. In regards to the maternal depletion syndrome mechanism, the effects of intervals in child mortality are greater for the shortest intervals, which are the ones that give the littlest time for mother’s recovery (DaVanzo, et al., 2008; Rutstein, 2005; Sweemer, 1984); while King (2003) confirms that depletion syndrome through the analysis of deficiencies in micronutrients, iron and folate in closely spaced pregnancies, which are at high risk of mortality, lastly, Boerma and Bicego (1992) provide evidence of both, maternal depletion and breastfeeding-pregnancy overlap causal mechanism, of how shortly spaced births affect mother's physiology and nutritional status, which in turn impacts the odds of child survival. Regardless, other empirical studies have not found evidence for maternal. 政治大. depletion syndrome or inconsistent proof. For instance, Dewey (2007) found that longer. 立. birth intervals are associated with lower child malnutrition in some populations analyzed,. ‧ 國. 學. but not all of them. She also found little evidence of the inverse relationship, shorter intervals with higher child nutrition, which remarks about the lack of statistical. ‧. significance of this relationship. Winkvist, et al. (1994) propose that how the nutrients get assigned to mothers or children is affected primarily by the mother’s nutritional status. Nat. sit. y. rather than the child spacing. In this case, the authors suggest than endorsing longer. io. women at all stages of her reproductive cycle.. n. al. Ch. er. intervals is not effective enough, and that a better approach is to support nutrition for. i Un. v. As for the sibling competition hypothesis, DaVanzo, et al. (2008) and Sweemer. engchi. (1984) found supporting evidence of this effect. Particularly the former found for the postneonatal period and childhood, the detrimental effects of close spacing are greater if the preceding child is still alive at the time of the subsequent child’s birth –giving them room to compete for family resources– than if the preceding had died. On the contrary, Boerma and Bicego (1992) controlled for survival status of the preceding child and found that it does not reflect on increasing the effects of close spacing on mortality when the previous child is still alive, i.e. a supposed ‘competition’ environment. Therefore, they conclude that the sibling competition mechanism is not evidenced nor operative at all, but rather that the effects of familiar mortality risks are stronger than the competition mechanism. Thus, prenatal mechanisms are more relevant than postnatal ones, when explaining the causal nature of the child spacing effects on child mortality. 18 DOI:10.6814/NCCU202001257.

(19) For the breastfeeding-pregnancy overlap, most studies argue for an effect of early cessation of breastfeeding, weaning, as a result of a closely spaced conception (Hobcraft, et al.,1983, Sweemer, 1984; Forste, 1994; DaVanzo, et al., 2008). Despite medical literature assessing the impact in breast milk nutrients and child weight, there’s little direct evidence of these quality effects affecting child mortality through a shorter birth interval (Marquis, et al., 2002; Marquis, et al., 2003). Research that aims to untangle the relationship between child spacing and child mortality is very broad, expands through disciplines and deals with complex multilateral relationships between variables and mechanisms. Experts fail to agree on the existence of certain effects and channels, as the discussion grows into different realities. In fact, human fertility is subject to many unmeasurable variables –culture, religiousness– and fundamental differences –developed and developing countries, health care systems– than. 政治大. unanimity upon the subject is not expected.. 立. Data. ‧ 國. 3.1.. 學. 3 Data and Methods. ‧. To study the impact of the interbirth interval on infant mortality among Nicaraguan families and the mechanism by which it affects, data from the Demographic. y. Nat. sit. and Health Surveys (DHS) were used. The DHS started in 1984, building on the. al. er. io. experience of its predecessors the World Fertility Surveys and the Contraceptive. v. n. Prevalence Surveys. To date, it has become a widely spread, nationally representative,. Ch. i Un. and comparable household data source, allowing to document demographic dynamics,. engchi. such as fertility, family planning, maternal and child health in intervals of approximately five years (Fabic, Choi & Bird, 2012). Nicaragua first enrolled in the DHS program in 1997, after years of battling the economic downfall inherited from the Sandinista government and a decade of civil conflicts, during its third phase primarily financed by the United States Agency for International Development (USAID). Thereafter, the country has continuously teamed up with different international organizations to gather the data until the last DHS developed in 2011-2012 (see Table 1). No more data has been available ever since, possibly due to ambiguous and hostile policies of the Ortega government towards foreign aid agencies – that led to the departure of the United Nations Development Program (UNDP) in 2016– and the halting of funds due to the 2018 sociopolitical crisis (Martí, 2019).. 19 DOI:10.6814/NCCU202001257.

(20) Table 1: Nicaraguan DHS (1998-2011) general description Data. Primary donor. Period 1997-1998. USAID. 2001 Demographic and Health Survey 2006-2007 (DHS). USAID. 2011-2012 1 2. Source. DHS Program. UNFPA1. World Bank. The Global Fund. INIDE2. Selection criteria Households: • National censusbased sampling Women: • Resident of the household • Fertile age: 15 to 49 years old • Under five years old offspring of each selected women. Sample size Households Women 11,528. 13,634. 11,328. 13,060. 17,209. 14,221. 21,960. 15,266. United Nations Fund for Population Activities National Institute of Information for Development (Nicaragua, Spanish acronym). 政治大. Data on each DHS is cross-sectional; thus, the datasets were pooled to have a more comprehensive sample. The main dependent variable, infant mortality, is defined as a. 立. binary variable that depicts the occurrence of under-one-year old death. The DHS only. ‧ 國. 學. gathers important nutritional and live outcomes variables from alive children under five at the time of the interview but reports the history of age at death for each woman’s. ‧. offspring. Therefore, in this study, all chosen variables that report on child-specific aspects will be those that cover the full record of offspring and not those later expanded. Nat. sit. y. in the dataset. On the contrary, the main independent variable will be defined as the. al. er. io. interbirth interval (IBI), i.e. the time measured in months from the childbirth of the. n. preceding child to the birth of the index child. This is mainly because there is no. Ch. i Un. v. information on each pregnancy’s duration, thus, other time measures such as birth-to-. engchi. pregnancy (recommended by the WHO (2007)) cannot be obtained; nor there’s data on the outcome of each pregnancy besides live birth, thus, neither the inter-outcome intervals can be found (used by DaVanzo, et al. (2008)). To be included in the empirical model, the IBI was coded into 4 categories: firstborn, index children born first (inapplicable for the calculation of IBI); and IBI groups of: less than 18 months, between 18 to 35 months, and more than 36 months. These categories reflect on previous literature findings regarding the deleterious effects of short (less than 18 months) intervals (WHO, 2007). Additionally, the selection of covariates serves two purposes: (1) control for confounding factors that may also explain infant mortality; and (2) address the objectives of assessing the existence and direction of effects of the causal mechanisms described in Section 2.3.1., such as: maternal depletion and sibling competition for Nicaraguan 20 DOI:10.6814/NCCU202001257.

(21) families. Nonetheless, one of the causal mechanisms that it’s not possible to discuss due to the scope of the DHS data is the breastfeeding-pregnancy overlap. As mentioned above, DHS data only follows children that are reported alive, living at the household and younger than 5 years old at the time of the interview. Thus, information on breastfeeding practices, nutrition, immunization and pregnancy durations are not available for the main interest group. Covariates are split into: a) index child-specific and referenced variable: interbirth intervals, gender of index child, singleton birth (single or multiple), birth order, and death of the preceding child; b) mother specific variables, such as: the highest level of education reached, mother’s age, whether or not the mother has experienced a miscarriage; and c) household variables: a measure of the wealth of the household, number of adults living in the household and distance to health services. Additionally, by-groups specifications. 政治大. on: mortality of previous child, mother’s age, birth order, household wealth and area of. 立. residence will be used to explore and discuss the empirical evidence of causal. ‧ 國. 學. mechanisms and assess which effect prevails over the other possible channels. These variables can be grouped by the mechanism each address, in this sense,. ‧. variables such as IBI<18 months and the death of preceding child could reflect on the mother’s depletion; and the sibling competition can be evidenced in variables such as. Nat. sit. y. birth order and multiple births. Lastly, to account for the effect of previous miscarriages. io. er. or interruptions, binary variables for mothers that have had each of these occurrences were created. Although it is not possible to link these events to each child record, it still. n. al. Ch. i Un. v. provides valuable information on the maternal reproductive and health history.. engchi. For the most part, the selection of these variables responds to a synthesis of the previous empirical literature and the viability of finding them in the DHS datasets. Primarily, the models followed are DaVanzo, et al. (2008), Fotso, et al. (2013) and Becher, et al. (2004). All variables are described in detail in Table 2 below. Table 2: Description of variables used in the empirical model Variable. Reference. Index child-level variables Interbirth interval (IBI). Infant mortality of index child. Levels First born, <18 months, 18-35, 36+. DaVanzo, et al. (2008). Binary; 0=for surviving children, 1= died. Description Difference in months from the day of birth of the preceding child to the birth date of the index child Whether index child died while being under-one year old or survived (infant mortality criteria). (Continued) 21 DOI:10.6814/NCCU202001257.

(22) Table 2: Description of variables used in the empirical model Variable. Reference. Levels. Description. Index child-level variables Infant mortality of preceding child. DaVanzo, et al. (2008). Sex of the index child Singleton birth Birth order. Fotso, et al. (2014) Becher, et al. (2004). Binary; 0= if preceding child survived, 1= died Binary; 0= male, 1= female. Whether preceding child experienced infant mortality or survived Sex of the index child. Binary; 0= singleton birth, 1= multiple birth. Whether the birth was singleton or multiple. First born, 2nd to 4th, ≥5th. Categories that group children by the order in which they were born. No schooling or primary; and secondary, tertiary or higher. Highest level of education reached by the mother. Mother-level variables Mother’s education. Low= DHS WI<0, Middle= DHS WI of 0 to 2, High= DHS WI>2. Categories created out of a composite measure of household's cumulative living conditions following the DHS Wealth Index methodology.. y. n. al. Proxy to the one used by Becher, et al. (2004). Variables for by-groups specifications Area of residence Fotso, et al. (2014). Ch. engchi. sit. io. Proxy to the one used by Fotso, et al. (2014). Adults living in the household. Remoteness to health services. Whether the mother has had a pregnancy interruption (DHS 19982001) or a miscarriage (DHS 20062011). er. Wealth index. Nat. Household-level variables. Binary; 0= didn’t have one, 1= has had a miscarriage/interruption. ‧. Proxy to the effects discussed in DaVanzo, et al. (2008). Mother’s age at the time of birth of the index child measured in years. 學. Miscarriages. 政治大. 立 <18, 18-35, ≥36. ‧ 國. Mother’s age at birth. DaVanzo, et al. (2008). i Un. v. Alone, adults=1; accompanied by 1, adults=2; accompanied by 2+, adults>2 Binary; 0= not far, 1= for reported to be far. Number of adults (age>18) living with the mother in the household.. Binary; 0= urban, 1= rural. Whether the household is located in an urban or rural area. Approximation using reported “remoteness” of health services in questions regarding usage of health care.. 22 DOI:10.6814/NCCU202001257.

(23) 3.2.. Empirical methods. 3.2.1. Survival analysis An analysis of the promptness of a child to die before reaching one year of age due to the influence of the IBI and a vector of covariates could potentially be measured by using a logistical regression or a probabilistic approach. The issue is, then, we would only be measuring the likelihood of an event to occur subject to its control variables. A variable such as infant mortality does not only consider that the event –death– happens, but also when it happens. Thus, timing matters because there’s a time frame of 12 months for it to be considered that a subject suffered from an ‘infant death’ and not any other category. Another crucial factor being, the fact that the mortality of children accelerates dramatically the closer it is to their birth date. This is evidenced in the fact that large. 治政大much more so in the very in neonatal mortality (within 28 days postpartum) and 立 vulnerable group of perinatal mortality (within 1 week after childbirth). Thus, the function percentages of children that died under the category of infant mortality are concentrated. ‧ 國. 學. for the survival of these children is a non-linear function highly concentrated within the very first periods, behavior that is best captured by a survival analysis approach.. ‧. When the outcome variable of interest is the time until a specific event takes place, the statistical analysis can be done using the non-parametric and parametric estimations. y. Nat. sit. contained in the so-called survival analysis. Therefore, the dependent variable now has. er. io. two important components: time, i.e. time elapsed from the beginning of the study until. al. iv n C that the individual studied had the experience h e n g cofhinterest i U (Kleinbaum & Klein, 2010). These components are usually defined in survival analysis as the “survival time”, for the n. the event occurs or the study ends; and the other part is the event, that is, the indication. time to event, and “failure” to the occurrence of the event; terms derived from the initial heavy influence of biostatistics in these methods that usually contemplated a survival time to death, diseases or other negative life outcomes (Kleinbaum & Klein, 2010). Regarding one of the components of analysis, the event, there are different classifications for it. For instance, there’s single events, i.e. those that account for duration for one event for each studied unit. Usually these events are assumed to be absorbing, i.e. can only happen once. In contrast, there’s also the case of multiple events, which can be: (1) of multiple types, that is, different and absorbing events; and (2) recurrent events, when the same event is studied in repeated occasions (Skrondal & Rabe-Hesketh, 2004).. 23 DOI:10.6814/NCCU202001257.

(24) Additionally, following Hosmer, Lemeshow & May, 2008, while analyzing the other important component, ‘survival time’, it’s key to understand the issue of “censoring”. As a time measurement, the survival time has to properly define and count units of time elapsed from a beginning to an ending point. In the process, the observation of time might become incomplete, issues which are called censoring and truncation. The authors describe that an observation can be ‘right-’ or ‘left-censored’, the former, occurring when the ‘time’ finished before the ‘event’ or outcome of interested has occurred; and the latter, happens when, on the contrary, the event of interest has already happened when the observation begins. In regards to truncation, observations are incomplete because of the design of the study selection process. It’s possible to encounter left truncation, also known as delayed entry, when the time to observe an individual is deliberately delayed; as well as, right truncation or length biased sampling, when all the. 政治大. studied population has experienced the event of interest and was selected for the analysis. 立. precisely because of that way before the study starts. The estimations contained in. ‧ 國. 學. survival analysis can be divided into two main methodologies: a) Non-parametric estimations. ‧. Due to the particular issues described above, i.e. censoring and truncation, standard descriptive statistics will not properly estimate the parameters. Thus, Hosmer,. y. Nat. sit. Lemeshow & May (2008) suggest finding the cumulative distribution that can generate. al. v. 𝑆(𝑡) = 𝑃𝑟(𝑇 > 𝑡) , that expresses the probability that an. n. function, denoted as. er. io. statistics in line with the interest parameters. This measurement is found in the survival. Ch. i Un. observation’s survival time (T) exceeds a specific point in time t. This is the most. engchi. common measure, as the majority of studies are interested in subjects not to fail (e.g. live), rather than experience the failure (e.g. death), although focus on failure it’s also possible by using the hazard function. Generally, the Kaplan-Meier survival curves are used to estimate the survival probability, since it considers all the available information from the observations, censored or uncensored. Its functional form is given by Equation 1: 𝑓−1. ̂ (𝑇 > 𝑡(𝑖) | 𝑇 ≥ 𝑡(𝑖) ) 𝑆̂(𝑡(𝑓−1) ) = ∏ 𝑃𝑟. (1). 𝑖=1. This definition indicates that the estimator derivates from the products of the sequence of conditional survival probability past the failure time (𝑡(𝑓) ), thus aiding to observe the shape of the survival function. The Kaplan-Meier estimator allows each 24 DOI:10.6814/NCCU202001257.

(25) observation to contribute information while they are under the status of “surviving”, those who experienced the event or are right-censored provide information for the at-risk group and later the former sums to the number of observations that failed. Once the survival probability has been observed, it’s key to determine whether or not the Kaplan-Meier survival curves are proportional or statically equivalent for relevant groups originated from the set of covariates, particularly, those that depict effects that are believed to be related to the survival of the study units. Specifically, it’s important to measure differences among groups in order to assess the validity of including those variables in the final model. In this sense, common statistical test such as two sample hypothesis testing or the rank-sum test, will not yield proper estimations when dealing with censored data observations. Hence, it’s suggested to use the long-rank test, which builds on the survival curves. 政治大. (Kaplan-Meier) to provide evidence on differences at the population-level. Thus, the log-. 立. rank test runs a sample-wide χ2 test to compare the curves, by comparing per categories. ‧ 國. 學. the cell counts of observed and expected events over all failure times. Ultimately, the long-rank test helps to test the null hypothesis that there is no difference between two or. ‧. more survival curves (Kleinbaum & Klein, 2010).. In addition to the KM survival curves, there are alternative estimators, the main. Nat. sit. y. one being the Nelson-Aalen one that instead of using the estimator 𝑆(𝑡) defined in. io. er. Equation 1, it developed one based on 𝐻(𝑡) . This estimator is also known as the cumulative hazard function in survival analysis and its graphical representation would. n. al. Ch. i Un. v. emulate that of the survival function but in opposite direction, since, as 𝐻(𝑡)or the. engchi. cumulative hazard increases there will be a decrease of the same magnitude in the survival function 𝑆(𝑡). The estimator is given by Equation 2: ̃ (𝑡) = ∑ 𝐻 𝑡(𝑖)≤1. 𝑑𝑖 𝑛𝑖. (2). Where 𝐻(𝑡) is the cumulative hazard, given the observed deaths 𝑑𝑖 and those at risk of dying 𝑛𝑖 at time 𝑡. Therefore, for large size of risk-to-events ratios, the survival functions found by both of the estimators will not yield great practical differences. b) Semi-parametric estimation: The Cox proportional hazard model The non-parametric methods described above cover a variety of methods within the so-called univariate analysis. Nonetheless, survival analysis can also exploit the timeto-event analysis with a set of variables that are thought to affect the occurrence of the 25 DOI:10.6814/NCCU202001257.

(26) event. Indeed, strong theoretically or empirically associated variables should not be omitted and should be treated as potential confounders. Thus, more complex analysis is only feasible through a multivariate analysis, namely a parametric regression model under the time-to-event framework. One empirical method that serves this purpose is the Cox proportional hazard model, proposed by Cox (1972) as an expansion on the work of Kaplan Meier while incorporating regression parameters, that is, including explanatory variables that provide coefficients on the basis of a time function. Following Kleinbaum & Klein (2010), the Cox proportional hazard model can be defined as: 𝑝. (3). ℎ(𝑡, 𝑋) = ℎ0 (𝑡) 𝑒 ∑𝑖=1 𝛽𝑖 𝑥𝑖. Where the first term at the right of Equation 3, ℎ0 (𝑡), represents the baseline. 治政 variables). Meanwhile, the second term 𝑒 is 大 the exponential expression, it 立 addresses the covariates but not the time, since X’s are assumed to be time-independent. hazard which considers time (𝑡), but not any effects on the X vector (explanatory ∑𝑝 𝑖=1 𝛽𝑖 𝑥𝑖. ‧ 國. 學. This assumption is the proportional hazards which ultimately proposes that a change in an individual’s explanatory factors induces a proportional change in his/her hazard rate.. ‧. (thus, the multiplicative relation).. Among the strengths of the Cox proportional hazard model are: (1) it offers a. y. Nat. sit. robust estimation, i.e. the results will be consistent with those of the correct parametric. er. io. model, which in turn, it’s hard to establish the appropriate model; and (2) the Cox PH. al. n. iv n C to the event, as described by Hosmer, h Lemeshow & MayU e n g c h i (2008). Therefore, a hazard ratio that’s equal to 1, will indicate a non-existing effect; a hazard ratio under 1 expresses a. model relies on the introduction of the hazard ratio (HR) to measure the risk of exposure. reduction in hazard; and finally, a HR greater than the unit means an increase in the hazard of exposure to the event. Additionally, the Cox PH model also allows to compare outcomes of hazard among groups, functioning as a “relative-risk” ratio when interpreting binary variables, for example. Finally, to validate the use of the Cox PH model the assumptions of proportional hazards have to be assessed. In other words, assessing during postestimation the goodness of fit through hypothesis testing for relevant predictors. Majorly used, the Schoenfeld residuals, help provide a statistical test for covariates, both individually and globally, and whether they are or not related with the survival time. Testing for a null hypothesis of. 26 DOI:10.6814/NCCU202001257.

(27) proportional hazard, the χ2 statistic will indicate the rejection or non-rejection of the null hypothesis described above. c) Extended Cox proportional hazard model for time-dependent variables When the test for the independence of predictors with the survival time fails to reject its null hypothesis, those predictors are concluded to be time-dependent. This invalidates the proportional hazard assumption for the Cox PH model. When encountering this situation, the Cox model can be extended to include terms of interaction between the time-dependent variable and a specific function of time. In a similar way to the Cox PH model definition contained in equation 3, the extended model also includes a baseline hazard denoted by ℎ0 (𝑡) multiplied by an exponential term. Nevertheless, according to Kleinbaum & Klein (2010) the exponential. 治政 covariates X and the time-dependent covariates X , 大 seen in the right-hand side of 立 Equation 4, while all predictors at time t are denoted by X(t) on the left-hand side of the function for the extended model now introduces the recurrent time-independent i. ‧ 國. 學. equation:. j(t). ℎ(𝑡, 𝑋(𝑡)) = ℎ0 (𝑡) 𝑒 [. ∑𝑝1 ∑𝑝2 𝑖=1 𝛽𝑖 𝑥𝑖 + 𝑗=1 𝛿𝑗 𝑥𝑗 (𝑡)]. (4). ‧. The authors also point out the vital assumption of the extended Cox model being. y. Nat. that the effect of a time-dependent variable Xj(t) on the survival probability at time t. sit. depends on the value of the predictor at that same time t. Thus, the model provides only. er. io. one coefficient for each time-dependent variable, depicted in δj of equation 4. The. al. n. iv n C h eofn the function of time represents the violation h i U hazard assumption for that g cproportional statistical significance of the interaction term between a time-dependent covariate and the. specific covariate.. d) Parametric estimation: The Weibull model The main characteristic of parametric survival models is that they assume a known distribution for the survival time. Parametric models are preferred when an assumption on the distribution is feasible and estimated parameters can fully specify the survival and hazard functions. Among them, the Weibull model is the most popular one as it is deemed to be more flexible, while the hazard function remains simple as it only rescales t to a fixed power (Kleinbaum & Klein, 2010). In addition, the Weibull model is the only parametric model that is able to hold both accelerated failure time (AFT) assumption and the proportional hazard (PH) assumption. Thus, making it suitable for modelling data with 27 DOI:10.6814/NCCU202001257.

(28) hazard rates that either increase or decrease over time. The hazard function under the Weibull model is given by the form: ℎ(𝑡) = 𝜆 𝑝(𝑡)𝑝−1. (5). Where λ is reparametrized in terms of predictor variables and the newly added parameter p, also called the shape parameter, serves as the indicator of the shape of the hazard function. For instance, when p>1 the hazard function increases over time; when p=1 the hazard function is constant and it reverts back to an exponential approach, and lastly, when p<1 then the hazard function decreases as time goes on. It is from this added parameter that the Weibull model is considered of great flexibility, as it adapts to the behavior of the hazard over time rather than assuming it from the beginning. 3.2.2. Empirical model. 政治大. Using the pooled data from the 1998-2011 Nicaraguan DHS, the two main components of the dependent variable, event and survival time, are defined as: event,. 立. binary variable for infant mortality (under-one year old deaths); and the survival time, as. ‧ 國. 學. the age at death for under one year-old children and for surviving children, their age up until the cutoff of the event.3 The event, infant mortality, is –according to the definitions. ‧. observed in Section 3.2.1.– a single and absorbing type of event.. In regards to censoring, the model for survival analysis of Nicaraguan children. y. Nat. sit. subject to the interbirth intervals incurs in right-censoring. This happens for all children. al. er. io. that indeed experienced the event, i.e. they passed away but where not accounted for since. v. n. they were older than 1 year old. On the other hand, the nature of the data collected by the. Ch. i Un. DHS also allows to discuss the existence of unobserved left-censoring. That is because. engchi. mothers could effectively have had a non-live outcome in her reproductive history, such as terminations of pregnancy and miscarriages, although those are not recorded by the DHS data. Therefore, there are children that experienced the event before being born, thus not becoming a live birth, but this is also the reason why they are not observations on the DHS, losing this information completely. Starting with the non-parametric estimations, the Kaplan Meier survival curves will be estimated by groups of IBI categories and placed in the same graph, this definition will aid in recognizing graphically the survival differences among categories for the IBI ranging from very short, short and recommended birth intervals. It’s expected to find a 3. The rationale behind this is simulating a study that individually followed each child for a period of 1 year from their birth date. Thus, the variable “survival time” will stop counting after their first birthday for those who survived, as it simulates the study ‘ending’.. 28 DOI:10.6814/NCCU202001257.

(29) lower survival function and curves for very short interval, while a higher survival probability for those with a recommended length of IBI. Moving towards a proper definition of the semi-parametric model, log-rank tests will be used in all proposed explanatory variables to assess the differences among groups and provide evidence to support the inclusion of those variables in the final model. Finally, on the non-parametric methods, the consistency of the behavior found in the survival curves will be assessed through the calculation of the hazard functions using the Nelson-Aalen estimator and its graphical representations. In respect to the semi-parametric proposed empirical strategy, the Cox proportional model will be used as depicted in Equation 3. Adjusted to the covariates selected for this study, the first model will have the form: 12. (6). ℎ(𝑠𝑡𝑖𝑚𝑒, 𝑋) = ℎ0 (𝑠𝑡𝑖𝑚𝑒) 𝑒 ∑𝑖=1 𝛽𝑖 𝑥𝑖. 政治大. Where 𝑠𝑡𝑖𝑚𝑒 represents the survival time, 𝑋 is a vector of explanatory variables. 立. only at the child-level that include: 𝐼𝐵𝐼 (interbirth interval); 𝑚𝑜𝑟𝑡𝑝𝑐 (mortality of. ‧ 國. 學. preceding child); 𝑔𝑒𝑛𝑑𝑒𝑟 (gender of index child); 𝑏𝑖𝑟𝑡ℎ𝑜𝑟𝑑 (birth order); and 𝑠𝑡𝑏𝑖𝑟𝑡ℎ (singleton/multiple birth). A second model, will add to the vector of explanatory variables. ‧. the controls at the mother and households levels: 𝑚𝑜𝑡ℎ𝑒𝑟𝑒𝑑𝑢𝑐 (mother’s educational level); 𝑚𝑖𝑠𝑐𝑎𝑟𝑟 (has had a miscarriage); 𝑊𝐼 (wealth index); 𝑡𝑜𝑡𝑎𝑑𝑢𝑙𝑡𝑠 (total number of. y. Nat. sit. adults living in the household) and ℎ𝑒𝑎𝑙𝑡ℎ𝑠𝑒𝑟 (remoteness of health services).. al. er. io. Additionally, the following variables will be used to 𝑚𝑜𝑡ℎ𝑒𝑟𝑎𝑔𝑒 (age of mother at birth);. v. n. 𝑎𝑟𝑒𝑎 (area of residence). After the estimation of the three models, the Schoenfeld. Ch. i Un. residuals will be used to globally test each estimation, and thus, determine the proportionality of hazards.. engchi. If some predictors were found to have non-proportional hazard functions, i.e. to be time-dependent, the initial Cox model will be modified to the extended Cox PH model of the form: ℎ(𝑠𝑡𝑖𝑚𝑒, 𝑋(𝑠𝑡𝑖𝑚𝑒)) = ℎ0 (𝑠𝑡𝑖𝑚𝑒) 𝑒 [. 12 ∑12 𝑖=1 𝛽𝑖 𝑥𝑖 + ∑𝑗=1 𝛿𝑗 𝑥𝑗 (𝑠𝑡𝑖𝑚𝑒)]. (7). Where 𝑠𝑡𝑖𝑚𝑒 is the survival time, 𝑋(𝑖) is the same vector of explanatory variables depicted in Equation 6 for all three models, and 𝑋(𝑗) comprises variables found to fail to reject the null hypothesis of time dependency in that specific predictor, as an interaction term with the time function. Finally, the specification of the parametric model using the Weibull distribution will be given by Equation 5, where λ will be reparametrized in terms of the vector of covariates at child level for model 1, at mother and household level for 29 DOI:10.6814/NCCU202001257.