Propensity score analysis for the impact of referral on colonoscopy

Table 4.1.7 shows the estimated results on the impact of non-referral on

colonoscopy regarding CRC mortality and the risk of advanced CRC. After adjusting for the propensity of referral, the behavior of non-referral brings the detrimental effect on the risk of CRC mortality and advanced CRC by 82% (95% CI: 22-170%) and 49% (5-113%), respectively. Compared with the estimated results on the harmful effect of non-referral for colonoscopy estimated by using conventional Cox regression model, the adjustment using propensity score results in an estimate away from the null.

Analysis with propensity score matching

In addition to making use of propensity score as an integrated covariate taking into account all factors that may have effect on referral behaviour, we also adopted the propensity score matching aimed for the derivation of a comparable group for the estimation of the effect of non-referral for colonoscopy. The demographic characteristic for the cohort of 1,023 matched subjects are listed in Table 4.1.8. After using the

propensity score matching, the distribution of factors among the referral and non-referral group showed a homogenous result. Table 4.1.9 shows the results by using the propensity score matching approach. The estimated results on the non-referral behavior on

colonoscopy for CRC mortality is 2.04 (95% CI: 1.30-3.23), corresponding to the increase in the risk by 104% (95% CI: 30-223%). The result is consistent after further adjusting for FHbC (108%, 95% CI: 32-223%).

Regarding the non-referral on the risk of having advanced CRC, the estimated results based on propensity matching approach is 1.67 (95% CI: 1.11-2.50, Table 4.1.10), which gives the increase in risk by 67% (95% CI: 11-150%). The estimated result with further adjustment for FHbC gives the figure of increase in the risk of advanced CRC by 61% (95% CI: 8-144%, Table 4.1.10).

4.2 Results on the analysis for the impact of referral for colonoscopy based on Taiwan nationwide colorectal cancer screening programme

4.2.1 Demographic characteristics of FIT positive subjects

During the period, there were 497 CRC deaths and 1450 advanced CRCs (defined as AJCC staging above 2) among non-referred group and referred for colonoscopy group.

The proportion of CRC death and advanced CRC among subjects without referral are higher than those with referral (Table 4.2.1). Male, elderly, southern residents, those underwent screening at hospital and screened at first round, and those with higher FHbC have higher risk of CRC death as well as advanced CRC. In Table 4.2.2, there are not much difference on the referral rate between gender, age group, and FHbC. Those lived in southern Taiwan, underwent screening at public health centers, and screened at

subsequent round have more likelihood of referral with confirmatory exam. For those compliers, the median waiting times for confirmatory exam are distinct among

geographic area, and type of screening units. The overall median waiting time is around 27 days.

4.2.2 Estimated results by using Cox regression model

In Table 4.2.3 (a), the result of univariate analysis shows the effect of non-referral for colonoscopy increased by 65% CRC mortality (crude HR=1.65, 95% CI=1.36-2.00) and non-referral for all confirmatory exam by 53% (crude HR=1.53, 95% CI=1.27-1.84).

In the multivariate analysis after adjusting gender, age group, geographic are, type of screening units, screening round, and FHbC, it shows 59% (aHR=1.59, 95% CI=1.30-1.92) and 46% (aHR=1.46, 95% CI=1.21-1.77) CRC mortality increased in comparison with referral with colonoscopy and all confirmatory exam, separately. Table 4.2.3 (b) lists the estimated results on the impact of referral taking into account all confirmatory

examination. The crude HR of non-referral on the risk or CRC mortality was estimated as 1.53 (95% CI: 1.27-1.84). After adjusting for factors associated with referral, the aHR for non-referral was estimated as 1.46 (95% CI: 1.21-1.77).

In Table 4.2.4 (a) and (b), compared with non-referral group, the crude HRs on advanced CRC are 1.37 (95% CI=1.22-1.54) and 1.30 (95% CI=1.16-1.46) in referral with colonoscopy group and with all confirmatory exam, respectively. After adjustment on confounding factors, the corresponding aHRs decline to 1.22 (95% CI=1.09-1.39) and 1.18 (95% CI=1.05-1.33). Table 4.2.4 (b) shows the corresponding results for

FIT-positive subjects referral for all confirmatory examinations with the HR and aHR of non-referral estimated as 1.30 (95% CI: 1.16-1.46) and 1.18 (95% CI: 1.05-1.33),

respectively.

4.2.3 Results on two-stage referral process Hurdle Poisson regression model

Table 4.2.5 shows the results on the regression coefficients derived by using Hurdle Poisson regression model. The left column lists the estimated regression

coefficients of the hurdle part (whether subject referred or not) and the left column lists that of non-hurdle part (how long subject waited among compliers). The estimated coefficients were further used for the derivation of the score for non-noncompliance and the score for waiting time as follows.

Score of noncompliance= -0.7344 - 0.0767×Male + 0.0312×Age(55-59) + 0.0323 ×Age(60-64) + 0.2188×Age(65-69)

- 0.2437×Area(Northern) - 0.0457×Area(Middle) - 0.1724×Area(Southern) + 0.1531×Unit(Hospital)

- 0.7677×Unit(Public health centers) - 0.6407×round(Subsequent), and

Score of waiting time = | -4.0137 + 0.0055×Male - 0.0137×Age(55-59) - 0.0046 ×Age(60-64) - 0.0053×Age(65-69)

+ 0.1525×Area(Northern) + 0.2359×Area(Middle) + 0.1600×Area(Southern) - 0.0982×Unit(Hospital)

+ 0.2047×Unit(Public health centers) + 0.0737×round(Subsequent) |.

The two scores representing the two-stage of the referral process, namely the compliant to referral and the waiting time among those compliant with referral and thus further be used for the propensity score analysis. In the propensity score analysis, we use the score of compliance to be a propensity score for adjustment and also matching with

non-complier and non-complier.

Table 4.2.6 and Table 4.2.7 show the estimated results by using the Hurdle Poisson regression in conjunction with the propensity score adjusting analysis for assessing the two-stage process for referral on the risk of CRC mortality and that for advanced CRC, respectively. In the propensity score analysis adjusting for the non-referral score, the estimated results show that compared to non-referral for colonoscopy, aHR is 1.59 (95% CI=1.32-1.92, Table 4.2.6 (a)) on CRC death and 1.23 (95% CI=1.10-1.39, Table 4.2.7 (a)) on advanced CRC after adjusted non-compliance score, and FHbC.

Regarding the referral for all confirmatory examinations, the estimated aHR decrease to 1.46 (95% CI: 1.21-1.77, Table 4.2.6 (b)) on CRC death and 1.19 (95% CI:

1.06-1.34, Table 4.2.7 (b)) on advanced CRC. Both of these models demonstrate the greater the non-compliance score, the higher risk on CRC death and advanced CRC. After taking into account the score of waiting time, the estimated results on the effect of non-referral are robust for both the risk of CRC mortality and advanced CRC. Although greater score of non-compliance or score of waiting time has higher risk of CRC death, both of these covariates are not statistically significance for CRC death.

We further applied the propensity score matching together with the Hurdle Poisson mode to elucidate the impact of referral process on colonoscopy with the

estimated results shown in Table 4.2.8 (for CRC morality) and Table 4.2.9 (for advanced CRC incidence). The score of non-compliance (score 1) derived as mentioned above was used as the propensity score to match between the compliers and non-compliers. The results show that the aHR of non-referral reduce to 1.49 (95% CI=1.15-1.92, Table 4.2.8 (a)) on CRC mortality and 1.22 (95% CI=1.04-1.43, Table 4.2.9 (a)) on advanced CRC

incidence in comparison with referral for colonoscopy.

The corresponding estimated results for the effect of non-referral taking into account all referral examinations are 1.40 (95% CI:1.09-1.81, Table 4.2.8 (b)) and 1.15 (95% CI: 0.99-1.34, Table 4.2.9 (b)) for CRC death and advanced cancer incidence, respectively. Similar to the analysis regarding only referral for colonoscopy, the effect of waiting time was significantly associated with the risk of advance CRC (aHR: 3.56, 95％

CI: 2.17-3.85, Table 4.2.9 (b)) but not for the risk of CRC mortality (aHR: 1.67, 95% CI:

0.72-3.91, Table 4.2.8 (b)).

Hurdle Coxian phase-type regression model

In addition to the Hurdle Poission model, we also adopted the Hurdle Coxian phase-type regression model to disentangle the effect of two-stage process of referral on CRC mortality and the occurrence of advanced CRC. Regarding the determination of number of phases required for depicting the waiting process among those compliant with referral, a BIC criteria was adopted. Based on the results of model selection, the optimal number of phases describing the process of waiting for colonoscopy is 2, corresponding to the short-waiting state and long-waiting state. The compliers were thus classified into high-risk group (higher waiting time score) and low-risk group (lower waiting time score) by using the estimated results of transition probability from short-wait status to long-wait status.

The estimated results on the detrimental effect of non-referral for colonoscopy by using the propensity score adjustment analysis show that after taking score of

non-compliance and the probability of long-wait status, the aHR is 1.61 (95% CI=1.32-1.96,

Table 4.2.6 (a)) for CRC death and 1.25 (95% CI=1.11-1.41, Table 4.2.7 (a)) for advanced CRC. The corresponding results taking into account all confirmatory examination show that the aHR is 1.47 (95% CI=1.21-1.78, 4.2.6 (b)) for CRC death and 1.21 (95%

CI=1.07-1.36, 4.2.7 (b)) for advanced CRC.

In the propensity score mating analysis, the aHR of non-referral was estimate as 1.52 (95% CI=1.16-1.96, Table 4.2.8 (a)) for CRC mortality and 1.28 (95% CI=1.09-1.49, Table 4.2.9 (a)) for the risk of advanced cancer. The corresponding results taking into account all confirmatory examination show that the aHR is 1.42 (95% CI=1.10-1.85, 4.2.8 (b)) for CRC death and 1.20 (95% CI=1.03-1.41, 4.2.9 (b)) for advanced CRC.

By using the Hurdle Coxian phase-type model, the long-wait status has a significant impact on the risk of advanced CRC but which is not statistically significant for CRC mortality. This can be interpreted as that in comparison with those with lower tendency for transition into long-waiting status, subjects with high tendency in such a transition have a 4-fold and 3.7-fold risk for advanced CRC regarding the referral for colonoscopy and all confirmatory examinations, respectively.

4.3 Analysis of Intent-to-untreat and Noncompliance Adjustment Intention-to-untreat analysis

We further applied an intent-to-untreat analysis for assessing the impact of referral on colonoscopy among the FIT-positive subjects identified through the Taiwanese

nationwide colorectal cancer screening programme. In this approach, the heterogeneity between the areas in Taiwan and the adenoma detection rate (ADR) representing the quality of colonoscopy was considering by using a Bayesian regression model for

adjustment their effect during the evaluation for the effect of non-referral. Table 4.3.1 shows the demographic characteristics regarding the for areas, northern, central, southern, and eastern/offshore islands in Taiwan by referral status and also the rank of ADR (less than 40%, 40-59%, higher than 60%). The non-referral group has the risk of CRC

mortality (2.1 per 1,000) close to that of control derived by historical data in Taiwan (2.28 per 1000) as mentioned in the section of Statistical methods. The compliant subjects have a lower risk of CRC death (1.29 per 1,000). Among the four area in Taiwan, northern and central area have a lower CRC mortality compared with southern and eastern/offshore island. For the risk of CRC mortality by the rank of ADR, although the overall FIT-positive population shows a higher risk of CRC mortality for the rank of 40-59%, there are heterogeneities across areas and the obvious imbalance for the three ranks of ADR.

In Table 4.3.3, the results show that under 81% compliance rate, those without colonoscopy exam (non-referral) have higher risk of CRC death (aRR=1.65, 95%

CI=1.44-1.86) in comparison with those with colonoscopy after adjusted for areas and increasing incidence of CRC. For referral with all confirmatory exam, the RR is 1.56 (95% CI=1.38-1.75). After taking into account the adenoma detection rates, the result did not change a lot, which shows CRC mortality increased 66% (aRR=1.66, 95% CI=1.46-1.87) for non-referral compared to referral for colonoscopy, and 59% (aRR=1.59, 95%

CI=1.41-1.79) in comparison with referral for all confirmatory exam. The estimated results based on the intent-to-untreat approach are in line with that derived by using the Cox regression model with the adjustment for area and ADR (Table 4.3.2 (a), referral for colonoscopy; Table 4.3.2 (b), referral for all confirmatory examiniations).

Non-compliance adjustment analysis

Table 4.3.4 shows the estimated results by using the non-compliance adjustment for the referral on colonoscopy and that on confirmatory examinations. Suppose

compliance rate increases to 100%, the results demonstrate that those with referral for colonoscopy has the effect of 47% CRC mortality reduction (aRR=0.53, 95% CI=0.45-0.61) and those with referral for all confirmatory exam has 43% CRC mortality reduction (aRR=0.57, 95% CI=0.49-0.66) after adjusted for areas and increasing incidence of CRC.

For the analysis further taking into account the quality of colonoscopy represented by ADR, the effect of referral results in CRC mortality reduction by 48% (aRR=0.52, 95%

CI=0.45-0.61) and 45% (aRR=0.55, 95% CI=0.47-0.63) for referral with colonoscopy and all confirmatory exam, respectively.

Chapter 5 Discussion

5.1 The impact of referral on colonoscopy

Table 5.1.1 summarized the estimated results on the impact of referral on colonoscopy based on the KCIS cohort with positive FIT. The detrimental effect of non-referral results in the increase in the risk of CRC mortality and advanced CRC by 108%

(95% CI: 32-223%) and 61%(95 % CI: 8-144%), respectively by using the propensity score matching approach. The magnitude on non-referral derived by using the

conventional method was lower compared with that derived by using the propensity score matching approach.

Regarding the impact of non-referral at the nationwide scale, Table 5.1.2 summarized the estimated results by using a series of statistical methods including the conventional Cox regression model, two-stage referral process with Hurdle Poisson and Hurdle Coxian-phase type approach in conjunction with propensity score adjustment and propensity score matching to quantify the impact of referral on colonoscopy with the consideration of waiting process for a FIT-positive subjects to receiving the confirmatory diagnosis. By using the Hurdle Coxian-phase type in conjunction with the propensity score matching analysis, the impact non-referral behavior results in the increase in the risk of CRC mortality and advanced CRC by 52% (95% CI: 16-96%) and 28% (95% CI:

9-49%). While the tendency of being the type of long-waiting shows a significant impact on the risk of advanced CRC (aHR: 4.02, 95% CI: 1.71-9.46), the detrimental impact for CRC mortality was not statistically significant (aHR: 1.74, 95% CI: 0.24-12.65).

Compared with conventional Cox regression model, the effect of long-waiting explains the 7% of risk of CRC mortality attributable to non-compliance behavior. When taking

into account all confirmatory examinations, the proportion of the detrimental effect due to non-compliance behavior on CRC mortality explained by long-waiting is 4%.

The intention-to-untreat estimate gives the estimated results on the impact of non-referral for colonoscopy in the increase of CRC mortality risk by 66% (95% CI: 46-87%), which is compatible with that derived by using the Cox regression model (Table 4.3.2 (a)). Given the scenario that all FIT-positive subjects compliant with referral, the efficacy of colonoscopy will reduce the risk of CRC mortality by 48% (95% CI: 39-56%) based on the results of non-compliance adjustment approach (Table 4.3.4 (a)). Taking into account all confirmatory examinations, the corresponding efficacy brought of the

complete referral was estimated as 45% (95% CI: 37-53%).

5.2 Elucidation the process of non-referral and the impact of referral on colonoscopy We explored the impact of referral on colonoscopy by using a series of statistical methods. In addition to the convention approach by using the Cox regression model, we also applied the Hurdle Poisson regression model to identify factors associated with non-compliance and waiting time for referral and further quantify their impact on

colonoscopy referral by using the propensity score analyses.

Propensity score adjustment analysis

The hurdle part of hurdle Poisson model is the same as propensity score analysis, because both of them are to identify which factors influence their behavior of referral for confirmatory exam. Therefore, we took the score of non-referral for adjustment in the Cox regression model (Table 4.2.6-Table 4.2.7, Left column), the result is comparable to the multivariate analysis of conventional Cox regression model (Table 4.2.3-Table 4.2.4).

If we further included score of waiting time in the model (Table 4.2.6-Table 4.2.7, Middle column), the effects of non-referral still remained stable. However, we found that when we only focused on colonoscopy exam, the score of waiting time had a negative effect that the longer the waiting time, the lower risk of CRC death, but when this approach was applied to considering all confirmatory examinations, the estimated effect of waiting time score shows the longer the waiting time, the higher risk of CRC death. This indicates that there is heterogeneity between individuals complied with different examination. The similar phenomenon is also demonstrated for advanced cancer incidence.

We further applied the Coxian phase-type distribution to depict the tendency of being long-waiting, namely delay for colonoscopy. Notably, different from the direct implication of long waiting time that can be applied to the score 2 in the Hurdle Poisson regression model, the transition probability is used here representing the tendency of turning into the state of long-waiting from the state of short waiting as implied by the meaning of transition probability. The results demonstrate the effects of non-referral inclined only 1-2%, but the effects of long-wait status were stronger for colonoscopy than for all confirmatory exam despite there were no significance with wide range of

confidence interval.

Propensity score matching analysis

We further used the score of noncompliance to match compliers and non-compliers.

Compared to propensity score adjusted analysis, the effect of non-referral on CRC death reduced from 1.59 to 1.49 and from 1.46 to 1.40 for referral with colonoscopy and all confirmatory exams, separately. But for the advanced cancer incidence, the effect of

non-referral just declined by 1%-4%. In addition, after matching the noncompliance scores, the effects of non-referral between model with score of waiting time and without score of waiting time barely changed.

As using the Coxian phase-type model, it revealed that waiting time can explain 7%

and 4% effects on CRC mortality for referral with colonoscopy and with all confirmatory exams, respectively, in comparison with the conventional Cox regression model (Table 4.2.3).

5.3 Implication from Intention-to-untreat analysis and non-compliance adjustment One should bear in mind that the results derived from conventional Cox

regression model and the propensity score analysis with standard adjustment and matching approach or combined with the two-stage referral process are aimed at the derivation of the impact of referral on colonoscopy following the intention-to-untreat as used in the tradition of RCT. The estimated results demonstrated in 4.3 and also the results summarized in Table 5.2 show the consistency between the two streams of approaches. The estimated results under the rationale of intention-to-untreat and also a series of regression and propensity-based approach are to allowing for a proportion of non-referral as those occurred in the scenario of RCT. Under the context of service screen as that for Taiwanese nationwide colorectal cancer screening programme, although such an estimate provides information on the magnitude of effect size for non-referral, a more attractive issue to be addressed is the efficacy of colonoscopy given a full compliance.

The non-compliance adjustment analysis provides such an information.

5.4 Limitation

The issue of referral and waiting time have been demonstrated in the studies of Taiwan nationwide colorectal cancer screening programme (Lee et al., 2015; Jen HH et al., 2019). Previous studies showed that female sex and younger age are more reluctant to confirmation colonoscopy, and insurance type also influenced the willing of receiving colonoscopy (Thomas D Denberg, 2005). On the other hands, those subjects with family history of CRC have more willing to receive colonoscopy (Taylor DP, 2011). The study in Taiwan also demonstrated that higher perceived threat, higher cues for action, lower perceived barriers and higher health behaviour scores were associated the tendency of being compliant with referral for colonoscopy. The elderly and unmarried subjects have a lower probability of complied with referral for colonoscopy (Cheng et al., 2018).

Physician’s recommendation is considered as one of the most important component of cue to action (Cheng et al., 2018). In our study, most of the factors used for the derivation of propensity score did not demonstrate the significant influence on referral behaviour (Table 4.1.3) and thus impeded our intention to distinguish between complier and noncomplier. Further study is thus required to address the factors and to quantify the

Physician’s recommendation is considered as one of the most important component of cue to action (Cheng et al., 2018). In our study, most of the factors used for the derivation of propensity score did not demonstrate the significant influence on referral behaviour (Table 4.1.3) and thus impeded our intention to distinguish between complier and noncomplier. Further study is thus required to address the factors and to quantify the