第六章、 結論與建議
第二節、 建議
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配對與傾向分數配對合併使用」確實會有較好的表現，但表現的好壞也取決於確 切配對的變數。
實證分析部份，探討的主題為「家庭結構與青少年偏差行為之關聯探討」， 資料為「內政部民國 92 年臺閩地區少年身心狀況調查」。依據直接進行 PS 配對，
與針對變數 Fam_pro 作 Exact-PS 配對所得到兩組配對樣本，我們進行邊際勝算 比的估計。結果顯示在 PS 配對樣本中，非完整家庭青少年會有偏差行為的可能 性為完整家庭青少年的 1.329 倍，而 Exact-PS 配對樣本中，非完整家庭青少年 會有偏差行為的可能性為完整家庭青少年的 1.317 倍。至於原始樣本，則為 1.708 倍。由於顯著性檢定結果皆為顯著，故本實證分析結果顯示家庭結構完整與否確 實會對為青少年偏差行為有顯著影響。若定義為三種偏差行為類別，則配對樣本 中，「與性相關之偏差行為」與「暴力滋事類之偏差行為」為顯著結果，分別為 2.1 倍和 1.3 倍，而「菸酒毒品類之偏差行為」則不顯著，約為 1.1 倍。
第二節 建議
本文建議有四。其一，我們必須了解到配對是一種再抽樣的方法，於觀察性 研究中使用配對方法所得到的配對樣本，相較於原始樣本，可推論的廣度是較低 的，因此若是原始樣本的兩群體已達到平衡性，則可以不需要經由配對而直接進 行分析。此外，資料調查對象為來自臺閩地區的青少年，故實證研究推論範圍僅 限於臺閩地區青少年，而此研究主題仍需要更多實證研究結果來佐證。
其二，根據模擬研究結果，顯示與處理指派中度相關且與反應變數高度相關 的變數最適合作 Exact-PS 配對，而本文實證資料中則缺少與模擬結果相符特性 的二元變數。因此，對於蒙地卡羅模擬實驗的設計，可在模擬情境的設定上作更 多的變化與改良，例如探討變數與處理指派和反應變數相關程度的定義、增加情 境數量、及將二元類別變數改為多元類別變數。
其三，對於「探討不同配對方法合併使用的效果」，其中的配對方法並不局 限於傾向分數配對與確切配對，任何配對方法的合併使用都可能會有不同的效果，
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例如馬氏距離配對搭配線性傾向分數門檻值、傾向分數的四種使用方式之合併使 用、確切配對與最適配對的合併使用等。
其四，模擬架構中，亦可嘗試將各變數交互作用項放入反應變數與傾向分數 模型中。
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參考文獻
中文部份
侯崇文(2001)-家庭結構、家庭關係與青少年偏差行為
《應用心理研究 , 第 11 期 , 25-43 頁》
英文部份
Agresti, A. , Min, Y.(2004).Effects and non-effects of paired identical observations in comparing proportions with binary matched-pairs data. Statistics in Medicine, 23, 65–75.
Austin, P. C.(2007). The performance of different propensity score methods for estimating marginal odds ratios. Statistics in Medicine, 26, 3078–3094.
Austin, P. C., Mamdani, M. M. (2006). A comparison of propensity score methods: A case-study estimating the effectiveness of post-AMI statin use. Statistics in Medicine, 25, 2084–2106.
Cochran, W.G., Rubin, D.B.(1973). Controlling bias in observational studies: A review.
The Indian Journal of Statistics, Series A, 35, 417–446.
D’Agostino, R. B., Jr. (1998). Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group. Statistics in Medicine, 17, 2265–2281.
Gu, X. S., Rosenbaum, P. R. (1993).Comparison of multivariate matching methods:
Structures, distances, and algorithms. Journal of Computational and Graphical Statistics, 2, 405–420.
Hansen, B. B. (2004). Full matching in an observational study of coaching for the SAT.
Journal of the American Statistical Association, 99, 609–618.
Imai, K., King, G., Stuart, E.A.(2008). Misunderstandings between experimentalists and observationalists about causal inference. Journal of the Royal Statistical Society, Series A, 171:481-502.
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Neyman, J.(1923). On the application of probability theory to agricultural experiments. Statistical Science, 5(4), 465-472.
Normand, S. L. T., Landrum, M. B., Guadagnoli, E., Ayanian, J. Z., Ryan, T. J., Cleary, P.
D., McNeil, B.J.(2001). Validating recommendations for coronary angiography following an acute myocardial infarction in the elderly: a matched analysis using propensity scores. Journal of Clinical Epidemiology, 54, 387-398.
Rosenbaum, P. R.(1987). Model-based direct adjustment. Journal of the American Statistical Association, 82, 387–394.
Rosenbaum, P. R.(1989). Optimal matching for observational Studies Journal of the American Statistical Association, 1024-1032.
Rosenbaum, P. R.(2010). Design of Observational Studies. Springer series in Statistics.
Rosenbaum, P. R., Rubin, D. B.(1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41–55.
Rosenbaum, P. R., Rubin, D. B. (1985a). The bias due to incomplete matching.
Biometrics, 41, 103–116.
Rosenbaum, P. R., Rubin, D. B. (1985b). Constructing a control group using multivariate matched sampling methods that incorporate the propensity score.
The American Statistician, 39, 33–38.
Rosenbaum, P. R., Ross, R. N., Silber, J. H.(2007). Minimum distance matched
sampling with fine balance in an observational study of treatment for ovarian cancer.
Journal of the American Statistical Association, 102, 75–83.
Rubin, D. B. (1973). Matching to remove bias in observational studies.
Biometrics, 29:159–184.
Rubin, D. B.(1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688–701.
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Rubin, D. B.(2001). Using Propensity Scores to Help Design Observational Studies:
Application to the Tobacco Litigation. Health Services & Outcomes Research Methodology 2, 169–188.
Stuart, E. A. (2010). Matching methods for causal inference: A review and a look forward . Statistics Science, 25(1), 1–21.
Yoon, F. B., Huskamp, H. A. Busch, A. B., Normand, SLT. (2011). Using multiple control groups and matching to address unobserved biases in comparative
effectiveness research an observational study of the effectiveness of mental health parity. Statistics in Biosciences, 3, 63–78.
Zhao, Z.(2004). Using matching to estimate treatment effects: Data requirements, matching metrics, and montecarlo evidence. Review of Economics and Statistics, 86(1), 91–107.
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附錄一、對數勝算比分配
情境一:PS 配對(上)與 Exact-PS 配對(下)對數勝算比分配
情境二:PS 配對(上)與 Exact-PS 配對(下)對數勝算比分配
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情境三:PS 配對(上)與 Exact-PS 配對(下)對數勝算比分配
情境四:PS 配對(上)與 Exact-PS 配對(下)對數勝算比分配
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Exact-PS 配對樣本 Odds Ratio SE[log-odds ratio)]
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(1)□ 知道：電話號碼為_____________________ (2)□ 不知道
26.您知道下列機構中，那些機構有提供心理衛生諮商服務?(可複選，尌您知道
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x1=rbinom(1000,1,0.5) x2=rbinom(1000,1,0.5) x3=rbinom(1000,1,0.5) x4=rbinom(1000,1,0.5) x5=rbinom(1000,1,0.5) x6=rbinom(1000,1,0.5) x7=rbinom(1000,1,0.5) x8=rbinom(1000,1,0.5)
beta1=beta3=beta5=log(5) beta2=beta4=beta6=log(2)
alpha1=alpha2=alpha3=log(5) alpha4=alpha5=alpha6=log(2)
alpha0outcome=-4.4 beta0trt=-6.3
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z=rbinom(1000, 1, prob=ps)
prob.outcome1=exp.b1/(1+exp.b1)
y1=rbinom(1000, 1, prob=prob.outcome1) prob.outcome2=exp.b2/(1+exp.b2)
y2=rbinom(1000, 1, prob=prob.outcome2) prob.outcome3=exp.b4/(1+exp.b4)
y3=rbinom(1000, 1, prob=prob.outcome3) prob.outcome4=exp.b6/(1+exp.b6)
y4=rbinom(1000, 1, prob=prob.outcome4) prob.outcome5=exp.b8/(1+exp.b8)
y5=rbinom(1000, 1, prob=prob.outcome5)
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c1=cbind(x1,x2,x3,x4,x5,x6,x7,x8,z,ps,y1) table1=data.frame(c1)
z1_1=table1[table1$z==1,]
z0_1=table1[table1$z==0,]
or1_1=mean(z1_1$y1)/(1-mean(z1_1$y1))/(mean(z0_1$y1)/(1-mean(z0_1$y1) ))
or1_1
c2=cbind(x1,x2,x3,x4,x5,x6,x7,x8,z,ps,y2) table2=data.frame(c2)
z1_2=table2[table2$z==1,]
z0_2=table2[table2$z==0,]
or2_1=mean(z1_2$y2)/(1-mean(z1_2$y2))/(mean(z0_2$y2)/(1-mean(z0_2$y2) ))
or2_1
c3=cbind(x1,x2,x3,x4,x5,x6,x7,x8,z,ps,y3) table3=data.frame(c3)
z1_3=table3[table3$z==1,]
z0_3=table3[table3$z==0,]
or3_1=mean(z1_3$y3)/(1-mean(z1_3$y3))/(mean(z0_3$y3)/(1-mean(z0_3$y3) ))
or3_1
c4=cbind(x1,x2,x3,x4,x5,x6,x7,x8,z,ps,y4) table4=data.frame(c4)
z1_4=table4[table4$z==1,]
z0_4=table4[table4$z==0,]
or4_1=mean(z1_4$y4)/(1-mean(z1_4$y4))/(mean(z0_4$y4)/(1-mean(z0_4$y4) ))
or4_1
c5=cbind(x1,x2,x3,x4,x5,x6,x7,x8,z,ps,y5) table5=data.frame(c5)
z1_5=table5[table5$z==1,]
z0_5=table5[table5$z==0,]
or5_1=mean(z1_5$y5)/(1-mean(z1_5$y5))/(mean(z0_5$y5)/(1-mean(z0_5$y5)
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table1_x1_0=subset(table1,table1$x1=="0") table1_x1_1=subset(table1,table1$x1=="1") glm1_1= ps.estimate(object = match1_1,resp =
"y1",family="binomial",treat="z")
estimate.se1_1= glm1_1$ps.estimation$unadj$se estmate.or1_1= glm1_1$ps.estimation$unadj$effect
data.match1=ps.match(object=table1,ratio=1,x=0.2,caliper="logit",trea t="z",who.treated=1,matched.by="ps",setseed=FALSE,combine.output=T) glm1= ps.estimate(object = data.match1$data.matched,resp =
"y1",family="binomial",treat="z")
estimate.se1= glm1$ps.estimation$unadj$se estmate.or1= glm1$ps.estimation$unadj$effect table2_x1_0=subset(table2,table1$x1=="0") table2_x1_1=subset(table2,table1$x1=="1")
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glm2_1= ps.estimate(object = match2_1,resp =
"y2",family="binomial",treat="z")
estimate.se2_1= glm2_1$ps.estimation$unadj$se estmate.or2_1= glm2_1$ps.estimation$unadj$effect
data.match2=ps.match(object=table2,ratio=1,x=0.2,caliper="logit",trea t="z",who.treated=1,matched.by="ps",setseed=FALSE,combine.output=T) glm2= ps.estimate(object = data.match2$data.matched,resp =
"y2",family="binomial",treat="z")
estimate.se2= glm2$ps.estimation$unadj$se estmate.or2= glm2$ps.estimation$unadj$effect table3_x1_0=subset(table3,table1$x1=="0") table3_x1_1=subset(table3,table1$x1=="1") glm3_1= ps.estimate(object = match3_1,resp =
"y3",family="binomial",treat="z")
estimate.se3_1= glm3_1$ps.estimation$unadj$se estmate.or3_1= glm3_1$ps.estimation$unadj$effect
data.match3=ps.match(object=table3,ratio=1,x=0.2,caliper="logit",trea t="z",who.treated=1,matched.by="ps",setseed=FALSE,combine.output=T) glm3= ps.estimate(object = data.match3$data.matched,resp =
"y3",family="binomial",treat="z")
estimate.se3= glm3$ps.estimation$unadj$se estmate.or3= glm3$ps.estimation$unadj$effect table4_x1_0=subset(table4,table1$x1=="0") table4_x1_1=subset(table4,table1$x1=="1")
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glm4_1= ps.estimate(object = match4_1,resp ="y4",family="binomial",treat="z")
estimate.se4_1= glm4_1$ps.estimation$unadj$se estmate.or4_1= glm4_1$ps.estimation$unadj$effect
data.match4=ps.match(object=table4,ratio=1,x=0.2,caliper="logit",trea t="z",who.treated=1,matched.by="ps",setseed=FALSE,combine.output=T) glm4= ps.estimate(object = data.match4$data.matched,resp =
"y4",family="binomial",treat="z")
estimate.se4=glm4$ps.estimation$unadj$se estmate.or4=glm4$ps.estimation$unadj$effect table5_x1_0=subset(table5,table1$x1=="0") table5_x1_1=subset(table5,table1$x1=="1")
estimate.se5_1= glm 5_1$ps.estimation$unadj$se
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estmate.or5_1= glm 5_1$ps.estimation$unadj$effect
data.match5=ps.match(object=table5,ratio=1,x=0.2,caliper="logit",trea t="z",who.treated=1,matched.by="ps",setseed=FALSE,combine.output=T) glm5= ps.estimate(object = data.match5$data.matched,resp =
"y5",family="binomial",treat="z")
estimate.se5=glm5$ps.estimation$unadj$se estmate.or5= glm 5$ps.estimation$unadj$effect
unex_matched=c(estmate.or1,estmate.or2,estmate.or3,estmate.or4,estmat e.or5)
unex_selogor=c(estimate.se1,estimate.se2,estimate.se3,estimate.se4,es timate.se5)
crude=c(or1_1,or2_1,or3_1,or4_1,or5_1)
temp1=c(temp1,crude) temp2=c(temp2,matched) temp3=c(temp3,selogor) temp4=c(temp4,unex_matched) temp5=c(temp5,unex_selogor) }
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temp1=c(temp1,CI)}
or1_CI=temp1
or1_CI=matrix(or1_CI,1000,2,byrow=T) temp2=NULL
for(i in 1:1000){
if(or1_CI[i,1]<=1 && 1<=or1_CI[i,2])w=1 else w=0 temp2=c(temp2,w)
}
temp1=c(temp1,CI) }
or2_CI=temp1
or2_CI=matrix(or2_CI,1000,2,byrow=T) temp2=NULL
for(i in 1:1000){
if(or2_CI[i,1]<=2 && 2<=or2_CI[i,2])w=1 else w=0 temp2=c(temp2,w)
}
temp1=c(temp1,CI)
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if(or4_CI[i,1]<=4 && 4<=or4_CI[i,2])w=1 else w=0 temp2=c(temp2,w)
}
temp1=c(temp1,CI) }
or6_CI=temp1
or6_CI=matrix(or6_CI,1000,2,byrow=T) temp2=NULL
for(i in 1:1000){
if(or6_CI[i,1]<=6 && 6<=or6_CI[i,2])w=1 else w=0 temp2=c(temp2,w)
}
temp1=c(temp1,CI) }
or8_CI=temp1
or8_CI=matrix(or8_CI,1000,2,byrow=T)
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if(or8_CI[i,1]<=8 && 8<=or8_CI[i,2])w=1 else w=0 temp2=c(temp2,w)
}
var(log(matched_log6[1,]))+(mean(log(matched_log6[1,]))-log(1))^2, var(log(matched_log6[2,]))+(mean(log(matched_log6[2,]))-log(2))^2, var(log(matched_log6[3,]))+(mean(log(matched_log6[3,]))-log(4))^2, var(log(matched_log6[4,]))+(mean(log(matched_log6[4,]))-log(6))^2, var(log(matched_log6[5,]))+(mean(log(matched_log6[5,]))-log(8))^2 )
M_MSE_log6_m=matrix(M_MSE_log6,6,1) C_MSE_log6=c(
var(log(crude_log6[1,]))+(mean(log(crude_log6[1,]))-log(1))^2, var(log(crude_log6[2,]))+(mean(log(crude_log6[2,]))-log(2))^2, var(log(crude_log6[3,]))+(mean(log(crude_log6[3,]))-log(4))^2, var(log(crude_log6[4,]))+(mean(log(crude_log6[4,]))-log(6))^2, var(log(crude_log6[5,]))+(mean(log(crude_log6[5,]))-log(8))^2 )
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nex_matched_log6[3,]))-log(4))^2,var(log(unex_matched_log6[4,]))+
(mean(log(unex_matched_log6[4,]))-log(6))^2,var(log(unex_matched_
log6[5,]))+(mean(log(unex_matched_log6[5,]))-log(8))^2,var(log(un ex_matched_log6[6,]))+(mean(log(unex_matched_log6[6,]))-log(10))^
2 )
unex_MSE_log6_m=matrix(unex_MSE_log6,6,1)