傾向スコアマッチと多重補完法の解説 その23. After PSM (欠損値なし)
Stratified by treat
0 1 p test
n 150 150
age (mean (sd)) 25.41 (6.86) 25.48 (7.29) 0.929
educ (mean (sd)) 10.11 (1.67) 10.29 (1.77) 0.349
black (mean (sd)) 0.87 (0.33) 0.87 (0.34) 0.864
hisp (mean (sd)) 0.05 (0.23) 0.06 (0.24) 0.804
married (mean (sd)) 0.18 (0.39) 0.16 (0.37) 0.646
nodegr (mean (sd)) 0.81 (0.40) 0.77 (0.42) 0.399
re74 (mean (sd)) 1821.88 (4792.12) 1517.04 (4370.13) 0.565
re75 (mean (sd)) 1329.82 (3350.84) 914.13 (1943.45) 0.190
re78 (mean (sd)) 4064.76 (4568.86) 6149.53 (7960.04) 0.006
u74 (mean (sd)) 0.76 (0.43) 0.78 (0.42) 0.682
u75 (mean (sd)) 0.68 (0.47) 0.68 (0.47) 1.000
4. After PSM (欠損値あり)
Stratified by treat
0 1 p test
n 36 36
age (mean (sd)) 24.69 (4.60) 24.94 (6.37) 0.849
educ (mean (sd)) 10.44 (1.40) 10.22 (1.91) 0.576
black (mean (sd)) 0.86 (0.35) 0.83 (0.38) 0.747
hisp (mean (sd)) 0.06 (0.23) 0.08 (0.28) 0.649
married (mean (sd)) 0.14 (0.35) 0.11 (0.32) 0.726
nodegr (mean (sd)) 0.78 (0.42) 0.72 (0.45) 0.592
re74 (mean (sd)) 2525.86 (6186.79) 1184.89 (3236.43) 0.253
re75 (mean (sd)) 1160.82 (3337.37) 761.30 (1286.41) 0.505
re78 (mean (sd)) 4705.77 (5523.46) 6854.06 (10779.25) 0.291
u74 (mean (sd)) 0.72 (0.45) 0.78 (0.42) 0.592
u75 (mean (sd)) 0.69 (0.47) 0.64 (0.49) 0.623
7. SeqID Gender Age Severity Year Treat Outcome
1 M 66 4 2007 NA Good
2 F 72 9 2006 No Poor
3 M NA 12 2010 Yes NA
4 F 57 19 2014 Yes Poor
5 F 29 8 2007 Yes Good
… … … … … … …
154 F 84 21 NA No Poor
155 M 75 NA 2011 Yes Good
… … … … … … …
Multiple imputation
8. SeqID Gender Age Severity Year Treat Outcome
1 M 66 4 2007 NA Good
2 F 72 9 2006 No Poor
3 M NA 12 2010 Yes NA
4 F 57 19 2014 Yes Poor
5 F 29 8 2007 Yes Good
… … … … … … …
154 F 84 21 NA No Poor
155 M 75 NA 2011 Yes Good
… … … … … … …
Multiple imputation
9. SeqID Gender Age Severity Year Treat Outcome
1 M 66 4 2007 NA Good
2 F 72 9 2006 No Poor
3 M NA 12 2010 Yes NA
4 F 57 19 2014 Yes Poor
5 F 29 8 2007 Yes Good
… … … … … … …
154 F 84 21 NA No Poor
155 M 75 NA 2011 Yes Good
… … … … … … …
分布に応じて、データセット数
の値を乱数的に発生させる
重回帰分析などを用
いて、値を予測する
Multiple imputation
16. After PSM (欠損値なし)
Stratified by treat
0 1 p test
n 150 150
age (mean (sd)) 25.41 (6.86) 25.48 (7.29) 0.929
educ (mean (sd)) 10.11 (1.67) 10.29 (1.77) 0.349
black (mean (sd)) 0.87 (0.33) 0.87 (0.34) 0.864
hisp (mean (sd)) 0.05 (0.23) 0.06 (0.24) 0.804
married (mean (sd)) 0.18 (0.39) 0.16 (0.37) 0.646
nodegr (mean (sd)) 0.81 (0.40) 0.77 (0.42) 0.399
re74 (mean (sd)) 1821.88 (4792.12) 1517.04 (4370.13) 0.565
re75 (mean (sd)) 1329.82 (3350.84) 914.13 (1943.45) 0.190
re78 (mean (sd)) 4064.76 (4568.86) 6149.53 (7960.04) 0.006
u74 (mean (sd)) 0.76 (0.43) 0.78 (0.42) 0.682
u75 (mean (sd)) 0.68 (0.47) 0.68 (0.47) 1.000
17. After PSM (欠損値有り)
Stratified by treat
0 1 p test
n 36 36
age (mean (sd)) 24.69 (4.60) 24.94 (6.37) 0.849
educ (mean (sd)) 10.44 (1.40) 10.22 (1.91) 0.576
black (mean (sd)) 0.86 (0.35) 0.83 (0.38) 0.747
hisp (mean (sd)) 0.06 (0.23) 0.08 (0.28) 0.649
married (mean (sd)) 0.14 (0.35) 0.11 (0.32) 0.726
nodegr (mean (sd)) 0.78 (0.42) 0.72 (0.45) 0.592
re74 (mean (sd)) 2525.86 (6186.79) 1184.89 (3236.43) 0.253
re75 (mean (sd)) 1160.82 (3337.37) 761.30 (1286.41) 0.505
re78 (mean (sd)) 4705.77 (5523.46) 6854.06 (10779.25) 0.291
u74 (mean (sd)) 0.72 (0.45) 0.78 (0.42) 0.592
u75 (mean (sd)) 0.69 (0.47) 0.64 (0.49) 0.623
18. After MI+PSM
Stratified by treat
0 1 p test
n 139 139
age (mean (sd)) 25.58 (6.61) 26.02 (7.11) 0.588
educ (mean (sd)) 10.29 (1.70) 10.22 (1.94) 0.767
black (mean (sd)) 0.87 (0.34) 0.91 (0.29) 0.343
hisp (mean (sd)) 0.05 (0.22) 0.05 (0.22) 1.000
married (mean (sd)) 0.19 (0.39) 0.19 (0.39) 1.000
nodegr (mean (sd)) 0.76 (0.43) 0.76 (0.43) 1.000
re74 (mean (sd)) 1500.88 (4143.39) 1443.69 (3509.35) 0.901
re75 (mean (sd)) 1068.95 (2424.18) 1021.02 (1941.02) 0.856
re78 (mean (sd)) 3886.44 (4330.99) 5724.39 (7367.12) 0.012
u74 (mean (sd)) 0.79 (0.41) 0.77 (0.42) 0.665
u75 (mean (sd)) 0.70 (0.46) 0.66 (0.47) 0.522
21. Propensity score matching after
multiple imputation
• 後ろ向きデータで因果関係に言及できる方法です。
• ビッグデータ推奨。
• ランダム化試験より低コストで倫理審査の壁が低くランダム化
が不可能な介入の解析もできます。
• バイアスは小さくできると信じられています。
• PSMの検出力は高くないが、MIと組み合わせることでその低
下を限ることができます。