Propensity Score Analysis with Partially Observed Baseline Covariates: A Practical Comparison of Methods for Handling Missing Data
Abstract
:1. Introduction
1.1. Motivating Example
1.2. Propensity Score Framework
2. Materials and Methods
2.1. Propensity Score and Missing Data in Non-Interventional Studies
2.2. Statistical Analysis
2.2.1. Propensity Score Estimation
2.2.2. Missing Data Methods
2.2.3. Measures of Balance
3. Results
3.1. Missing Data
3.2. Propensity Score Estimation and Common Support
3.3. Balance
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Variable | N | Combined (N = 478) | Angiography Guidance (N = 263) | IVUS or OCT (N = 215) | SMD |
---|---|---|---|---|---|
Gender: male | 465 | 83% (385) | 80% (205) | 86% (180) | 0.14 |
Age | 471 | 65/72/79 | 65/73/80 | 64/72/79 | −0.06 |
BMI | 423 | 24/26/28 | 24/27/29 | 24/26/28 | −0.01 |
Hypertension | 478 | 78% (371) | 79% (207) | 76% (164) | −0.06 |
Diabetes | 477 | 30% (142) | 30% (79) | 29% (63) | −0.02 |
Smoker | 476 | 46% (221) | 45% (119) | 48% (102) | 0.04 |
CAD | 475 | 25% (117) | 21% (56) | 29% (61) | 0.17 |
Hyperlipidemia | 474 | 66% (311) | 62% (162) | 70% (149) | 0.18 |
Previous PCI | 476 | 35% (167) | 34% (88) | 37% (79) | 0.06 |
Previous MI | 476 | 25% (117) | 25% (65) | 24% (52) | −0.01 |
Previous stroke/TIA | 475 | 5% (25) | 5% (13) | 6% (12) | 0.03 |
COPD | 476 | 7% (34) | 7% (18) | 7% (16) | 0.02 |
PAD | 475 | 15% (73) | 16% (42) | 14% (31) | −0.05 |
Clinical Presentation: NSTEMI | 474 | 31% (145) | 37% (96) | 23% (49) | −0.30 |
Other | 11% (54) | 10% (25) | 14% (29) | 0.13 | |
Stable CAD | 33% (155) | 31% (81) | 35% (74) | 0.08 | |
STEMI | 11% (50) | 10% (27) | 11% (23) | 0.01 | |
Unstable Angina | 15% (70) | 12% (32) | 18% (38) | 0.16 | |
NYHA: I | 459 | 56% (256) | 54% (136) | 58% (120) | 0.09 |
II | 28% (130) | 28% (72) | 28% (58) | −0.01 | |
III | 13% (59) | 14% (36) | 11% (23) | −0.09 | |
IV | 3% (14) | 4% (9) | 2% (5) | −0.07 | |
CCS: 0 | 391 | 26% (100) | 27% (59) | 24% (41) | −0.07 |
1 | 16% (63) | 18% (40) | 13% (23) | −0.13 | |
2 | 25% (97) | 25% (54) | 25% (43) | 0.01 | |
3 | 16% (63) | 14% (30) | 19% (33) | 0.15 | |
4 | 17% (68) | 16% (36) | 19% (32) | 0.06 | |
EuroSCORE II | 303 | 0.94/1.52/3.00 | 1.07/1.72/3.15 | 0.80/1.38/2.60 | −0.20 |
GFR | 439 | 56/74/90 | 53/69/90 | 58/75/90 | 0.17 |
Hemoglobin | 454 | 12/13/15 | 12/13/15 | 12/14/15 | 0.08 |
LVEF: poor (<30%) | 462 | 4% (17) | 3% (8) | 4% (9) | 0.06 |
fair (30–50%) | 36% (166) | 41% (104) | 30% (62) | −0.25 | |
good (>50%) | 60% (279) | 56% (140) | 66% (139) | 0.22 | |
Aspirin | 471 | 79% (373) | 80% (208) | 79% (165) | −0.03 |
Thienidopiridine | 471 | 54% (255) | 52% (135) | 57% (120) | 0.11 |
Syntax score | 188 | 18/23/29 | 19/25/30 | 17/22/27 | −0.27 |
LAD | 472 | 83% (394) | 85% (220) | 82% (174) | −0.09 |
LCX | 475 | 51% (242) | 56% (147) | 44% (95) | −0.24 |
RCA | 474 | 46% (218) | 52% (135) | 39% (83) | −0.26 |
Measure of Balance | ||||
---|---|---|---|---|
Missing Data | PS Estimation | SMD | OVL | C-Statistc |
CC | LR | 1.09 | 0.42 | 0.33 |
GBM | 2.44 | 0.73 | 0.46 | |
CBPS | 1.07 | 0.38 | 0.29 | |
MIND | LR | 0.53 | 0.35 | 0.25 |
GBM | 2.11 | 0.69 | 0.44 | |
CBPS | 0.53 | 0.33 | 0.24 | |
SAEM | LR (SAEM) | 0.7 | 0.28 | 0.19 |
GBM (surr.) | GBM | 1.76 | 0.59 | 0.39 |
MI-AREGIMP | CBPS | 0.7 (0.64;0.81) | 0.27 (0.25;0.31) | 0.19 (0.17;0.21) |
GBM | 1.86 (1.56;2.3) | 0.63 (0.54;0.74) | 0.41 (0.37;0.45) | |
LR | 0.73 (0.68;0.84) | 0.28 (0.26;0.3) | 0.19 (0.18;0.22) | |
MI-BBPMM | CBPS | 0.69 (0.65;0.75) | 0.27 (0.25;0.29) | 0.18 (0.17;0.2) |
GBM | 1.99 (1.7;2.29) | 0.67 (0.56;0.72) | 0.43 (0.39;0.45) | |
LR | 0.72 (0.67;0.82) | 0.27 (0.25;0.33) | 0.19 (0.18;0.22) | |
MI-MICE | CBPS | 0.74 (0.67;0.81) | 0.28 (0.25;0.31) | 0.2 (0.18;0.21) |
GBM | 1.9 (1.69;2.31) | 0.63 (0.58;0.74) | 0.41 (0.39;0.46) | |
LR | 0.76 (0.71;0.84) | 0.29 (0.27;0.32) | 0.2 (0.19;0.22) |
PS Based Methods | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
NN | FM | PS-IPTW | |||||||||||
Missing Data | PS Estimation | SMD | OVL | C-Statistic | PRI | SMD | OVL | C-Statistic | PRI | SMD | OVL | C-Statistic | PRI |
CC | LR | 0.36 | 0.24 | 0.2 | 0.74 | 0.1 | 0.07 | 0.12 | 1 | 0.1 | 0.05 | 0.03 | 0.54 |
GBM | 0.16 | 0.09 | 0.1 | 0.21 | 0.44 | 0.26 | 0.32 | 1 | 2.19 | 0.66 | 0.44 | 0.97 | |
CBPS | 0.27 | 0.13 | 0.12 | 0.74 | 0.19 | 0.15 | 0.13 | 1 | 0.28 | 0.22 | 0.06 | 0.8 | |
MIND | LR | 0.24 | 0.33 | 0.23 | 0.88 | 0.1 | 0.05 | 0.07 | 1 | 0.13 | 0.1 | 0.02 | 0.81 |
GBM | 0.2 | 0.13 | 0.11 | 0.32 | 0.32 | 0.22 | 0.22 | 1 | 1.79 | 0.58 | 0.39 | 0.95 | |
CBPS | 0.25 | 0.31 | 0.23 | 0.88 | 0.1 | 0.06 | 0.1 | 1 | 0.2 | 0.11 | 0.04 | 0.85 | |
SAEM | LR (SAEM) | 0 | 0 | 0 | 0.42 | 0.01 | 0.01 | 0.06 | 1 | 0.03 | 0.1 | 0 | 0.88 |
GBM (surr.) | GBM | 0 | 0 | 0 | 0.26 | 0.06 | 0.04 | 0.11 | 1 | 1.29 | 0.44 | 0.31 | 0.94 |
MI-AREGIMP | CBPS | 0.06 (0.04;0.08) | 0.04 (0.03;0.05) | 0.02 (−0.01;0.03) | 0.72 (0.69;0.75) | 0.02 (0.01;0.04) | 0.02 (0.01;0.03) | 0.04 (0;0.09) | 1 | 0.16 (0.1;0.19) | 0.1 (0.06;0.13) | 0.04 (0.02;0.05) | 0.92 (0.9;0.93) |
GBM | 0.14 (0.1;0.27) | 0.1 (0.07;0.19) | 0.07 (0.05;0.15) | 0.39 (0.29;0.46) | 0.12 (0.02;0.39) | 0.1 (0.03;0.29) | 0.12 (0.06;0.23) | 1 | 1.5 (1.17;1.99) | 0.5 (0.41;0.61) | 0.34 (0.29;0.39) | 0.95 (0.93;0.96) | |
LR | 0.08 (0.06;0.1) | 0.05 (0.04;0.06) | 0.03 (0.02;0.04) | 0.72 (0.67;0.76) | 0.02 (0.01;0.03) | 0.02 (0.01;0.03) | 0.03 (−0.01;0.08) | 1 | 0.03 (0.01;0.06) | 0.08 (0.03;0.11) | 0 (0;0.01) | 0.87 (0.84;0.89) | |
MI-BBPMM | CBPS | 0.06 (0.04;0.08) | 0.04 (0.03;0.05) | 0.02 (0.01;0.03) | 0.73 (0.7;0.76) | 0.02 (0.01;0.03) | 0.01 (0.01;0.02) | 0.02 (−0.03;0.09) | 1 | 0.14 (0.07;0.19) | 0.08 (0.07;0.11) | 0.04 (0.02;0.05) | 0.93 (0.88;0.94) |
GBM | 0.18 (0.11;0.22) | 0.12 (0.06;0.16) | 0.09 (0.05;0.13) | 0.37 (0.29;0.46) | 0.2 (0.06;0.41) | 0.15 (0.05;0.28) | 0.13 (0.08;0.29) | 1 | 1.66 (1.3;1.99) | 0.55 (0.41;0.62) | 0.36 (0.31;0.4) | 0.95 (0.94;0.96) | |
LR | 0.08 (0.06;0.1) | 0.05 (0.04;0.07) | 0.03 (0.02;0.04) | 0.73 (0.68;0.76) | 0.02 (0.01;0.03) | 0.01 (0.01;0.02) | 0.04 (−0.02;0.09) | 1 | 0.03 (0.02;0.05) | 0.08 (0.06;0.11) | 0.01 (0;0.01) | 0.88 (0.83;0.89) | |
MI-MICE | CBPS | 0.07 (0.05;0.09) | 0.04 (0.03;0.06) | 0.03 (−0.02;0.03) | 0.72 (0.68;0.74) | 0.02 (0.01;0.03) | 0.01 (0.01;0.02) | 0.04 (−0.04;0.07) | 1 | 0.14 (0.06;0.2) | 0.08 (0.05;0.1) | 0.04 (0.01;0.05) | 0.91 (0.88;0.93) |
GBM | 0.16 (0.12;0.26) | 0.11 (0.08;0.19) | 0.08 (0.06;0.15) | 0.39 (0.29;0.46) | 0.14 (0.05;0.24) | 0.1 (0.04;0.18) | 0.13 (0.08;0.19) | 1 | 1.46 (1.3;2.05) | 0.49 (0.44;0.64) | 0.34 (0.31;0.41) | 0.94 (0.93;0.95) | |
LR | 0.1 (0.08;0.11) | 0.06 (0.04;0.07) | 0.04 (0.03;0.04) | 0.72 (0.67;0.74) | 0.01 (0.01;0.02) | 0.01 (0.01;0.02) | 0.03 (−0.02;0.1) | 1 | 0.02 (0;0.05) | 0.07 (0.04;0.12) | 0 (0;0.01) | 0.85 (0.83;0.88) |
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Bottigliengo, D.; Lorenzoni, G.; Ocagli, H.; Martinato, M.; Berchialla, P.; Gregori, D. Propensity Score Analysis with Partially Observed Baseline Covariates: A Practical Comparison of Methods for Handling Missing Data. Int. J. Environ. Res. Public Health 2021, 18, 6694. https://doi.org/10.3390/ijerph18136694
Bottigliengo D, Lorenzoni G, Ocagli H, Martinato M, Berchialla P, Gregori D. Propensity Score Analysis with Partially Observed Baseline Covariates: A Practical Comparison of Methods for Handling Missing Data. International Journal of Environmental Research and Public Health. 2021; 18(13):6694. https://doi.org/10.3390/ijerph18136694
Chicago/Turabian StyleBottigliengo, Daniele, Giulia Lorenzoni, Honoria Ocagli, Matteo Martinato, Paola Berchialla, and Dario Gregori. 2021. "Propensity Score Analysis with Partially Observed Baseline Covariates: A Practical Comparison of Methods for Handling Missing Data" International Journal of Environmental Research and Public Health 18, no. 13: 6694. https://doi.org/10.3390/ijerph18136694