Construction and comparison of propensity score weighting models for multiple treatments_Chinese Journal of Evidence-Based Medicine

Authors：

XU Xiao ¹ , TU Boxiang ² ,  QIN Yingyi ² ,  HE Jia ^1,2

1. School of Medicine, Tongji University, Shanghai 200092, P. R. China;
2. Department of Military Health Statistics, Naval Medical University, Shanghai 200433, P. R. China;

Corresponding author：

QIN Yingyi, Email: yingyi_qin@163.com; HE Jia, Email: hejia63@yeah.net

Keywords：

Propensity score weighting; Overlap weighting; Multiple treatments; Generalized boosting model; Inverse probability weighting

DOI：

10.7507/1672-2531.202210097

Video：

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Objective To compare the ability of three propensity score weighting methods to balance the covariates and the advantages and disadvantages to estimate the treatment effects when dealing with multiple treatment data under different sample sizes. Methods Monte Carlo simulation was used to generate data sets and the advantages and disadvantages of balancing covariates and estimating the treatment effects of three propensity score weighting methods, Logistic-IPTW, Logistic-OW and GBM-OW were compared. The evaluation index of covariate equilibrium level was the absolute standard mean difference. The evaluation indexes of effect estimation included the point estimate of treatment effect, root mean square error and confidence interval coverage. Results Compared with Logistic-IPTW and Logistic-OW, GBM-OW was better in effect estimation and had a smaller root mean square error in five scenarios where covariates were related to treatment factors and outcome variables with different varying degrees of complexity. In terms of covariate equilibrium, all three methods had good effects. GBM-OW method performed better when the overlap of propensity score distribution of multiple treatment data was relatively low and covariables had increasingly complex nonlinear relationships with treatment factors and outcome variables. Conclusion When dealing with multiple treatment data, GBM-OW method has advantages over the other two methods when there is nonlinearity and/or interaction between covariates and treatment factors and outcome variables. Using this method, the effect estimation is closer to the real value, which is a better choice.

Citation： XU Xiao, TU Boxiang, QIN Yingyi, HE Jia. Construction and comparison of propensity score weighting models for multiple treatments. Chinese Journal of Evidence-Based Medicine, 2023, 23(3): 362-372. doi: 10.7507/1672-2531.202210097 Copy

1.	Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika, 1983, 70(1): 41-55.
2.	王永吉, 蔡宏伟, 夏结来, 等. 倾向指数第一讲倾向指数的基本概念和研究步骤. 中华流行病学杂志, 2010, 31(3): 347-348.
3.	CSCO生物统计学专家委员会RWS方法学组. 倾向性评分方法及其规范化应用的统计学共识. 中国卫生统计, 2020, 37(6): 952-958.
4.	吴美京, 吴骋, 王睿, 等. 倾向性评分法中评分值的估计方法及比较. 中国卫生统计, 2013, 30(3): 440-444.
5.	McCaffrey DF, Ridgeway G, Morral AR. Propensity score estimation with boosted regression for evaluating causal effects in observational studies. Psychol Methods, 2004, 9(4): 403-425.
6.	黎国威, 张玲, 陈裕明, 等. 倾向性评分方法在观察性研究中的应用. 中国循证医学杂志, 2021, 21(4): 469-474.
7.	王永吉, 蔡宏伟, 夏结来, 等. 倾向指数第二讲倾向指数常用研究方法. 中华流行病学杂志, 2010, 31(5): 584-585.
8.	李智文, 刘建蒙, 任爱国. 基于个体的标准化法—倾向评分加权. 中华流行病学杂志, 2010, 31(2): 223-226.
9.	Robins JM, Rotnitzky A. Semiparametric efficiency in multivariate regression-models with missing data. J Am Stat Assoc, 1995, 90(429): 122-129.
10.	Robins JM, Rotnitzky A, Zhao LP. Analysis of semiparametric regression-models for repeated outcomes in the presence of missing data. J Am Stat Assoc, 1995, 90(429): 106-121.
11.	Li F, Thomas LE, Li F. Addressing extreme propensity scores via the overlap weights. Am J Epidemiol, 2019, 188(1): 250-257.
12.	Li F, Morgan KL, Zaslavsky AM. Balancing covariates via propensity score weighting. J Am Stat Assoc, 2018, 113(521): 390-400.
13.	秦宇辰, 郭威, 阮一鸣, 等. 重叠加权法在医学研究混杂因素控制中的应用. 中国卫生统计, 2020, 37(3): 363-366.
14.	Desai RJ, Franklin JM. Alternative approaches for confounding adjustment in observational studies using weighting based on the propensity score: a primer for practitioners. BMJ, 2019, 367: l5657.
15.	Mlcoch T, Hrnciarova T, Tuzil J, et al. Propensity score weighting using overlap weights: a new method applied to regorafenib clinical data and a cost-effectiveness analysis. Value Health, 2019, 22(12): 1370-1377.
16.	Imbens GW. The role of the propensity score in estimating dose-response functions. Biometrika, 2000, 87(3): 706-710.
17.	Li F. Propensity score weighting for causal inference with multiple treatments. Ann Appl Stat, 2019, 13(4): 2389-2415.
18.	Austin PC. The relative ability of different propensity score methods to balance measured covariates between treated and untreated subjects in observational studies. Med Decis Making, 2009, 29(6): 661-677.
19.	Austin PC, Grootendorst P, Anderson GM. A comparison of the ability of different propensity score models to balance measured variables between treated and untreated subjects: a Monte Carlo study. Stat Med, 2007, 26(4): 734-753.
20.	Zhang Z, Kim HJ, Lonjon G, et al. Balance diagnostics after propensity score matching. Ann Transl Med, 2019, 7(1): 16.
21.	王永吉, 蔡宏伟, 夏结来, 等. 倾向指数第三讲应用中的关键问题. 中华流行病学杂志, 2010, 31(7): 823-825.
22.	Friedman JH. Greedy function approximation: a gradient boosting machine. Ann Stat, 2001, 29(5): 1189-1232.
23.	Harder VS, Morral AR, Arkes J. Marijuana use and depression among adults: Testing for causal associations. Addiction, 2006, 101(10): 1463-1472.
24.	Harder VS, Stuart EA, Anthony JC. Propensity score techniques and the assessment of measured covariate balance to test causal associations in psychological research. Psychol Methods, 2010, 15(3): 234-249.
25.	Rubin DB. Estimating causal effects from large data sets using propensity scores. Ann Intern Med, 1997, 127(8 Pt 2): 757-763.

1. Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika, 1983, 70(1): 41-55.
2. 王永吉, 蔡宏伟, 夏结来, 等. 倾向指数第一讲倾向指数的基本概念和研究步骤. 中华流行病学杂志, 2010, 31(3): 347-348.
3. CSCO生物统计学专家委员会RWS方法学组. 倾向性评分方法及其规范化应用的统计学共识. 中国卫生统计, 2020, 37(6): 952-958.
4. 吴美京, 吴骋, 王睿, 等. 倾向性评分法中评分值的估计方法及比较. 中国卫生统计, 2013, 30(3): 440-444.
5. McCaffrey DF, Ridgeway G, Morral AR. Propensity score estimation with boosted regression for evaluating causal effects in observational studies. Psychol Methods, 2004, 9(4): 403-425.
6. 黎国威, 张玲, 陈裕明, 等. 倾向性评分方法在观察性研究中的应用. 中国循证医学杂志, 2021, 21(4): 469-474.
7. 王永吉, 蔡宏伟, 夏结来, 等. 倾向指数第二讲倾向指数常用研究方法. 中华流行病学杂志, 2010, 31(5): 584-585.
8. 李智文, 刘建蒙, 任爱国. 基于个体的标准化法—倾向评分加权. 中华流行病学杂志, 2010, 31(2): 223-226.
9. Robins JM, Rotnitzky A. Semiparametric efficiency in multivariate regression-models with missing data. J Am Stat Assoc, 1995, 90(429): 122-129.
10. Robins JM, Rotnitzky A, Zhao LP. Analysis of semiparametric regression-models for repeated outcomes in the presence of missing data. J Am Stat Assoc, 1995, 90(429): 106-121.
11. Li F, Thomas LE, Li F. Addressing extreme propensity scores via the overlap weights. Am J Epidemiol, 2019, 188(1): 250-257.
12. Li F, Morgan KL, Zaslavsky AM. Balancing covariates via propensity score weighting. J Am Stat Assoc, 2018, 113(521): 390-400.
13. 秦宇辰, 郭威, 阮一鸣, 等. 重叠加权法在医学研究混杂因素控制中的应用. 中国卫生统计, 2020, 37(3): 363-366.
14. Desai RJ, Franklin JM. Alternative approaches for confounding adjustment in observational studies using weighting based on the propensity score: a primer for practitioners. BMJ, 2019, 367: l5657.
15. Mlcoch T, Hrnciarova T, Tuzil J, et al. Propensity score weighting using overlap weights: a new method applied to regorafenib clinical data and a cost-effectiveness analysis. Value Health, 2019, 22(12): 1370-1377.
16. Imbens GW. The role of the propensity score in estimating dose-response functions. Biometrika, 2000, 87(3): 706-710.
17. Li F. Propensity score weighting for causal inference with multiple treatments. Ann Appl Stat, 2019, 13(4): 2389-2415.
18. Austin PC. The relative ability of different propensity score methods to balance measured covariates between treated and untreated subjects in observational studies. Med Decis Making, 2009, 29(6): 661-677.
19. Austin PC, Grootendorst P, Anderson GM. A comparison of the ability of different propensity score models to balance measured variables between treated and untreated subjects: a Monte Carlo study. Stat Med, 2007, 26(4): 734-753.
20. Zhang Z, Kim HJ, Lonjon G, et al. Balance diagnostics after propensity score matching. Ann Transl Med, 2019, 7(1): 16.
21. 王永吉, 蔡宏伟, 夏结来, 等. 倾向指数第三讲应用中的关键问题. 中华流行病学杂志, 2010, 31(7): 823-825.
22. Friedman JH. Greedy function approximation: a gradient boosting machine. Ann Stat, 2001, 29(5): 1189-1232.
23. Harder VS, Morral AR, Arkes J. Marijuana use and depression among adults: Testing for causal associations. Addiction, 2006, 101(10): 1463-1472.
24. Harder VS, Stuart EA, Anthony JC. Propensity score techniques and the assessment of measured covariate balance to test causal associations in psychological research. Psychol Methods, 2010, 15(3): 234-249.
25. Rubin DB. Estimating causal effects from large data sets using propensity scores. Ann Intern Med, 1997, 127(8 Pt 2): 757-763.

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