Joint Models Based On Propensity Score Matching For Non-randomized Data

Objective: We aim to control variation within groups and ensure balance between groups by building joint models based on propensity score matching for nonrandomized data. In this article,we hope to reduce possible selection bias and improve the reliability of statistical inference.Method: The two-step clustering was used to deal with the sub-group question in non-randomized data. For extreme outliers, the centralized distance or propensity score was calculated. Combining with different matching method and different cut-off points, Monte Carlo simulation was conducted to estimate average intervention effects. The results were evaluated using the deviation(Dev) and mean square error(MSE). At the same time, according to the characteristics of clinical data, the most suitable joint model was applied. In addition to the two-step clustering, all the processes are implemented in STATA.Result:(1) The two-step clustering was used to deal with the sub-group characteristic in non-randomized data. Monte Carlo simulation was conducted when n was 300, 600, 1200, 2400, 4800, and 9600, respectively. The results show that the deviation of Mahalanobis distance matching(Dev=-0.0018) is slightly smaller than the caliper nearest neighbor matching(Dev=0.0019) when n was 4800, but the MSE of former was 0.0703, higher than the latter(MSE=0.0658).(2) For extreme outliers, the following centralized distance 1 T 2 2 21 11 2 21 1 2 22 2(...)(...)...i i i im m i im m im mmd x l x l x l x l x l x l-= XV X? ? ? ? ? ? ? ? ? or the propensity score ? ?0 1 1 2 2 3 3 4logit P(W ?1) ?? ??x ??x ??x ??Z was calculated. 99%, 95% and 90% confidence interval of the centralized distance or propensity score was respectively set as cut-off points, in the tendency of value based on model matching, combined with different matching method, Monte Carlo simulation. Combining with different matching method and different cut-off points, Monte Carlo simulation was conducted to estimate average intervention effects. The results show that when cut-off points were 95% CI, the number of removed samples was close to the default. When the sample size is large enough(n=4800), there were no obvious differences in the estimated deviation between the 95% and 90% CI, and propensity score matching is more robust than the mahalanobis distance matching.(3) According to the results of Monte Carlo simulation, when omitting the important covariate Z influencing intervention, obvious deviation will occurred.(4) When dealing with the clinical data, the result of traditional Cox regression show that male has a lower hazard ratio than female. Differences between gender was statistical significant(P=0.0169); After caliper nearest neighbor matching, the differences still had statistical significance(P=0.0448), relatively close to 0.05. After jointing caliper nearest neighbor matching, the differences had no statistical significance(P=0.1725).Conclusion: Propensity score matching joint with two-step clustering, centralized distance and propensity score threshold can effectively control variations within groups in non-randomized data and ensure balances between groups. The three joint methods based on propensity score matching all have good applicability, and provide a new statistical method for non-randomized data with heterogeneity.