| Background:Randomized controlled trial?RCT?is considered to be the design which is the highest level of evidence and the gold standard for causal effects.But RCT research can't solve all the problems in medical research.Because observational studies do not divide the subjects into groups randomly,and they can save more cost and time than RCT.So observational studies absorb more and more attention from researchers.However,the baseline in the observational study were significantly different between groups,and there were confounding bias,which can affect the accuracy of treatment effects estimation.Propensity score?PS?is a common method which can control observable confoundings.Propensity score matching?PSM?method is the most widely used propensity score method.The basic idea of PSM is to match the same or similar propensity scores of treatment group with the control group,which can balance the baseline covariates between two groups after matching and to control the confoundings which make bias on treatment effects estimation.In order to control the matching quality,only when the PS distance between the treatment group and the control group is less than a set value?caliper?,this match can be formed.This matching method is called propensity score caliper matching?PSCM?.At this time,some of the treated objects cannot find objects whose PS distance is less than the caliper value in the control group,and exclude from matching.So part of the objects will be lost.The loss of sample size is related to the size of caliper setting.The traditional PSMs use the point estimation of PS without considering the sampling error and it will lose part of the information of propensity score.Therefore,some researchers have proposed the matching method using confidence interval?CI?of propensity score to match,which is called Propensity Score Interval Matching?PSIM?.PSIM can significantly improve the matching rate,especially when the sample size is small.However,it may lead to poor balance of covariates between groups after matching.The global optimal matching based on the basic idea of assignment problem in integer programming aims at minimizing the sum of distances of propensity score of all paired objects or maximizing the sum of propensity score confidence intervals,which can improve the matching quality and improve the balance of covariates among groups.Therefore,in this study,the global optimal matching algorithm is used to optimize PSIM,construct the global optimal propensity score interval matching?GOPSIM?algorithm,increase the matching rate while further balancing the covariates between groups,and extend the algorithm to the case when processing factors are divided into three disordered categories to meet the needs of practical research.Objective:In the case of strong confounder bias or small sample size in observational studies,PSCM will result in loss of some sample.If caliper matching is not used,the balance of covariates between groups may be poor.In order to solve these problems,the PSIM is proposed,which can improve the matching rate,the accuracy of effect estimation and the statistical efficiency.The global optimal algorithm based on assignment problem,which can further optimize the matching quality and improve the baseline balance after matching,is applied to PSIM.The matching algorithm is extended from two classifications to three disordered classifications.Through data simulation research,the optimal caliper overlap of confidence interval of PSIM will be explored,and the accuracy and accuracy of estimating the effect of interval matching for evaluating the global optimal propensity score are evaluated,so as to construct the optimal matching algorithm.Then the optimal matching algorithm is applied to the case study of the fifth National Health Service Survey?Shanghai?.Methods:1.Construction of Matching AlgorithmsIn this study,we construct matching algorithms for two classifications and disorderly three classifications,from three levels of combination of optimization performance?local optimal,global optimal?,matching method?point estimation matching,confidence interval matching?and caliper setting?caliper value,caliper interval?.Each of them constructs2*2*2=8 matching algorithms,it is 16 in all2.Generation of simulated data sets?1?binomial treatment effectsFirstly,the independent variables are generated.Eighteen independent variables are generated according to the relationship matrix of variables.Nine of them?X1-X9?obey the Bernoulli distribution with the occurrence rate of 0.5,and nine(X1 0-X18)obey the normal distribution continuity independent variables with the mean of 0 and the variance of 1.The logit function and Bernoulli function are used to generate two classified processing variables according to the three intensity of the hybrid effect.By adjusting the intercept,proportion of the treated objects can be controlled to about 30%.Finally,according to the correlation between outcome variables and processing variables and covariates,logit function and Bernoulli function are used to generate binomial outcome variables,and the proportion of outcomes is controlled to about 20%by adjusting the constant term.Three sample sizes?200,500 and 1000?,three hybrid effects and six treatment effects were set up in the simulation study of the two classification factors,which were 3*3*6=54 cases.In each case,1000 data sets were generated and 54,000simulated data sets were generated.?2?Disordered three-class treatment effectsThe generation of independent variables is consistent with the treatment factors.Logit function and polynomial distribution function are used to generate three kinds of processing variables according to the three intensities of hybrid effect,and the proportion of three processing levels is controlled at about 2:3:5 by adjusting the constant term.Finally,according to the relationship among processing variables,covariates and outcome variables,logit function and Bernoulli function generate two kinds of outcome variables,and adjust the constant term to control the proportion of outcome variables to about 20%.Two sample sizes?500 and 1000?,three confounding effects and two treatment effects were set up in the simulation study of the disordered three-class treatment factors.The total number of cases was 2*3*2=12.In each case,1000 data sets are generated,totaling 12,000simulated data sets.3.Evaluation of Matching AlgorithmsThis study evaluates the performance of different matching algorithms based on the following seven evaluation indicators:absolute bias of processing effect estimation,relative bias of processing effect estimation,variance of processing effect estimation,square error of processing effect estimation,95%confidence interval coverage of processing effect estimation.?coverage of 95%CI?,matching rate and standardized difference among covariate groups.The general linear model?GLM?is used to estimate the marginal means of seven evaluation indexes of different matching methods,so as to judge the matching performance of different matching methods.4.Case studyThe data of the fifth National Health Service Survey in Shanghai are used as the data source of the case analysis.The case with two categories of treatment factors is the difference of self-rated health status between elderly people over 65 years old living alone and non-elderly people living alone in suburbs of Shanghai,and the case with disorderly three categories of treatment factors is the comparative analysis of health service utilization of elderly female residents over 65 years old who are insured with three different basic medical insurance in a district of Shanghai.Results:1.Results of Simulation Study?1?Interval matching of propensity score?1?Binominal treatmentThere are four kinds of local optimal matching in the two classifications.They are PSNNM2,PSCM2,PSMIOM2 and PSIM2.These four matching methods can greatly reduce the estimation bias of processing effects and make the covariates relatively balanced among groups.Before matching,the absolute bias and relative bias of processing effect estimation are very large.The absolute bias and relative bias of PSNNM2,PSCM2 and PSMIOM2with optimal caliper values are larger than those of other methods.The other matching methods can achieve very good treatment effect estimation accuracy.Except for PSMIOM2,other matching methods can make the covariates become balanced.The absolute value of PSIM2 absolute bias is less than the optimal caliper matching in most caliper intervals,and has a higher matching rate.With the decrease of caliper interval,the absolute bias increases.When the caliper interval is 0.60,the absolute bias is closest to 0.In addition,with the increase of caliper interval,the matching rate decreases gradually.On the contrary,the balance between group become better.The matching rate and the balance of covariate groups are contradictory,and the increase of matching rate will make the balance of covariate groups worse.?2?Disordered classification treatment factorThere are four kinds of local optimal matching for disordered triangulation,namely,disordered triangulation propensity score nearest neighbor matching?PSNNM3?,proneness score caliper matching?PSCM3?,propensity score maximum interval coincidence matching?PSMIOM3?and propensity score interval matching?PSIM3?.For PSIM3 with different caliper intervals,with the increase of caliper intervals,the average standardization difference of covariates decreases.Accordingly,the matching rate will also decrease.When the baseline covariates of the three treatment groups of actual data are quite different,the simulation results show that when the caliper interval is set to2.8,the balance of covariates among groups can be better controlled.Conversely,when the baseline covariates are more balanced,2.4 can be selected as the caliper interval to ensure a higher matching rate,so that more objects can form matching.?2?Global Optimal Tendency Score Matching?1?Binomial treatment factorsThere are four kinds of global optimal propensity matching in binomial treatment factors:the binomial global optimal propensity score nearest neighbor matching?GOPSNNM2?,the global optimal propensity score caliper matching?GOPSCM2?,the global optimal propensity score maximum interval overlap matching?GOPSMIOM2?and the global optimal propensity score interval matching?GOPSIM2?.The absolute bias and relative bias of GOPSMIOM2 treatment effect estimation are larger,but the variance of GOPSMIOM2 treatment effect estimation is similar to other matching methods.Because of the large bias,the mean square error of the matching method is large,the 95%confidence interval coverage of processing effect estimation is low,and the balance of covariates is poor.The absolute bias of treatment effect estimation increases with the increase of caliper value in GOPSIM2 with different caliper interval overlap.The difference of matching rate and average SD of covariate increases with the increase of caliper interval overlap.When the overlap caliper interval is 0.45,the matching rate is low,and the average SD is the smallest.When the overlap of caliper interval is 0.90,the matching rate is higher.At this time,the average SD of the covariate is 5.02%,which is far less than the threshold of 10%.Generally speaking,all matching methods can get a less bias of treatment effect estimation.The matching method with maximum absolute bias is GOPSMIOM2,and the smallest is GOPSIM2-60.The results of relative bias is similar to absolute bias.The variance of processing effect estimation of each matching method is small and close.The average SD of baseline covariates is proportional to the matching rate.Before caliper interval screening,the average SD of covariates is quite high.By using caliper interval matching,the average SD of covariates decreased significantly.With the increase of caliper interval overlap,the average SD decreases gradually.The matching rate also decreases.Generally speaking,the SD of GOPSIM2-90 is smallest and the matching rate is highest.?2?Disordered classification treatment effectIn GOPSCM3 and GOPSNNM3,the absolute bias and relative bias of treatment effect estimation obtained by different matching methods are relatively close.The maximum absolute bias matching method is GOPSCM3 with caliper value of 0.01.The minimum absolute bias matching method is GOPSCM3 with caliper value of 0.02.The variance of treatment effect estimation is inversely proportional to the bias,and the smaller the bias,the larger the variance.There is little difference in variance between different matching methods.The average SD of baseline covariates is proportional to the matching rate.The higher the matching rate is,the greater the average standardization difference is.The matching rate of GOPSNNM3 is 100.00%.As the caliper value decreases from 0.5 to0.01,the matching rate decreases from 99.04%to 56.47%,and the average SD decreases from 18.62%to 6.44%.Except GOPSCM3 with caliper value of 0.01,the average normalized difference of covariates of all matching methods is less than 10%,which can be considered that covariates are balanced.In GOPSMOIM3 and GOPSIM3,the maximum absolute bias matching method is GOPSMIOM3?0.096?,and the smallest is GOPSIM3-75?0.069?.Relative bias is similar to absolute bias,and GOPSMIOM is the largest?5.903%?and GOPSIM3-75 is the smallest?4.384%?.The variance of the treatment effect estimation of each matching method is small,which are about 0.075.Because the bias and variance of GOPSMIOM3 treatment effect are large,the MSE of its treatment effect estimation is also the largest?5.094?.The MSE of GOPSIM3 in seven calipers is close.The average SD of baseline covariates is proportional to the matching rate.Before caliper interval matching,the average SD of covariates varied significantly?16.14%?and exceeded the recommended threshold of 10%.After interval matching,the average SD of covariates decreased significantly.Generally speaking,the standardization difference of GOPSIM3 is small and the matching rate is high.2.Results of case studies?1?Study on self-rated health status of living alone or not elderly living alone residents over 65 years old in Shanghai suburbsIn the end,477 elderly residents living alone and 902 not living alone residents were included in the model of propensity score estimation.The matching rates of PSNNM2,PSMIOM2,GOPSNNM2 and GOPSMIOM2 are all 100%.The matching rates of GOPSCM2 are the lowest?38.99%?and PSIM2 is the highest?45.49%?.The average SD of covariate was 23.01%before matching,and there was no caliper value and caliper interval in the four methods.Therefore,the average SD of the four methods was larger than10%.The average SD of PSCM2 was 5.28%.Wilcoxon rank sum test was used to compare the self-rated health status of the elderly living alone and not living alone.Before matching,the self-rated health of the elderly living alone and not living alone had significant difference?P<0.0001?.However,after PSM,there was no significant difference in self-rated health status between living alone and not living alone elderly?P>0.05?.The matching rate of PSCM2 is increased from 41.51%to 45.49%of PSIM2 and38.99%of GOPSNNM2 to 44.86%of GOPSIM2.However,the SD of covariates did not change much,increasing by less than 2%.It shows that interval matching can improve the matching rate to a certain extent without affecting the balance of covariates,especially when the sample size is small or the distribution of covariates between the two groups is significantly different.?2?Impact of medical insurance on health service utilization of elderly female residents in a district of ShanghaiThe inclusion criteria of this case study are elderly female residents over 65 years of age in a district of Shanghai,excluding this cases if their basic medical insurance status is missing.After cleaning the data,532 UEBMI insured residents,343 URBMI insured residents and 235 NRCMS insured residents were included in this case,1110 in all.The matching rate of PSNNM3,PSMIOM3,GOPSNNM3 and GOPSMIOM3 is100%.However,the covariate balance of the four matching methods is poor,which is greater than 10%,but significantly lower than 27.88%before matching.The matching rate of PSIM3 is the highest among the other four matching methods,reaching 58.88%.The matching rate of GOPSCM3 is the lowest,only 42.26%.With the control of caliper or caliper interval,the covariate balance of the four matching methods has been greatly improved,and the average SD of the covariate is less than 10%.The covariate balance of GOPSCM3 is the best,and the average SD is only 6.42%.Before matching,due to a large number of confounding bias,the difference of two-week visiting rate between the three groups was not detected.However,after PSM,the P-values of PSNNM3,PSIM3,GOPSNNM3 and GOPSMIOM3 chi-square test are all less than 0.05.It can be concluded that the two-week visiting rate of residents of the three types of medical insurance has significant difference.Similar to the simulation study,the four matching methods of PSNNM3,PSMIOM3,GOPSNNM3 and GOPSMIOM3 have no caliper value or caliper interval,and the matching rate is 100%,but the covariate balance of the four methods is slightly worse.The other four methods set the caliper value or caliper interval,so the covariate equilibrium is improved.The matching of PSNNM3 has statistical significance,but PSCM3 has no statistical significance after setting caliper value.This may be due to the loss of sample size caused by setting calipers,which reduces the efficiency of inspection.However,after using interval matching,the matching rate of PSIM3 is higher than that of PSCM3,which improves the efficiency of part of the test,so the statistical difference is tested.Conclusions:PSIM2 with 0.60 caliper interval has the best performance in 16 caliper intervals explored.Therefore,through the simulation research of this study,it is recommended that PSIM2 with caliper interval of 0.60 can get better matching when using PSM,especially when the sample size is relatively small.With the decrease of caliper value or the increase of caliper interval overlap,the covariate of PSCM3 or PSIM3 will become more balanced,but the matching rate will decrease.In this study,PSIM3 with a caliper interval of 2.6 is recommended to deal with disordered three-class PSM by weighing the two and combining the indicators of treatment effect estimation.Through the case study,it is further verified that the matching algorithm has better performance.Through the matching analysis of eight binominal of propensity scores,there was no significant difference in self-evaluation status between elderly female residents over 65 years old living alone and non-living alone in Shanghai suburbs,and the results of sensitivity analysis also showed the same results.Eight disordered three-class propensity score matching was used to analyze whether there were differences in two-week visiting rate among elderly female residents over 65 years old in a district of Shanghai.After PSNNM3,PSIM3,GOPSNNM3 and GOPSMIOM3,the hypothesis test P value is less than 0.05,which shows that there is a significant difference in the two-week visiting rate among the residents insured by the three basic medical insurance schemes.Similar results were obtained from sensitivity analysis. |
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