| Background:With the continuous development of information technology, observational studiesare constantly increasing in quantity and improving on accuracy. Observational studies oflarge samples is playing an increasingly important role in medical research. However, inthe observational studies, the study groups were not randomly assigned but naturallyexsiting, therefore, subjects with certain characteristics are more like to be assigned into atreatment group or a control group, leading to the presence of confounding bias betweendifferent groups. Propensity socre is a common research method to solve the confoundingbias existing in the observational studies. This method is easy to understand and theresearch steps have a high degree of standardization, so it has been widely used innon-randomized observational study of large sample in recent years. Application ofpropensity score methods includes matching, stratification and regression adjustment,where matching is the most advantageous method and has the most extensive range ofapplication. Propensity score matching (PSM) methods include nearest neighbourmatching, caliper matching, and mahalanobis metric matching, etc. There are some issuesyet to be resolved in the application of PSM currently. For example, there is stillcontroversy on what type of covariates should be placed in the propensity score model;there is still no conclusion on which PSM method is the most advantagous one; in addition,PSM is mainly used for observational studies in which the grouping factor is dichotomouscurrently, and it is seldomly used in the observational studies which have multiple groups.Aim:To establish PSM methods for three ordered treatment groups. Through simulationstudies, we plan to select covariates for propensity score model, compare various matchingmethods under the circumstance of three ordered treatment groups, detemine the mostadvantageous way of matching in data with different characteristics through adjusting theparameters, compare different application methods for propensity score under thecircumstance of three ordered treatment groups, and apply the optimal PSM methodestablished in the simulation study to a case study.Methods:In this study, the Monte Carlo method was used to simulate data sets. We simulated three ordered treatment groups, and the samples were adjusted in proportion of1:1:1,2:3:5,1:2:3, and1:4:5, respectively, among different groups. Different types of covariates weresimulated based on their association with group factor and outcome, including covariatesassociated with both group factor and outcome, covariates associated with group factor,covariables associated with outcome, and covariates associated with neither group factornor outcome. Determine the type of covariables that should be included in the propensityscore model under the circumstance of three ordered treatment groups by includingdifferent types of covariables in the model. According to the basic idea of PSM fordichotomous groups, we established PSM method for three ordered treatment groups,including nearest neighbour matching, caliper matching, and mahalanobis metric matching,and these methods were implemented through the SAS macro program. Different matchingparameters were set, such as proportion of matching and calipers. The most advantageousway of matching for data sets with different characteristics were determined by comparingdifferent matching methods. In addition, the simulated data were also used to comparedifferent applications for propensity score, including matching, stratification, regressionadjustment, and matching after regression adjustment.Ordered logistic regression was used to calculate the propensity score. The balance ofthe covariates should be assessed before and after PSM. In this study, the balance of thecovariables was assessed using standardized differences(SD). Obtained by preliminaryexperiments, when there are three ordered treatment groups, the absolute value of themaximum SD between different groups greater than0.1represents meaningful imbalancein a given covariate among the three treatment groups. After completion of the PSM, thebias and precision of the model should be evaluated. In this study, relative bias(RB) wasused to evaluate the bias of the model, and the smaller of the absolute value of RBindicating the smaller the bias of the model; mean squared error(MSE) was used toevaluate the precision of the model, and the smaller MSE indicating the higher precision ofthe model.Finally, the PSM method established in the simulation study was applied to theanalysis of a case study. Data for the case study came from the “Gastrointestinal disesesepidemiological survey in mainland, China” carried out by Second Military MedicalUniversity. General information of the subjects, questionnaire for physical examinationand SF-36health survey questionnaire were used to assess the relationship betweenabdominal obesity and health-related quality of life(HRQOL). Demographic information includes gender, age, height, weight, educational level, occupation, and the incidence ofchronic diseases. Abdominal characteristic was defined as “normal”,“mild abdominalobesity”, and “severe abdominal obesity”. HRQOL was assessed by using the Mandarinversion of the Short Form36Health Survey questionnaire (SF-36). The propensity scoremodel was established using abdominal characteristic as a grouping factor, the score ofvarious dimensions of HRQOL as outcome, and the selected demograpic informationvariables as covariates. The PSM method established in the simulation study was used tocontrol for confouding factors influencing the outcome, and the impact of abdominalobesity on HRQOL was assessed.Results:(1) Covariables selection: Under the circumstance of three ordered treatment groups,the propensity score model including covariates associated with the outcome can get arelatively high proportion of matches, with relatively minimal bias and highest precision inthe estimated treatment effect. Then we gradually removed one covariate from the model.If the removed covariate was associated with both group factor and outcome, there will bea great increase in bias and decrease in precision in the estimated treatment effect,indicating that all the covariates associated with both group factor and outcome should beincluded, and then the inclusion of the covariables associated with outcome but not groupfactor can further reduce the bias in the estimated treatment effect and increase theprecision in the estimated treatment effect. Therefore, under the circumstance of threeordered treatment groups, the propensity score model should include the covariatesassociated with outcome, regardless of whether they are associated with the group factor.(2) Establishment and comparison of matching methods: In this study, we establishedthe PSM method for three ordered threatment groups, including nearest neighbourmatching, caliper matching, and mahalanobis metric matching, and compared the differentmatching methods. In different proprotions of sample size among the three groups, theeffect of caliper matching achieved the best. When the proportion of sample size amongthe three group was1:1:1, the best matching method was caliper matching (caliper value0.005) matched with1:1:1; when the proportion of sample size among the three group was2:3:5, the best matching method was caliper matching (caliper value0.01) matched with1:1:1; when the proportion of sample size among the three group was1:2:3, the bestmatching method was caliper matching (caliper value0.01) matched with1:1:1; when theproportion of sample size among the three group was1:4:5, the best matching method was caliper matching (caliper value0.01) matched with1:2:2.(3) Comparison of different applications for propensity score: All the propensity scoremethods can greatly reduce the bias and increase the precision in the estimated treatmenteffect. However, matching and regression adjustment after matching were better than othermethods. When the proportion of sample size among the three groups was1:1:1, regressionadjustment was superior to stratification; when the proportion of sample size among thethree groups gradually widening, stratification is superior to regression adjustment.(4) Case study: After PSM, all the covariates associated with the outcome werebalanced among different abdominal characteristic groups, so we can evaluate the impactof abdominal obesity on HRQOL directly. The results showed that on the dimension ofphysical functioning, the mean score was significantly lower in subjects with severeabdominal obesity than that in those with normal WC, but the mean score was significantlyhigher in subjects with mild abdominal obesity than that those with normal WC. On thedimension of social function, only subjects with severe abdominal obesity had lower scorethan those with normal WC.Conclusions:Under circumstance of three ordered treatment groups, the propensity score modelshould include the covariables associated with outcome. When conducting PSM, thecaliper matching had the best effect, and the caliper value and matching proportion shouldbe adjusted according to the proprotion of sample size among different groups. Among thedifferent applications of propensity score method, matching and regression adjustmentafter matching work best. Compared with the traditional multivariate statistical methods,the PSM method for three ordered treatment groups established in this study couldquantitatively evaluate the differences of continuous outcome variables among differenttreatment groups by controlling for the confounding factors. |
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