A Statistical Simulation Study Of Bias Correction When The Different Missing Mechanism Coexist

Objective In the study of medical expenses investigation, the phenomenon of missingdata in the dependent variabale arise from both random non-response and sample selection biaswhich caused by censoring at zero that the people should have seeking medical treatment, butthey didn’t due to poverty and other reasons.This study proposes two-stage correction method toprovide methodological basis for accurately estimating medical costs and their impact factors ofmedical insurance object of relatively disadvantaged urban residents when the two types ofimportant missing mechanisms coexist.Methods Simulating the multiple data sets, each of which has the coexistence of missingat random and not missing at random at different degree respectively. Firstly, making use ofnon-missing data (excluding the individual observations with non-random missing data) toimpute the random non-response data which are missing at random (MAR) by multipleimputation, including Predictive Mean Matching (PMM) Method, Propensity Score (PS) Method,Markov chain Monte Carlo (MCMC) method and EMB algorithm (the first stage) ; secondly, onthis basis sample selection model can be used to fit the missing data which are not missing atrandom to calibrate selection bias(the second stage); finally, the mutiple fitting results of sampleselection model are combined. The standardized bias, the root-mean-square error and the averagelength of confidence interval are used as evaluation criterias to describe the performance of thevarious methods.Results The simulation results indicate that with the increase of missing rate at randomand missing rate not at random respectively, the values of all the criterias are increased withdifferent degrees. In any case, because the absolute value of the standardized bias of the PSmethod exceeds the prescribed boundary value, this method is not undesirable; the PMM，EMBand MCMC methods all perform well. When the level of not missing at random is mild, thechioce of imputation methods in the condition of different degree of missing at random is asfollows: when the degree of missing at random is mild, the MCMC method is the best; when thedegree of missing at random is moderate, the EMB method is the best; when the degree ofmissing at random is severe, the PMM method is the best; When the level of not missing atrandom is moderate, no matter what degree the missing at random is, the MCMC method is thebest; When the level of not missing at random is severe, no matter what degree the missing atrandom is, the PMM method is the best. Conclusion The PMM, EMB and MCMC are all great imputation methods to deal withmissing data which are missing at random. The imputation methods can be selectively applied tothe actual investigation of different situations of missing data according to this simulation results.The expected results can also provide the foundation of the statistical methodology for the datain which the two types of missing mechanisms coexist in the similar survey.