Research And Application In Handling Methods For Incomplete Longitudinal Binary Data

Background:In the fields such as biomedicine and sociology,longitudinal study is a common method to explore and interpret development process of something.Because longitudinal study is to investigate study objects repeatedly during a period of time,the change of study objects can be observed over time.However,longitudinal study often show inevitable data incompleteness due to dropouts or lack of follow-up.The common methods to deal with missing data contain complete case analysis and last observation carried forward(LOCF).The advantage of these methods is easy to implement,however these methods both require the stronger missing completely at random(MCAR)mechanism to hold.In practice,the MCAR is often difficult to satisfy,so the results from these methods are biased.Multiple imputation(MI)is an common approach used to deal with missing data,which can get a valid estimation under an assumption of missing at random mechanism.Although there are a variety of multiple imputation methods for the longitudinal binary data,a limited number of researches have reported on relative performances of the methods.Aim:Due to the estimation from the common methods used to deal with incomplete longitudinal binary data under MCAR mechanism is biased and MI methods can get a valid estimation under MAR mechanism,the study conducted an extensive simulation study to examine comparative performance of the common methods for incomplete longitudinal binary data and seven MI methods,hoped to provide reference for choosing methods to deal with incomplete longitudinal binary data.Method:The study contains two parts,including simulation study and application.The study simulated two missing mechanism,which are MAR mechanism and MCAR mechanism,and simulated different situation according correlation coefficient and sample size under each missing mechanism.Under each situation,we used nine analysis methods to estimate the rate of single group and the rate difference between groups,and to evaluate the analysis methods from bias,standard error,mean square error and power of test.In application,the study methods were used to a randomized,double-blind,parallel group,multicenter study for the comparison of two oral treatments for toenail dermatophyte onychomycosis,we also used tipping point analysis to conduct sensitivity analysis.Result:The simulation study reveals,when missing mechanism is MAR,the estimation from complete case analysis and LOCF is biased,while MI methods could reduce bias.In MI methods,Propensity score-based multiple imputation(PS-MI),Monotone method with logistic regression(MONO-L),Full conditional specification with MONO-L regression(FCS-L),Markov chain Monte Carlo with adaptive rounding(MCMC-A)could control bias better than Markov chain Monte Carlo with coin flipping(MCMC-C),Monotone method with discriminant function(MONO-D),Full conditional specification with discriminant function(FCS-D).Meanwhile,the standard error of estimation from MI methods is smaller than complete case analysis.The standard error from MCMC-A is smallest in MI methods,especially when sample size is small.When consider mean square error,MI methods are also better than complete case analysis and LOCF.According to power of test,MI methods are also better than complete case analysis in most situations,especially MCMC-A.When the missing mechanism is MCAR,LOCF still produces large bias,and bias from complete case analysis is small,MI methods are not better than complete case analysis on controlling bias,except PS-MI,other MI methods can even increase bias,but MI methods can decrease the standard error.In terms of MSE,MI methods are still better than complete case analysis.According to power of test,MI methods are better than complete case analysis in most situations,especially MCMC-A Conclusion:Researcher should not conduct complete case analysis of LOCF without thinking while analyzing longitudinal incomplete binary data,which can introduce bias when the missing mechanism is MAR.According to the results of the study,we recommend using MI methods.When the missing mechanism is MAR,MI methods can decrease bias,and when the missing mechanism is MCAR,MI methods can decrease the standard error.