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Missing data are a prevailing problem especially in longitudinal studies. A case of a variable is considered missing if the value of the case of the variable for the case is not observed, usually in random. There are many different imputation methods to use for missing data analysis. However, noticing that longitudinal studies measures variables over time, time is a key aspect that we can utilize in missing data analysis. Thus, we propose two Markov Bayesian imputation methods that incorporate time into the process. We propose imputation method based on first degree Markov - the model that impose causal relationship only between immediately adjacent time points - model and second degree Markov - the model that impose causal relationship between immediately adjacent time points and two time points before or after -- model. We also use Bayesian networks, a widely used probabilistic graphical method to express relationships (including that caused by time) among the variables, to implement those Markov imputation models (we call them Integrative Markov Bayesian Method (IMBM)). To compare the IMBM imputation performance, we compare them with widely used missing data analysis methods - simple averaging and Expected Maximization (EM) - using data collected from a longitudinal study of child and family functioning after pediatric head trauma. We selected group of three variables that were measured in different time points from the original dataset from the longitudinal study. We then remove all the missing cases of the three variables, resulting in a complete dataset with no missing data. We then randomly selected different portions (20%, 30%, and 40%) of the complete dataset to be randomly missing and report how each missing data analysis method performs in predicting the selected missing cases. We show that even with high (≥ 30%) missing rate for each variable, selecting proper subset of variables and using the relationships among them - that they were measured in different time points - integrative Markov Bayesian statistical methods better estimate the distribution of the missing data that are missing at random. Especially, IMBM with first degree Markov model performed surprising well, resulting in a method that could be easily scaled up to be used in imputation methods for a very large longitudinal studies.

Integrative biostatistical approach shows better performance in missing data analysis using longitudinal study of pediatric head trauma