An application of Markov chain modeling and semi-parametric regression for recurrent events in health data

Abstract

Longitudinal studies are best suited to describe the evolution of particular health conditions over time. In this study, data on the occurrence and transition of cough among post-operative cardiac surgery patients was analyzed using semi-parametric regression models for recurrent events. Cough severity was recorded as no cough, mild cough and severe cough. Transition probability matrix was calculated for the various transitions and across different covariate categories. Also, mean first passage time (MFPT) was calculated using Markov principles and Monte-Carlo simulation. The Andersen-Gill (AG) and Prentice, Williams and Peterson (PWP) semi-parametric regression models were used to test the effect of covariates on the cough transition. Ninety percent of the patients developed cough on the first post-operative day. The probability of transitioning from no cough to severe cough was 8% but the probability of resolution was just 3%. The mean first passage time from no cough to severe cough was about 7.2 (95% CI 6.8–7.5) days and the resolution time was 13.7 (13.0–14.5) days. The MFPT varied widely across the covariate categories. The regression models did not reveal any major significant influences by the measured covariates and the models without covariates were not significantly different from the covariate models. Applying these statistical techniques can serve as effective tools to help medical decision makers to provide better, consistent, efficient and evidence-based healthcare services.

Keyword:

• Longitudinal data
• semi-parametric regression models
• Markov chain
• mean first passage time
• cardiac surgery