The analysis of asthma control using homogeneous and non-homogeneous Markov models

Multi-state Markov models have proven useful in many concrete situations and have had successful applications, notably in analysing disease history data. Continuous-time Markov models with three transient states are considered for the study of asthma control evolution in a cohort of 406 patients with persistent asthma. Firstly, the model is considered in the homogeneous case. Covariates are taken into account to highlight the influence of risk factors on asthma evolution. A piecewise constant intensities model is fitted using an artificial covariate in order to test the assumption of time-homogeneity. Comparison with the homogeneous model highlights the restriction of the homogeneity assumption in the case of asthma. As an alternative a non-homogeneous model is fitted using a semi-parametric estimation method. The extension of the non-parametric Aalen-Johansen methodology to a semi-parametric multiplicative hazard model makes it possible to adjust the estimated intensities for differences in values of covariates using regression model techniques. Indeed, Markov models are useful tools for the modelling of asthma control even though the time-homogeneity assumption seems too stringent. Both homogeneous and non-homogeneous models indicate the impact of obesity on asthma control evolution.