Application of Markov process modelling to health status switching behaviour of infants

Abstract

Background. This study is an attempt to apply Markov process modelling to health status switching behaviour of infants. The data for the study consist of monthly records of diagnosed illnesses for 1152 children, each observed from the month of first contact with Kasangati Health Centre, Kampala, Uganda, until age 18 months. Methods. Only two states of health are considered in the study, a 'Health' state, denoted by W: (for Well), and an 'Illness' state denoted by S: (for Sick). The data are thus reduced to monthly records (W or S) of the states of health of the study sample. The simplest model of dependence of current health state on the past is one that links the current state to the immediately preceding month only; that is a Markov model. The starting point of this study was therefore to determine the proportions of children making the transitions W→W, W→S, S→W, S→S, from one month to the next, for each month from birth (month 0) to 18 months of age (month 18). These were used as estimates of the probabilities of making these transitions for each month from birth. This paper discusses the main features emerging from the study of these transition probabilities. Results. In the first 5 months after birth, the probabilities of making the transitions W→W, W→S, S→W, S→S from one month to the next, showed some dependence on the age of the child. From the sixth month on, however, the dependence on age seemed to wear off. The transition probabilities remained the same from then on, suggesting that the switching pattern between health states behaves, eventually, like a time-homogeneous Markov Chain. This time-homogeneous chain attained a steady state distribution at about 12 months from birth. Conclusions. The study has shown that the transitions between Health and Illness for infants, from month to month, can be modelled by a Markov Chain for which the (single-step) transition probabilities are generally time-dependent or age-dependent. After the first few months of life the dependence on age may wear off, as in this study, leading to a time-homogeneous Markov Chain, which eventually attains a steady state distribution in about 12 months. Interpretations of the transition probabilities as measures of disease prevalence are discussed.