Regression Models for Repeated Medical Random Counts

Abstract

An extension of the proportional hazards model of Cox (1972) to deal with certain types of Sequential State Processes which arise in the analysis of repeated medical random counts (MacKenzie, 1986) is discussed. The incidence of repeated events is modelled intra-individual on the real-time axis by assuming that the instantaneous incidence rate for the kth event takes the form:

$${\lambda _k}({t_k};{x_k}) = {\lambda _{ok}}(t).\exp ({x_k}.{\beta _k})$$

where: x_k is a vector of covariates measured at baseline and prior to each subsequent event (k≥1) and β_k is a vector of parameters. The model is applied to the analysis of a longitudinal survey of 641 patients admitted to hospital for a first valvotomy. Maximum Partial Likelihood estimators are obtained for β_k and for λ_ok(t) for k = 1,2 and the regression coefficients, β_k, are compared under the null hypothesis that β₁ = β₂ = β₃ for a fixed set of covariates. Other aspects of the analysis are discussed