Regression Models for Repeated Medical Random Counts

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: xk is a vector of covariates measured at baseline and prior to each subsequent event (k≥1) and βk 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 βk and for λok(t) for k = 1,2 and the regression coefficients, βk, are compared under the null hypothesis that β1 = β2 = β3 for a fixed set of covariates. Other aspects of the analysis are discussed