PARAMETRIC REGRESSION FOR LONGITUDINAL DATA WITH COUNTING PROCESS MEASUREMENT TIMES

The regression model Y-j = m(theta(0), tau(j)) + epsilon(j), where the chi(j) can be thought of as times, is studied in a marked point proce ss framework. This paper demonstrates the consistency and asymptotic n ormality of an estimator for the unknown parameter theta(0). The model Y-j = m(theta(0), V-tau j) + epsilon(j) is also discussed. Here, the V-tau j are covariates that can depend on the events prior to time tau (j), i.e. on the (Y-k, tau(k)) for tau(k) < tau(j). The model allows q uite general censoring schemes for the measurement times, and a quite general dependency structure amongst the observations. The model appea rs useful for longitudinal data applications and is applied to repeate d measurements of oestriol for 52 pregnant women, for a case where cen soring is present.