A conditional model for incomplete covariates in parametric regression models

Incomplete covariate data arise in many data sets. When the missing covariates are categorical, a useful technique for obtaining parameter estimates is the EM algorithm by the method of weights proposed in Ibrahim (1990). This method requires the estimation of many nuisance parameters for the distribution of the covariates. Unfortunately, in data sets when the percentage of missing data is high, and the missing covariate patterns are highly non-monotone, the estimates of the nuisance parameters can lead to highly unstable estimates of the parameters of interest. We propose a conditional model for the covariate distribution that has several modelling advantages for the E-step and provides a reduction in the number of nuisance parameters, thus providing more stable estimates in finite samples. We present a clinical trials example with six covariates, five of which have some missing values.