Projected partial likelihood and its application to longitudinal data

An estimating equation, which we call the projected partial score, is introduced for longitudinal data analysis. The estimating equation is obtained by projecting the partial likelihood score function onto the vector space spanned by a class of 'conditionally linear' estimating equations. We demonstrate that removing certain terms from the projection of the full likelihood score does not alter important inferential properties of the estimating equation, and doing so is advantageous in handling missing data and time-varying covariates. Within a prequential frame of reference it is shown that the estimating equation is optimal among the largest collection of estimating equations determined by the conditional moments. Furthermore, the method possesses similar properties to generalised estimating equations; in particular, the correct conditional variance specification is necessary for efficiency but not for asymptotic consistency and distribution theory.