7. Model-based estimating equations

The regression effect process, described in Chapter 9, shapes our main approach to inference. At its heart are differences between observations and their model-based expectations. The flavor is very much that of linear estimating equations (Appendix D.1). Before we study this process, we consider here an approach to inference that makes a more direct appeal to estimating equations. The two chapters are closely related and complement one another. This chapter leans less heavily on stochastic processes and links in a natural and direct way to the large body of theory available for estimating equations. Focusing attention on the expectation operator, leaning upon different population models and different working assumptions, makes several important results transparent. For example, it is readily seen that the so-called partial likelihood estimator is not consistent for average effect, \(E\{\beta (T) \},\) under independent censoring and non-constant \(\beta (t).\) One example we show, under heavy censoring, indicates the commonly used partial likelihood estimate to converge to a value greater than 4 times its true value. Linear estimating equations provide a way to investigate statistical behavior of estimates for small samples. Several examples are considered.