Structural Nested Models and Standard Software: A Mathematical Foundation through Partial Likelihood

Source abstract

Abstract. In observational studies treatment may be adapted to the patient's state during the course of time. These covariates may in turn also react on the treatment under study, and so on. This makes it hard to distinguish between treatment effect and selection bias. Structural nested models aim at estimating treatment effect in such complicated situations, even when treatment may change at any time. We show that structural nested models can often be calculated with standard software, by using standard models to predict treatment as a tool to estimate treatment effect. Robins ( Survival analysis, Volume 6 of Encyclopedia of Biostatistics , John Wiley and Sons, Chichester, 1998) conjectured this, but so far it was unproven. We use a partial likelihood approach to choose the estimators and tests as a subclass of the estimators and tests in Lok (math. ST/0410271 at http://arXiv.org , 2004). We show that this is the class of estimators and tests that can be calculated with standard software. The estimators are consistent and asymptotically normal, and have interesting asymptotic properties.