Marginal Structural Models for Partial Exposure Regimes

Intensive care unit (ICU) patients are ell known to be highly susceptible for nosocomial (i.e. hospital-acquired) infections due to their poor health and many invasive therapeutic treatments. The effects of acquiring such infections in ICU on mortality are however ill understood. Our goal is to quantify these effects using data from the National Surveillance Study of Nosocomial Infections in Intensive Care Units (Belgium). This is a challenging problem because of the presence of time-dependent confounders (such as exposure to mechanical ventilation)which lie on the causal path from infection to mortality. Standard statistical analyses may be severely misleading in such settings and have shown contradicting results. While inverse probability weighting for marginal structural models can be used to accommodate time-dependent confounders, inference for the effect of ?ICU acquired infections on mortality under such models is further complicated (a) by the fact that marginal structural models infer the effect of acquiring infection on a given, fixed day ?in ICU?, which is not well defined when ICU discharge comes prior to that day; (b) by informative censoring of the survival time due to hospital discharge; and (c) by the instability of the inverse weighting estimation procedure. We accommodate these problems by developing inference under a new class of marginal structural models which describe the hazard of death for patients if, possibly contrary to fact, they stayed in the ICU for at least a given number of days s and acquired infection or not on that day. Using these models we estimate that, if patients stayed in the ICU for at least s days, the effect of acquiring infection on day s would be to multiply the subsequent hazard of death by 2.74 (95 per cent conservative CI 1.48; 5.09).

MULTIPLE MODEL EVALUATION ABSENT THE GOLD STANDARD VIA MODEL COMBINATION

We describe a method for evaluating an ensemble of predictive models given a sample of observations comprising the model predictions and the outcome event measured with error. Our formulation allows us to simultaneously estimate measurement error parameters, true outcome — aka the gold standard — and a relative weighting of the predictive scores. We describe conditions necessary to estimate the gold standard and for these estimates to be calibrated and detail how our approach is related to, but distinct from, standard model combination techniques. We apply our approach to data from a study to evaluate a collection of BRCA1/BRCA2 gene mutation prediction scores. In this example, genotype is measured with error by one or more genetic assays. We estimate true genotype for each individual in the dataset, operating characteristics of the commonly used genotyping procedures and a relative weighting of the scores. Finally, we compare the scores against the gold standard genotype and find that Mendelian scores are, on average, the more refined and better calibrated of those considered and that the comparison is sensitive to measurement error in the gold standard.