Basic parametric analysis for a multi-state model in hospital epidemiology

Maja von Cube, Martin Schumacher, Martin Wolkewitz

The extended illness-death model is a useful tool to study the risks and consequences of hospital-acquired infections (HAIs). The statistical quantities of interest are the transition-specific hazard rates and the transition probabilities as well as attributable mortality (AM) and the population-attributable fraction (PAF). In the most general case calculation of these expressions is mathematically complex. When assuming time-constant hazards calculation of the quantities of interest is facilitated. In this situation the transition probabilities can be expressed in closed mathematical forms. The estimators for AM and PAF can be easily derived from these forms. In this paper, we show how to explicitly calculate all the transition probabilities of an extended-illness model with constant hazards. Using a parametric model to estimate the time-constant transition specific hazard rates of a data example, the transition probabilities, AM and PAF can be directly calculated. With a publicly available data example, we show how the approach provides first insights into principle time-dynamics and data structure. Assuming constant hazards facilitates the understanding of multi-state processes. Even in a non-constant hazards setting, the approach is a helpful first step for a comprehensive investigation of complex data.