A simulation approach for power calculation in large cohort studies based on multistate models

Realistic power calculations for large cohort studies and nested case control studies are essential for successfully answering important and complex research questions in epidemiology and clinical medicine. For this, we provide a methodical framework for general realistic power calculations via simulations that we put into practice by means of an R‐based template. We consider staggered recruitment and individual hazard rates, competing risks, interaction effects, and the misclassification of covariates. The study cohort is assembled with respect to given age‐, gender‐, and community distributions. Nested case‐control analyses with a varying number of controls enable comparisons of power with a full cohort analysis. Time‐to‐event generation under competing risks, including delayed study‐entry times, is realized on the basis of a six‐state Markov model. Incidence rates, prevalence of risk factors and prefixed hazard ratios allow for the assignment of age‐dependent transition rates given in the form of Cox models. These provide the basis for a central simulation‐algorithm, which is used for the generation of sample paths of the underlying time‐inhomogeneous Markov processes. With the inclusion of frailty terms into the Cox models the Markov property is specifically biased. An “individual Markov process given frailty” creates some unobserved heterogeneity between individuals. Different left‐truncation‐ and right‐censoring patterns call for the use of Cox models for data analysis. p‐values are recorded over repeated simulation runs to allow for the desired power calculations. For illustration, we consider scenarios with a “testing” character as well as realistic scenarios. This enables the validation of a correct implementation of theoretical concepts and concrete sample size recommendations against an actual epidemiological background, here given with possible substudy designs within the German National Cohort.