Two Cox-based multistate modeling approaches are compared for analyzing a complex multicohort event history process. The first approach incorporates cohort information as a fixed covariate, thereby providing a direct estimation of the cohort-specific effects. The second approach includes the cohort as stratum variable, thus giving an extra flexibility in estimating the transition probabilities. Additionally, both approaches may include possible interaction terms between the cohort and a given prognostic predictor. Furthermore, the Markov property conditional on observed prognostic covariates is assessed using a global score test. Whenever departures from the Markovian assumption are revealed for a given transition, the time of entry into the current state is incorporated as a fixed covariate, yielding a semi-Markov process. The two proposed methods are applied to a three-wave dataset of COVID-19-hospitalized adults in the southern Barcelona metropolitan area (Spain), and the corresponding performance is discussed. While both semi-Markovian approaches are shown to be useful, the preferred one will depend on the focus of the inference. To summarize, the cohort-covariate approach enables an insightful discussion on the the behavior of the cohort effects, whereas the stratum-cohort approach provides flexibility to estimate transition-specific underlying risks according with the different cohorts

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