AbstractBackgroundSurvival analysis methods are increasingly used to model the gestational age‐specific risk of perinatal phenomena such as stillbirth.ObjectivesTo compare two types of survival analysis models, and highlight differences by estimating the relationships between pre‐pregnancy BMI and gestational age‐specific rates of stillbirth.MethodsThe study was based on singleton live births and stillbirths in the United States in 2016–2017, with data obtained from the natality and fetal death files of the National Center for Health Statistics. We compared Cox regression versus piecewise exponential additive mixed models (PAMMs) for modelling the relationship between BMI and stillbirth across gestational age. In a second analysis, we illustrated the performance of both models for assessing the relationship between the trimester‐specific number of cigarettes smoked, a time‐dependent covariate, and stillbirth.ResultsThe study population included 7,567,316 births, of which 42,739 were stillbirths (5.6 per 1000 total births). Stillbirth rates increased with increasing pre‐pregnancy BMI and increasing gestational age. In analyses with BMI as a categorical variable, the Cox model and PAMM models yielded similar results. Analyses of BMI as a continuous variable also showed similar results when BMI associations were assumed to be linear, and the changes in gestational age‐specific rates were modelled parametrically. However, results differed slightly when PAMMs, modelled with data‐driven approaches, were used to estimate changes in BMI effects across gestational age; PAMMs provided a more nuanced modelling of time‐varying effects. PAMM models showed an approximately linear increase in the effect of smoking on stillbirth with increasing gestational age.ConclusionsFor survival analyses using the foetuses‐at‐risk approach, PAMMs provide a valuable alternative to the traditional Cox model, with increased modelling flexibility when proportional hazards assumptions are violated.