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There is increasing emphasis in medical research on fetal and childhood antecedents of disease, and how these interact with other exposures throughout the life course to influence later-life conditions. As outlined by Ben-Shlomo et al., answering questions about the relative importance of aspects and timing of growth, behaviour and health status for longer-term outcomes requires appropriate analyses of longitudinal data. Analysis of such data inevitably poses statistical challenges due to the complex temporal relationships between multiple factors across life. Analyses must account for dependencies between repeated observations on the same person: methods to do this (e.g. random effects models) are now widely available in standard statistical software packages. However, when repeated measures are taken frequently, there is likely to be serial autocorrelation among the measurements (greater correlation among measurements closer together in time), which requires more complex models. Where there are repeated measures of exposures related to a later-life outcome, standard regression models may be affected by multicollinearity among the repeated exposures. Measurement error may vary over time (e.g. absolute measurement error in weight will be larger in adulthood than childhood), which will need to be taken into account in any analysis. There will also usually be dropout over time due to death, illness or refusal to participate, which will limit the sample size and may result in bias in complete case analyses. When the initial life course models were proposed, statistical methods for addressing questions about repeated exposures and outcomes were under-developed. Life course epidemiology stimulated research on the methodology to be able to better address such research questions. The focus of life course methodology, initially at least, was in the analysis of repeated measures of the same exposure—and in many cases, specifically for the analysis of growth and its association with later outcomes. Simpler approaches are appropriate for a small number of repeated measures of an exposure, each recorded at the same age for all individuals (e.g. weight measured at 2, 4 and 6 years of age). Early on in life course epidemiology, one method was to plot average z-scores over time for the two groups formed by a dichotomous outcome. These z-score plots can be misinterpreted as growth trajectories, whereas in fact they show a series of cross-sectional associations of exposure with outcome. Further developments led to the use of regression models for the outcome, including various parameterizations of the exposure, depending on whether conditioning on previous measures of the same exposure, or using observed measures or change scores. In turn, this led to awareness of the dangers of conditioning on variables which are on the causal pathway from exposure to outcome—such as including adult weight in models relating birthweight to adult disease. More recently, increasingly complex approaches such as multilevel models or latent variable models have been used to describe patterns of change and relate these patterns to various health outcomes. Essentially, all approaches aim to relate changes in an exposure such as body size to a later outcome, with some of the methods, such as multilevel models, parameterizing average and individual change, and others, in particular latent class models, describing subpopulations with different patterns of growth. These types of models have been extended to relate trajectories of several repeatedly measured variables to each other, for example to relate repeated measures of mean arterial pressure to simultaneous weight gain during pregnancy. A simple structured modelling approach using regression was proposed in order to distinguish a critical period model from an accumulation model when relating a repeated binary exposure to an outcome. It is being International Journal of Epidemiology, 2016, Vol. 45, No. 4 1003

Commentary: The use and misuse of life course models