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Long-term behavioral and health risk factors constitute a primary focus of research on the etiology of chronic diseases. Yet, identifying critical time-windows during which risk factors have the strongest impact on disease risk is challenging. To assess the trajectory of association of an exposure history with an outcome, the weighted cumulative exposure index (WCIE) has been proposed, with weights reflecting the relative importance of exposures at different times. However, WCIE is restricted to a complete observed error-free exposure whereas exposures are often measured with intermittent missingness and error. Moreover, it rarely explores exposure history that is very distant from the outcome as usually sought in life-course epidemiology. We extend the WCIE methodology to (i) exposures that are intermittently measured with error, and (ii) contexts where the exposure time-window precedes the outcome time-window using a landmark approach. First, the individual exposure history up to the landmark time is estimated using a mixed model that handles missing data and error in exposure measurement, and the predicted complete error-free exposure history is derived. Then the WCIE methodology is applied to assess the trajectory of association between the predicted exposure history and the health outcome collected after the landmark time. In our context, the health outcome is a longitudinal marker analyzed using a mixed model. A simulation study first demonstrates the correct inference obtained with this approach. Then, applied to the Nurses' Health Study (19,415 women) to investigate the association between BMI history (collected from midlife) and subsequent cognitive decline after age 70. In conclusion, this approach, easy to implement, provides a flexible tool for studying complex dynamic relationships and identifying critical time windows while accounting for exposure measurement errors., Comment: Pages 35, Main Figures 5, Web Figures 13, Work presented at the Alzheimers Association International eConference (2020), eMELODEM conference, MEthods for LOngitudinal studies in DEMentia (2020), and ISCB, International Society for Clinical Biostatistics (2019)

A general framework is that the estimators of a distribution are obtained by minimizing a function (the estimating function) and they are assessed through another function (the assessment function). The estimating and assessment functions generally estimate risks. A classical case is that both functions estimate an information risk (specifically cross entropy); in that case Akaike information criterion (AIC) is relevant. In more general cases, the assessment risk can be estimated by leave-one-out crossvalidation. Since leave-one-out crossvalidation is computationally very demanding, an approximation formula can be very useful. A universal approximate crossvalidation criterion (UACV) for the leave-one-out crossvalidation is given. This criterion can be adapted to different types of estimators, including penalized likelihood and maximum a posteriori estimators, and of assessment risk functions, including information risk functions and continuous rank probability score (CRPS). This formula reduces to Takeuchi information criterion (TIC) when cross entropy is the risk for both estimation and assessment. The asymptotic distribution of UACV and of a difference of UACV is given. UACV can be used for comparing estimators of the distributions of ordered categorical data derived from threshold models and models based on continuous approximations. A simulation study and an analysis of real psychometric data are presented., Comment: 23 pages, 2 figures