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We propose a novel methodology to quantify the effect of stochastic interventions for a non-terminal intermediate time-to-event on a terminal time-to-event outcome. Investigating these effects is particularly important in health disparities research when we seek to quantify inequities in the timely delivery of treatment and its impact on patients' survival time. Current approaches fail to account for time-to-event intermediates and semi-competing risks arising in this setting. Under the potential outcome framework, we define causal contrasts relevant in health disparities research and provide identifiability conditions when stochastic interventions on an intermediate non-terminal time-to-event are of interest. Causal contrasts are estimated in continuous time within a multistate modeling framework and analytic formulae for the estimators of the causal contrasts are developed. We show via simulations that ignoring censoring in intermediate and/or terminal time-to-event processes or ignoring semi-competing risks may give misleading results. This work demonstrates that a rigorous definition of the causal effects and joint estimation of the terminal outcome and intermediate non-terminal time-to-event distributions are crucial for valid investigation of interventions and mechanisms in continuous time. We employ this novel methodology to investigate the role of delaying treatment uptake in explaining racial disparities in cancer survival in a cohort study of colon cancer patients.

Data on the long term evolution of renal function in essential hypertensive patients are scarce, showing a low incidence of end stage renal diseases but without information on how the renal function evolves. Our aim is to describe the long term evolution of renal function and possible trajectories in hypertensive patients. We included patients from an ongoing cohort with essential hypertension, no proteinuria at baseline and no diabetes during follow-up and with at least two creatinine dosages 4 years apart. A long term (average 16 years) follow-up was available in 609 patients (baseline age 51.8 ± 11.1 years, 52 % male, mean office BP 156//95 mmHg). The trajectories of creatinine were modeled through a flexible latent class mixed model. The analysis identified three classes of significantly different trajectories. In the first (n = 560), there was no significant variation of creatinine over time. In the second (n = 40), there was a significant rise of creatinine (117 ± 20 vs 85 ± 17 µmol/l, p < 0.0001). The third class (n = 9) was very heterogeneous, mainly composed of outliers. Further analysis showed the nonlinearity of the evolution of creatinine in classes 2 and 3. So the model of progressive renal deterioration in essential hypertension does not fit with our results. A large majority (92%) of patients show no significant change in creatinine level with time. In the others 8%, the increase in creatinine is not progressive but conversely show one or more sudden bouts of elevation.

Joint models for recurrent and terminal events have not been yet developed for clustered data. The goals of our study are to develop a statistical framework for modelling clustered recurrent and terminal events and to perform dynamic predictions of the terminal event in family studies. We propose a joint nested frailty model for colonoscopy screening visits and colorectal cancer onset in Lynch Syndrome families. The screening and disease processes could each depend on individuals' screening history and other measured covariates and be correlated within families; our approach allows for familial correlations to affect both the visit process and the terminal event and the dependence between the two processes is specified through frailty distributions. We provide dynamic predictions of colorectal cancer risk for an individual conditional on his/her own screening history, his/her family history of screening and disease and other important clinical covariates. We apply our model to 18 Lynch Syndrome families from Newfoundland for individualized dynamic predictions of colorectal cancer risks. We demonstrate that the screening visits are non-ignorable for estimating the disease risks, and the joint nested frailty model improves dynamic prediction accuracies compared to existing joint frailty models after accounting for familial and individual screening and cancer histories.

Background: Studies using health administrative databases (HAD) may lead to biased results since information on potential confounders is often missing. Methods that integrate confounder data from cohort studies, such as multivariate imputation by chained equations (MICE) and two-stage calibration (TSC), aim to reduce confounding bias. We provide new insights into their behavior under different deviations from representativeness of the cohort., Methods: We conducted an extensive simulation study to assess the performance of these two methods under different deviations from representativeness of the cohort. We illustrate these approaches by studying the association between benzodiazepine use and fractures in the elderly using the general sample of French health insurance beneficiaries (EGB) as main database and two French cohorts (Paquid and 3C) as validation samples., Results: When the cohort was representative from the same population as the HAD, the two methods are unbiased. TSC was more efficient and faster but its variance could be slightly underestimated when confounders were non-Gaussian. If the cohort was a subsample of the HAD (internal validation) with the probability of the subject being included in the cohort depending on both exposure and outcome, MICE was unbiased while TSC was biased. The two methods appeared biased when the inclusion probability in the cohort depended on unobserved confounders., Conclusion: When choosing the most appropriate method, epidemiologists should consider the origin of the cohort (internal or external validation) as well as the (anticipated or observed) selection biases of the validation sample., Competing Interests: The authors have declared that no competing interests exist.

Background: Identifying modifiable lifestyle correlates of cognitive decline and risk of dementia is complex, particularly as few population-based longitudinal studies jointly model these interlinked processes. Recent methodological developments allow us to examine statistically defined sub-populations with separate cognitive trajectories and dementia risks., Methods: Engagement in social, physical, or intellectual pursuits, social network size, self-perception of feeling well understood, and degree of satisfaction with social relationships were assessed in 2854 participants from the Paquid cohort (mean baseline age 77 years) and related to incident dementia and cognitive change over 20-years of follow-up. Multivariate repeated cognitive information was exploited by defining the global cognitive functioning as the latent common factor underlying the tests. In addition, three latent homogeneous sub-populations of cognitive change and dementia were identified and contrasted according to social environment variables., Results: In the whole population, we found associations between increased engagement in social, physical, or intellectual pursuits and increased cognitive ability (but not decline) and decreased risk of incident dementia, and between feeling understood and slower cognitive decline. There was evidence for three sub-populations of cognitive aging: fast, medium, and no cognitive decline. The social-environment measures at baseline did not help explain the heterogeneity of cognitive decline and incident dementia diagnosis between these sub-populations., Conclusions: We observed a complex series of relationships between social-environment variables and cognitive decline and dementia. In the whole population, factors such as increased engagement in social, physical, or intellectual pursuits were related to a decreased risk of dementia. However, in a sub-population analysis, the social-environment variables were not linked to the heterogeneous patterns of cognitive decline and dementia risk that defined the sub-groups.

Cognitive lifestyle measures such as education, occupation, and social engagement are commonly associated with late-life cognitive ability although their associations with cognitive decline tend to be mixed. However, longitudinal analyses of cognition rarely account for death and dropout, measurement error of the cognitive phenotype, and differing trajectories for different population sub-groups. This paper applies a joint latent class mixed model (and a multi-state model in a sensitivity analysis) that accounts for these issues to a large (n = 3,653), population-based cohort, Paquid, to model the relationship between cognitive lifestyle and cognitive decline. Cognition was assessed over a 20-year period using the Mini-Mental State Examination. Three cognitive lifestyle variables were assessed: education, mid-life occupation, and late-life social engagement. The analysis identified four latent sub-populations with class-specific longitudinal cognitive decline and mortality risk. Irrespective of the cognitive trajectory, increased social engagement was associated with a decreased mortality risk. High education was associated with the most favourable cognitive trajectory, and after adjusting for cognitive decline, with an increased mortality risk. Mid-life occupational complexity was also associated with more favourable trajectories but not with mortality risk. To realistically examine the link between cognitive lifestyle and cognitive decline, complex statistical models are required. This paper applies and compares in a sensitivity analysis two such models, and shows education to be linked to a compression of cognitive morbidity irrespective of cognitive trajectory. Furthermore, a potentially modifiable variable, late-life social engagement is associated with a decreased mortality risk in all of the population sub-groups.

Missing data and especially dropouts frequently arise in longitudinal data. Maximum likelihood estimates are consistent when data are missing at random (MAR) but, as this assumption is not checkable, pattern mixture models (PMM) have been developed to deal with informative dropout. More recently, latent class models (LCM) have been proposed as a way to relax PMM assumptions. The aim of this paper is to compare PMM and LCM in order to tackle informative dropout in a longitudinal study of cognitive ageing measured by several psychometric tests. Using a multivariate longitudinal model with a latent process, a sensitivity analysis was performed to compare estimates under the MAR assumption, from a PMM and from two LCM. In the PMM, dropout patterns are included as covariates in the multivariate longitudinal model. In the simple LCM, they are predictors of the class membership probabilities while, in the joint LCM, the dropout time is jointly modeled using a proportional hazard model depending on latent classes. We show that parameter interpretation is different in the two kinds of models and thus can lead to different estimated values. PMM parameters are adjusted on the dropout patterns while LCM parameters are adjusted on the latent classes. This difference is highlighted in our data set because the latent classes exhibit much more heterogeneity than dropout patterns. We suggest several complementary analyses to investigate the characteristics of latent classes in order to understand the meaning of the parameters when using LCM to deal with informative dropout.