Mixed models for longitudinal left-censored repeated measures

Longitudinal studies could be complicated by left-censored repeated measures. For example, in Human Immunodeficiency Virus infection, there is a detection limit of the assay used to quantify the plasma viral load. Simple imputation of the limit of the detection or of half of this limit for left-censored measures biases estimations and their standard errors. In this paper, we review two likelihood-based methods proposed to handle left-censoring of the outcome in linear mixed model. We show how to fit these models using SAS Proc NLMIXED and we compare this tool with other programs. Indications and limitations of the programs are discussed and an example in the field of HIV infection is shown

A location-scale joint model for studying the link between the time-dependent subject-specific variability of blood pressure and competing events

Given the high incidence of cardio and cerebrovascular diseases (CVD), and its association with morbidity and mortality, its prevention is a major public health issue. A high level of blood pressure is a well-known risk factor for these events and an increasing number of studies suggest that blood pressure variability may also be an independent risk factor. However, these studies suffer from significant methodological weaknesses. In this work we propose a new location-scale joint model for the repeated measures of a marker and competing events. This joint model combines a mixed model including a subject-specific and time-dependent residual variance modeled through random effects, and cause-specific proportional intensity models for the competing events. The risk of events may depend simultaneously on the current value of the variance, as well as, the current value and the current slope of the marker trajectory. The model is estimated by maximizing the likelihood function using the Marquardt-Levenberg algorithm. The estimation procedure is implemented in a R-package and is validated through a simulation study. This model is applied to study the association between blood pressure variability and the risk of CVD and death from other causes. Using data from a large clinical trial on the secondary prevention of stroke, we find that the current individual variability of blood pressure is associated with the risk of CVD and death. Moreover, the comparison with a model without heterogeneous variance shows the importance of taking into account this variability in the goodness-of-fit and for dynamic predictions

Score Test for Conditional Independence Between Longitudinal Outcome and Time to Event Given the Classes in the Joint Latent Class Model

Latent class models have been recently developed for the joint analysis of a longitudinal quantitative outcome and a time to event. These models assume that the population is divided in  G  latent classes characterized by different risk functions for the event, and different profiles of evolution for the markers that are described by a mixed model for each class. However, the key assumption of conditional independence between the marker and the event given the latent classes is difficult to evaluate because the latent classes are not observed. Using a joint model with latent classes and shared random effects, we propose a score test for the null hypothesis of independence between the marker and the outcome given the latent classes versus the alternative hypothesis that the risk of event depends on one or several random effects from the mixed model in addition to the latent classes. A simulation study was performed to compare the behavior of the score test to other previously proposed tests, including situations where the alternative hypothesis or the baseline risk function are misspecified. In all the investigated situations, the score test was the most powerful. The methodology was applied to develop a prognostic model for recurrence of prostate cancer given the evolution of prostate-specific antigen in a cohort of patients treated by radiation therapy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79185/1/j.1541-0420.2009.01234.x.pd

Social activity, cognitive decline and dementia risk: a 20-year prospective cohort study.

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

Estimation of dynamical model parameters taking into account undetectable marker values

BACKGROUND: Mathematical models are widely used for studying the dynamic of infectious agents such as hepatitis C virus (HCV). Most often, model parameters are estimated using standard least-square procedures for each individual. Hierarchical models have been proposed in such applications. However, another issue is the left-censoring (undetectable values) of plasma viral load due to the lack of sensitivity of assays used for quantification. A method is proposed to take into account left-censored values for estimating parameters of non linear mixed models and its impact is demonstrated through a simulation study and an actual clinical trial of anti-HCV drugs. METHODS: The method consists in a full likelihood approach distinguishing the contribution of observed and left-censored measurements assuming a lognormal distribution of the outcome. Parameters of analytical solution of system of differential equations taking into account left-censoring are estimated using standard software. RESULTS: A simulation study with only 14% of measurements being left-censored showed that model parameters were largely biased (from -55% to +133% according to the parameter) with the exception of the estimate of initial outcome value when left-censored viral load values are replaced by the value of the threshold. When left-censoring was taken into account, the relative bias on fixed effects was equal or less than 2%. Then, parameters were estimated using the 100 measurements of HCV RNA available (with 12% of left-censored values) during the first 4 weeks following treatment initiation in the 17 patients included in the trial. Differences between estimates according to the method used were clinically significant, particularly on the death rate of infected cells. With the crude approach the estimate was 0.13 day(-1 )(95% confidence interval [CI]: 0.11; 0.17) compared to 0.19 day(-1 )(CI: 0.14; 0.26) when taking into account left-censoring. The relative differences between estimates of individual treatment efficacy according to the method used varied from 0.001% to 37%. CONCLUSION: We proposed a method that gives unbiased estimates if the assumed distribution is correct (e.g. lognormal) and that is easy to use with standard software

PLoS One

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. 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. 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. 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