A curvilinear bivariate random changepoint model to assess temporal order of markers

In biomedical research, various longitudinal markers measuring different quantities are often collected over time. For example, repeated measures of psychometric scores are very informative about the degradation process toward dementia. These trajectories are generally nonlinear with an acceleration of the decline a few years before the diagnosis and a large heterogeneity between psychometric tests depending on the underlying cognitive function to be evaluated and the metrological properties of the test. Comparing the times of acceleration of the decline before diagnosis between cognitive tests is useful to better understand the natural history of the disease. Our objective is to propose a bivariate random changepoint model that allows for the comparison of the mean time of change between two markers. A frequentist approach is proposed that gives validated statistical tests to assess the temporal order of the changepoints. Using a spline transformation function, the model is designed to handle non-Gaussian data, that are common for cognitive scores which frequently exhibit a strong ceiling effect. The procedure is assessed through a simulation study and applied to a French cohort of elderly to identify the order of the decline of several cognitive scores. The whole methodology has been implemented in a R package freely available.

A joint model for multiple dynamic processes and clinical endpoints: Application to Alzheimer's disease

As other neurodegenerative diseases, Alzheimer's disease, the most frequent dementia in the elderly, is characterized by multiple progressive impairments in the brain structure and in clinical functions such as cognitive functioning and functional disability. Until recently, these components were mostly studied independently because no joint model for multivariate longitudinal data and time to event was available in the statistical community. Yet, these components are fundamentally interrelated in the degradation process toward dementia and should be analyzed together. We thus propose a joint model to simultaneously describe the dynamics of multiple correlated components. Each component, defined as a latent process, is measured by one or several continuous markers (not necessarily Gaussian). Rather than considering the associated time to diagnosis as in standard joint models, we assume diagnosis corresponds to the passing above a covariate-specific threshold (to be estimated) of a pathological process that is modeled as a combination of the component-specific latent processes. This definition captures the clinical complexity of diagnoses such as dementia diagnosis but also benefits from simplifications for the computation of maximum likelihood estimates. We show that the model and estimation procedure can also handle competing clinical endpoints. The estimation procedure, implemented in an R package, is validated by simulations and the method is illustrated on a large French population-based cohort of cerebral aging in which we focused on the dynamics of three clinical manifestations and the associated risk of dementia and death before dementia.

Longitudinal and time-to-drop-out joint models can lead to seriously biased estimates when the drop-out mechanism is at random

Missing data are common in longitudinal studies. Likelihood-based methods ignoring the missingness mechanism are unbiased provided missingness is at random (MAR); under not-at-random missingness (MNAR), joint modeling is commonly used, often as part of sensitivity analyses. In our motivating example of modeling CD4 count trajectories during untreated HIV infection, CD4 counts are mainly censored due to treatment initiation, with the nature of this mechanism remaining debatable. Here, we evaluate the bias in the disease progression marker's change over time (slope) of a specific class of joint models, termed shared-random-effects-models (SREMs), under MAR drop-out and propose an alternative SREM model. Our proposed model relates drop-out to both the observed marker's data and the corresponding random effects, in contrast to most SREMs, which assume that the marker and the drop-out processes are independent given the random effects. We analytically calculate the asymptotic bias in two SREMs under specific MAR drop-out mechanisms, showing that the bias in marker's slope increases as the drop-out probability increases. The performance of the proposed model, and other commonly used SREMs, is evaluated under specific MAR and MNAR scenarios through simulation studies. Under MAR, the proposed model yields nearly unbiased slope estimates, whereas the other SREMs yield seriously biased estimates. Under MNAR, the proposed model estimates are approximately unbiased, whereas those from the other SREMs are moderately to heavily biased, depending on the parameterization used. The examined models are also fitted to real data and results are compared/discussed in the light of our analytical and simulation-based findings.

Estimation of delay to diagnosis and incidence in HIV using indirect evidence of infection dates

BACKGROUND

Minimisation of the delay to diagnosis is critical to achieving optimal outcomes for HIV patients and to limiting the potential for further onward infections. However, investigation of diagnosis delay is hampered by the fact that in most newly diagnosed patients the exact timing of infection cannot be determined and so inferences must be drawn from biomarker data.

METHODS

We develop a Bayesian statistical model to evaluate delay-to-diagnosis distributions in HIV patients without known infection date, based on viral sequence genetic diversity and longitudinal viral load and CD4 count data. The delay to diagnosis is treated as a random variable for each patient and their biomarker data are modelled relative to the true time elapsed since infection, with this dependence used to obtain a posterior distribution for the delay to diagnosis. Data from a national seroconverter cohort with infection date known to within ± 6 months, linked to a database of viral sequences, are used to calibrate the model parameters. An exponential survival model is implemented that allows general inferences regarding diagnosis delay and pooling of information across groups of patients. If diagnoses are only observed within a given window period, then it is necessary to also model incidence as a function of time; we suggest a pragmatic approach to this problem when dealing with data from an established epidemic. The model developed is used to investigate delay-to-diagnosis distributions in men who have sex with men diagnosed with HIV in London in the period 2009-2013 with unknown date of infection.

RESULTS

Cross-validation and simulation analyses indicate that the models developed provide more accurate information regarding the timing of infection than does CD4 count-based estimation. Delay-to-diagnosis distributions were estimated in the London cohort, and substantial differences were observed according to ethnicity.

CONCLUSION

The combination of all available biomarker data with pooled estimation of the distribution of diagnosis-delays allows for more precise prediction of the true timing of infection in individual patients, and the models developed also provide useful population-level information.

Predictors of CD4 cell recovery following initiation of antiretroviral therapy among HIV-1 positive patients with well-estimated dates of seroconversion

OBJECTIVES

To investigate factors that predict speed of recovery and long-term CD4 cell count in HIV-1 seroconverters initiating combination antiretroviral therapy (cART), and to quantify the influence of very early treatment initiation. We make use of all pre-treatment CD4 counts, because analyses using only a single observation at initiation may be subject to biases.

METHODS

We used data from the CASCADE (Concerted Action on SeroConversion to AIDS and Death in Europe) multinational cohort collaboration of HIV-1 seroconverters. We analysed pre- and post-treatment data of patients with seroconversion dates estimated January 2003-March 2014 (n = 7600 for primary analysis) using a statistical model in which the characteristics of recovery in CD4 counts are determined by multiple predictive factors. Secondary analyses were performed incorporating uncertainty in the exact timing of seroconversion to allow more precise estimation of the benefit of very early treatment initiation.

RESULTS

'True' CD4 count at cART initiation was the strongest predictor of CD4 count beyond 3 years on cART. Allowing for lack of complete certainty in the date of seroconversion, CD4 recovery was more rapid for patients in whom treatment was initiated within 4 months. For a given CD4 count, higher viral load (VL) at initiation was strongly associated with higher post-treatment CD4 recovery. For other patient and drug characteristics, associations with recovery were statistically significant but small in magnitude.

CONCLUSIONS

CD4 count at cART initiation is the most important factor in predicting post-treatment recovery, but VL provides substantial additional information. If cART is initiated in the first 4 months following seroconversion, recovery of CD4 counts appears to be more rapid.

Determining the likely place of HIV acquisition for migrants in Europe combining subject-specific information and biomarkers data

In most HIV-positive individuals, infection time is only known to lie between the time an individual started being at risk for HIV and diagnosis time. However, a more accurate estimate of infection time is very important in certain cases. For example, one of the objectives of the Advancing Migrant Access to Health Services in Europe (aMASE) study was to determine if HIV-positive migrants, diagnosed in Europe, were infected pre- or post-migration. We propose a method to derive subject-specific estimates of unknown infection times using information from HIV biomarkers' measurements, demographic, clinical, and behavioral data. We assume that CD4 cell count (CD4) and HIV-RNA viral load trends after HIV infection follow a bivariate linear mixed model. Using post-diagnosis CD4 and viral load measurements and applying the Bayes' rule, we derived the posterior distribution of the HIV infection time, whereas the prior distribution was informed by AIDS status at diagnosis and behavioral data. Parameters of the CD4-viral load and time-to-AIDS models were estimated using data from a large study of individuals with known HIV infection times (CASCADE). Simulations showed substantial predictive ability (e.g. 84% of the infections were correctly classified as pre- or post-migration). Application to the aMASE study (n = 2009) showed that 47% of African migrants and 67% to 72% of migrants from other regions were most likely infected post-migration. Applying a Bayesian method based on bivariate modeling of CD4 and viral load, and subject-specific information, we found that the majority of HIV-positive migrants in aMASE were most likely infected after their migration to Europe.

Combined models for pre- and post-treatment longitudinal biomarker data: an application to CD4 counts in HIV-patients

BACKGROUND

There has been some debate in the literature as to whether baseline values of a measurement of interest at treatment initiation should be treated as an outcome variable as part of a model for longitudinal change or instead used as a predictive variable with respect to the response to treatment. We develop a new approach that involves a combined statistical model for all pre- and post-treatment observations of the biomarker of interest, in which the characteristics of response to treatment are treated as a function of the 'true' value of the biomarker at treatment initiation.

METHODS

The modelling strategy developed is applied to a dataset of CD4 counts from patients in the UK Register of HIV Seroconverters (UKR) cohort who initiated highly active antiretroviral therapy (HAART). The post-HAART recovery in CD4 counts for each individual is modelled as following an asymptotic curve in which the speed of response to treatment and long-term maximum are functions of the 'true' underlying CD4 count at initiation of HAART and the time elapsed since seroconversion. Following previous research in this field, the models developed incorporate non-stationary stochastic process components, and the possibility of between-patient differences in variability over time was also considered.

RESULTS

A variety of novel models were successfully fitted to the UKR dataset. These provide reinforcing evidence for findings that have previously been reported in the literature, in particular that there is a strong positive relationship between CD4 count at initiation of HAART and the long-term maximum in each patient, but also reveal potentially important features of the data that would not have been easily identified by other methods of analysis.

CONCLUSION

Our proposed methodology provides a unified framework for the analysis of pre- and post-treatment longitudinal biomarker data that will be useful for epidemiological investigations and simulations in this context. The approach developed allows use of all relevant data from observational cohorts in which many patients are missing pre-treatment measurements and in which the timing and number of observations vary widely between patients.

Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues

Background

Available methods for the joint modelling of longitudinal and time-to-event outcomes have typically only allowed for a single longitudinal outcome and a solitary event time. In practice, clinical studies are likely to record multiple longitudinal outcomes. Incorporating all sources of data will improve the predictive capability of any model and lead to more informative inferences for the purpose of medical decision-making.

Methods

We reviewed current methodologies of joint modelling for time-to-event data and multivariate longitudinal data including the distributional and modelling assumptions, the association structures, estimation approaches, software tools for implementation and clinical applications of the methodologies.

Results

We found that a large number of different models have recently been proposed. Most considered jointly modelling linear mixed models with proportional hazard models, with correlation between multiple longitudinal outcomes accounted for through multivariate normally distributed random effects. So-called current value and random effects parameterisations are commonly used to link the models. Despite developments, software is still lacking, which has translated into limited uptake by medical researchers.

Conclusion

Although, in an era of personalized medicine, the value of multivariate joint modelling has been established, researchers are currently limited in their ability to fit these models routinely. We make a series of recommendations for future research needs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-016-0212-5) contains supplementary material, which is available to authorized users.

Temporal trends in prognostic markers of HIV-1 virulence and transmissibility: an observational cohort study

BACKGROUND

Measures of CD4 T-cell count and HIV-1 plasma viral load before antiretroviral therapy are proxies for virulence. Whether these proxies are changing over time has implications for prevention and treatment. The aim of this study was to investigate those trends.

METHODS

Data were derived from the Concerted Action on SeroConversion to AIDS and Death in Europe (CASCADE) collaboration of mainly European seroconverter cohorts. Longitudinal CD4 cell counts and plasma viral load measurements before the initiation of antiretroviral therapy or AIDS onset were analysed by use of linear or fractional polynomials mixed models adjusting for all available potential confounders. Calendar time effects were modelled through natural cubic splines.

FINDINGS

15 875 individuals seroconverting from 1979 to 2008 fulfilled the inclusion criteria; 3215 (20·3%) were women; median follow-up was 31 months (IQR 14-62); dropout before starting antiretroviral therapy or AIDS onset was 8·1%. Estimated CD4 counts at seroconversion for a typical individual declined from about 770 cells per μL (95% CI 750-800) in the early 1980s to a plateau of about 570 cells per μL (555-585) after 2002. CD4 cell rate of loss increased up to 2002. Estimated set-point plasma viral loads increased from 4·05 log10 copies per mL (95% CI 3·98-4·12) in 1980 to 4·50 log10 copies per mL (4·45-4·54) in 2002 with a tendency of returning to lower loads thereafter. Results were similar when we restricted analyses to various subsets, including adjusting for plasma viral load assay, censored follow-up at 3 years, or used variations of the main statistical approach.

INTERPRETATION

Our results provide strong indications of increased HIV-1 virulence and transmissibility during the course of the epidemic and a potential plateau effect after about 2002.

FUNDING

European Union Seventh Framework Programme.

Dynamical models of biomarkers and clinical progression for personalized medicine: the HIV context

Mechanistic models, based on ordinary differential equation systems, can exhibit very good predictive abilities that will be useful to build treatment monitoring strategies. In this review, we present the potential and the limitations of such models for guiding treatment (monitoring and optimizing) in HIV-infected patients. In the context of antiretroviral therapy, several biological processes should be considered in addition to the interaction between viruses and the host immune system: the mechanisms of action of the drugs, their pharmacokinetics and pharmacodynamics, as well as the viral and host characteristics. Another important aspect to take into account is clinical progression, although its implementation in such modelling approaches is not easy. Finally, the control theory and the use of intrinsic properties of mechanistic models make them very relevant for dynamic treatment adaptation. Their implementation would nevertheless require their evaluation through clinical trials.

HIV DYNAMICS AND NATURAL HISTORY STUDIES: JOINT MODELING WITH DOUBLY INTERVAL-CENSORED EVENT TIME AND INFREQUENT LONGITUDINAL DATA

Hepatitis C virus (HCV) coinfection has become one of the most challenging clinical situations to manage in HIV-infected patients. Recently the effect of HCV coinfection on HIV dynamics following initiation of highly active antiretroviral therapy (HAART) has drawn considerable attention. Post-HAART HIV dynamics are commonly studied in short-term clinical trials with frequent data collection design. For example, the elimination process of plasma virus during treatment is closely monitored with daily assessments in viral dynamics studies of AIDS clinical trials. In this article instead we use infrequent cohort data from long-term natural history studies and develop a model for characterizing post-HAART HIV dynamics and their associations with HCV coinfection. Specifically, we propose a joint model for doubly interval-censored data for the time between HAART initiation and viral suppression, and the longitudinal CD4 count measurements relative to the viral suppression. Inference is accomplished using a fully Bayesian approach. Doubly interval-censored data are modeled semiparametrically by Dirichlet process priors and Bayesian penalized splines are used for modeling population-level and individual-level mean CD4 count profiles. We use the proposed methods and data from the HIV Epidemiology Research Study (HERS) to investigate the effect of HCV coinfection on the response to HAART.

Effect of Transient Antiretroviral Treatment during acute HIV Infection: Comparison of the Quest Trial Results with CASCADE Natural History Study

Objective

The benefit of transient combination antiretroviral treatment (CART) during acute HIV infection is uncertain. We used the seroconverter database CASCADE to provide a historical comparison for the Quest trial, in which 79 subjects with acute HIV infection received CART for an average of 2.6 years, and 17.7% (95% confidence interval [CI]: 10.9–27.6) fulfilled the primary endpoint of VL≤1,000 copies/ml 24 weeks after CART discontinuation.

Methods

We estimated the prevalence of VL ≤1,000 copies/ml three years after seroconversion and prior to any ART among 385 sexually infected subjects in CASCADE who seroconverted between 1988 and 1996. We conducted a pre-specified comparison with the recently published Quest results, and considered potential biases.

Results and discussion

The prevalence of VL ≤1,000 copies/ml at year three in CASCADE was 10.1% (95% CI: 7.5–13.5) (absolute difference compared to 17.7% in Quest: 7.6%; 95% CI: -0.1–17.8; P=0.053). In CASCADE, VL≤1,000 copies/ml was less common among homosexual and heterosexual men compared with women (8.5%, 7.3% and 17.6% respectively) and in subjects with symptomatic infection compared with those without (6.2% and 12.6%, respectively). As Quest had a much greater proportion of symptomatic subjects than CASCADE, any true difference in VL might be underestimated. Therefore this comparison suggests that transient CART in acute infection might result in a modest increase in the probability of low VL subsequently. However, several factors mitigate this conclusion. First, this historical comparison might be subject to other unmeasured confounders. Second, a comparison of median VL at the same time point was not significant (4.02 copies/ml and 4.20 copies/ml in Quest and CASCADE, respectively; P=0.55). Finally, additional analysis suggested that the observed difference in low VL at year three would be consistent with an immediate effect of CART only - a delay of usual VL decline without additional benefit.

Conclusions

A small but significant proportion of seroconverters have low VL without ART. Transient CART in acute infection might increase the probability of low VL after treatment discontinuation, but such an effect is likely to be modest, and might represent a delay of natural history rather than a long-term therapeutic benefit.