Dynamic modeling of multivariate dimensions and their temporal relationships using latent processes: Application to Alzheimer's disease

Alzheimer's disease gradually affects several components including the cerebral dimension with brain atrophies, the cognitive dimension with a decline in various functions, and the functional dimension with impairment in the daily living activities. Understanding how such dimensions interconnect is crucial for Alzheimer's disease research. However, it requires to simultaneously capture the dynamic and multidimensional aspects and to explore temporal relationships between dimensions. We propose an original dynamic structural model that accounts for all these features. The model defines dimensions as latent processes and combines a multivariate linear mixed model and a system of difference equations to model trajectories and temporal relationships between latent processes in finely discrete time. Dimensions are simultaneously related to their observed (possibly multivariate) markers through nonlinear equations of observation. Parameters are estimated in the maximum likelihood framework enjoying a closed form for the likelihood. We demonstrate in a simulation study that this dynamic model in discrete time benefits the same causal interpretation of temporal relationships as models defined in continuous time as long as the discretization step remains small. The model is then applied to the data of the Alzheimer's Disease Neuroimaging Initiative. Three longitudinal dimensions (cerebral anatomy, cognitive ability, and functional autonomy) measured by six markers are analyzed, and their temporal structure is contrasted between different clinical stages of Alzheimer's disease.

Dealing with death when studying disease or physiological marker: the stochastic system approach to causality

The stochastic system approach to causality is applied to situations where the risk of death is not negligible. This approach grounds causality on physical laws, distinguishes system and observation and represents the system by multivariate stochastic processes. The particular role of death is highlighted, and it is shown that local influences must be defined on the random horizon of time of death. We particularly study the problem of estimating the effect of a factor V on a process of interest Y, taking death into account. We unify the cases where Y is a counting process (describing an event) and the case where Y is quantitative; we examine the case of observations in continuous and discrete time and we study the issue of whether the mechanism leading to incomplete data can be ignored. Finally, we give an example of a situation where we are interested in estimating the effect of a factor (blood pressure) on cognitive ability in elderly.

Lasso regularization for left-censored Gaussian outcome and high-dimensional predictors

Background

Biological assays for the quantification of markers may suffer from a lack of sensitivity and thus from an analytical detection limit. This is the case of human immunodeficiency virus (HIV) viral load. Below this threshold the exact value is unknown and values are consequently left-censored. Statistical methods have been proposed to deal with left-censoring but few are adapted in the context of high-dimensional data.

Methods

We propose to reverse the Buckley-James least squares algorithm to handle left-censored data enhanced with a Lasso regularization to accommodate high-dimensional predictors. We present a Lasso-regularized Buckley-James least squares method with both non-parametric imputation using Kaplan-Meier and parametric imputation based on the Gaussian distribution, which is typically assumed for HIV viral load data after logarithmic transformation. Cross-validation for parameter-tuning is based on an appropriate loss function that takes into account the different contributions of censored and uncensored observations. We specify how these techniques can be easily implemented using available R packages. The Lasso-regularized Buckley-James least square method was compared to simple imputation strategies to predict the response to antiretroviral therapy measured by HIV viral load according to the HIV genotypic mutations. We used a dataset composed of several clinical trials and cohorts from the Forum for Collaborative HIV Research (HIV Med. 2008;7:27-40). The proposed methods were also assessed on simulated data mimicking the observed data.

Results

Approaches accounting for left-censoring outperformed simple imputation methods in a high-dimensional setting. The Gaussian Buckley-James method with cross-validation based on the appropriate loss function showed the lowest prediction error on simulated data and, using real data, the most valid results according to the current literature on HIV mutations.

Conclusions

The proposed approach deals with high-dimensional predictors and left-censored outcomes and has shown its interest for predicting HIV viral load according to HIV mutations.

Adaptive protocols based on predictions from a mechanistic model of the effect of IL7 on CD4 counts

In human immunodeficiency virus-infected patients, antiretroviral therapy suppresses the viral replication, which is followed in most patients by a restoration of CD4+ T cells pool. For patients who fail to do so, repeated injections of exogenous interleukin 7 (IL7) are experimented. The IL7 is a cytokine that is involved in the T cell homeostasis and the INSPIRE study has shown that injections of IL7 induced a proliferation of CD4+ T cells. Phase I/II INSPIRE 2 and 3 studies have evaluated a protocol in which a first cycle of three IL7 injections is followed by a new cycle at each visit when the patient has less than 550 CD4 cells/μL. Restoration of the CD4 concentration has been demonstrated, but the long-term best adaptive protocol is yet to be determined. A mechanistic model of the evolution of CD4 after IL7 injections has been developed, which is based on a system of ordinary differential equations and includes random effects. Based on the estimation of this model, we use a Bayesian approach to forecast the dynamics of CD4 in new patients. We propose four prediction-based adaptive protocols of injections to minimize the time spent under 500 CD4 cells/μL for each patient, without increasing the number of injections received too much. We show that our protocols significantly reduce the time spent under 500 CD4 over a period of two years, without increasing the number of injections. These protocols have the potential to increase the efficiency of this therapy.

A Non-homogeneous Markov Chain Model for Follow-up Studies with Application to Epilepsy

A non-homogeneous Markov chain model is proposed for diseases involving several pathological states. An estimator of the probability of being in a given state at a given time is presented together with an estimator of its variance. A method combining the Mantel-Haenszel and the sum of χ2 procedures enables us to test-whether two groups can be described by the same non-homogeneous Markov chain. Failure time data can be described by a system with two states, one being absorbing. In this case the proposed estimator reduces itself to the actuarial estimator and the test method to the logrank test. Applied to epilepsy this method is a useful tool for analysing the history of children suffering from typical absences (TA) and who can experience other forms of the disease such as grand mal (GM) and remission of TA or GM.

Evaluation of Some Strategies for Treating Concomitant Factors in Randomized Trials

In a randomized clinical trial, the design may or may not be stratified, the analysis may or may not be adjusted. The cross-classification of these alternatives leads to four different strategies. These strategies, plus another one, are evaluated within the framework of a linear model. A discussion about the conditional and unconditional points of view throws some light on the problem of bias in a randomized trial.

Cerebral and Functional Aging: First Results on Prevalence and Incidence of the Paquid Cohort

Paquid is an interdisciplinary study designed to investigate cerebral and functional aging. A cohort of 3,777 community residents living in two administrative areas of South-Western France was selected. A standardized questionnaire was administered at home by trained psychologists. The same procedure was applied one and three years after the baseline data collection. The identification of demented subjects was made with a two-step procedure. The first step is a systematic screening by the psychologists using the DSM-III criteria for dementia. Subjects who fulfilled the DSM-III criteria were examined by a neurologist. Diagnosis of dementia is confirmed according to the NINCDS-ADRDA criteria. The Paquid cohort is complemented by a random sample of 357 institutionalized subjects. First results of prevalence and incidence rates show an exponential increase of dementia with age.

A Rasch Analysis of the Charcot-Marie-Tooth Neuropathy Score (CMTNS) in a Cohort of Charcot-Marie-Tooth Type 1A Patients

The Charcot-Marie-Tooth Neuropathy Score (CMTNS) was developed as a main efficacy endpoint for application in clinical trials of Charcot-Marie-Tooth disease type 1A (CMT1A). However, the sensitivity of the CMTNS for measuring disease severity and progression in CMT1A patients has been questioned. Here, we applied a Rasch analysis in a French cohort of patients to evaluate the psychometrical properties of the CMTNS. Overall, our analysis supports the validity of the CMTNS for application to CMT1A patients though with some limitations such as certain items of the CMTNS being more suitable for moderate to severe forms of the disease, and some items being disordered. We suggest that additional items and/or categories be considered to better assess mild-to-moderate patients.

Dynamic models for estimating the effect of HAART on CD4 in observational studies: Application to the Aquitaine Cohort and the Swiss HIV Cohort Study

Highly active antiretroviral therapy (HAART) has proved efficient in increasing CD4 counts in many randomized clinical trials. Because randomized trials have some limitations (e.g., short duration, highly selected subjects), it is interesting to assess the effect of treatments using observational studies. This is challenging because treatment is started preferentially in subjects with severe conditions. This general problem had been treated using Marginal Structural Models (MSM) relying on the counterfactual formulation. Another approach to causality is based on dynamical models. We present three discrete-time dynamic models based on linear increments models (LIM): the first one based on one difference equation for CD4 counts, the second with an equilibrium point, and the third based on a system of two difference equations, which allows jointly modeling CD4 counts and viral load. We also consider continuous-time models based on ordinary differential equations with non-linear mixed effects (ODE-NLME). These mechanistic models allow incorporating biological knowledge when available, which leads to increased statistical evidence for detecting treatment effect. Because inference in ODE-NLME is numerically challenging and requires specific methods and softwares, LIM are a valuable intermediary option in terms of consistency, precision, and complexity. We compare the different approaches in simulation and in illustration on the ANRS CO3 Aquitaine Cohort and the Swiss HIV Cohort Study.

A Method to Estimate the Size and Characteristics of HIV-positive Populations Using an Individual-based Stochastic Simulation Model

It is important not only to collect epidemiologic data on HIV but to also fully utilize such information to understand the epidemic over time and to help inform and monitor the impact of policies and interventions. We describe and apply a novel method to estimate the size and characteristics of HIV-positive populations. The method was applied to data on men who have sex with men living in the UK and to a pseudo dataset to assess performance for different data availability. The individual-based simulation model was calibrated using an approximate Bayesian computation-based approach. In 2013, 48,310 (90% plausibility range: 39,900-45,560) men who have sex with men were estimated to be living with HIV in the UK, of whom 10,400 (6,160-17,350) were undiagnosed. There were an estimated 3,210 (1,730-5,350) infections per year on average between 2010 and 2013. Sixty-two percent of the total HIV-positive population are thought to have viral load <500 copies/ml. In the pseudo-epidemic example, HIV estimates have narrower plausibility ranges and are closer to the true number, the greater the data availability to calibrate the model. We demonstrate that our method can be applied to settings with less data, however plausibility ranges for estimates will be wider to reflect greater uncertainty of the data used to fit the model.

Repeated Cycles of Recombinant Human Interleukin 7 in HIV-Infected Patients With Low CD4 T-Cell Reconstitution on Antiretroviral Therapy: Results of 2 Phase II Multicenter Studies

BACKGROUND

Phase I/II studies in human immunodeficiency virus (HIV)-infected patients receiving antiretroviral therapy have shown that a single cycle of 3 weekly subcutaneous (s/c) injections of recombinant human interleukin 7 (r-hIL-7) is safe and improves immune CD4 T-cell restoration. Herein, we report data from 2 phase II trials evaluating the effect of repeated cycles of r-hIL-7 (20 µg/kg) with the objective of restoring a sustained CD4 T-cell count >500 cells/µL.

METHODS

INSPIRE 2 was a single-arm trial conducted in the United States and Canada. INSPIRE 3 was a 2 arm trial with 3:1 randomization to r-hIL-7 versus control conducted in Europe and South Africa. Participants with plasma HIV RNA levels <50 copies/mL during antiretroviral therapy and with CD4 T-cell counts between 101 and 400 cells/µL were eligible. A repeat cycle was administered when CD4 T-cell counts fell to <550 cells/µL.

RESULTS

A total of 107 patients were treated and received 1 (n = 107), 2 (n = 74), 3 (n = 14), or 4 (n = 1) r-hIL-7 cycles during a median follow-up of 23 months. r-hIL-7 was well tolerated. Four grade 4 events were observed, including 1 case of asymptomatic alanine aminotransferase elevation. After the second cycle, anti-r-hIL-7 binding antibodies developed in 82% and 77% of patients in INSPIRE 2 and 3, respectively (neutralizing antibodies in 38% and 37%), without impact on the CD4 T-cell response. Half of the patients spent >63% of their follow-up time with a CD4 T-cell count >500 cells/µL.

CONCLUSIONS

Repeated cycles of r-hIL-7 were well tolerated and achieved sustained CD4 T-cell restoration to >500 cells/µL in the majority of study participants.

CLINICAL TRIALS REGISTRATION

INSPIRE II: clinicaltrials.gov (NCT01190111) and INSPIRE III: EudraCT (No. 2010-019773-15) and clinicaltrials.gov (NCT01241643).

A universal approximate cross-validation criterion for regular risk functions

Selection of estimators is an essential task in modeling. A general framework is that the estimators of a distribution are obtained by minimizing a function (the estimating function) and assessed using another function (the assessment function). A classical case is that both functions estimate an information risk (specifically cross-entropy); this corresponds to using maximum likelihood estimators and assessing them by Akaike information criterion (AIC). In more general cases, the assessment risk can be estimated by leave-one-out cross-validation. Since leave-one-out cross-validation is computationally very demanding, we propose in this paper a universal approximate cross-validation criterion under regularity conditions (UACVR). This criterion can be adapted to different types of estimators, including penalized likelihood and maximum a posteriori estimators, and also to different assessment risk functions, including information risk functions and continuous rank probability score (CRPS). UACVR reduces to Takeuchi information criterion (TIC) when cross-entropy is the risk for both estimation and assessment. We provide the asymptotic distributions of UACVR and of a difference of UACVR values for two estimators. We validate UACVR using simulations and provide an illustration on real data both in the psychometric context where estimators of the distributions of ordered categorical data derived from threshold models and models based on continuous approximations are compared.

The stochastic system approach for estimating dynamic treatments effect

The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. As an example, we focus on the analysis of the effect of a HAART on CD4 counts, where attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models, and causal influence has been formalized in the framework of the Doob-Meyer decomposition of stochastic processes. Causal inference however needs assumptions that we detail in this paper and we call this approach to causality the "stochastic system" approach. First we treat this problem in discrete time, then in continuous time. This approach allows incorporating biological knowledge naturally. When working in continuous time, the mechanistic approach involves distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations, while observations are taken at discrete times. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results.

A Multi-Marker Genetic Association Test Based on the Rasch Model Applied to Alzheimer's Disease

Results from Genome-Wide Association Studies (GWAS) have shown that the genetic basis of complex traits often include many genetic variants with small to moderate effects whose identification remains a challenging problem. In this context multi-marker analysis at the gene and pathway level can complement traditional point-wise approaches that treat the genetic markers individually. In this paper we propose a novel statistical approach for multi-marker analysis based on the Rasch model. The method summarizes the categorical genotypes of SNPs by a generalized logistic function into a genetic score that can be used for association analysis. Through different sets of simulations, the false-positive rate and power of the proposed approach are compared to a set of existing methods, and shows good performances. The application of the Rasch model on Alzheimer's Disease (AD) ADNI GWAS dataset also allows a coherent interpretation of the results. Our analysis supports the idea that APOE is a major susceptibility gene for AD. In the top genes selected by proposed method, several could be functionally linked to AD. In particular, a pathway analysis of these genes also highlights the metabolism of cholesterol, that is known to play a key role in AD pathogenesis. Interestingly, many of these top genes can be integrated in a hypothetic signalling network.

State selection in Markov models for panel data with application to psoriatic arthritis

Markov multistate models in continuous-time are commonly used to understand the progression over time of disease or the effect of treatments and covariates on patient outcomes. The states in multistate models are related to categorisations of the disease status, but there is often uncertainty about the number of categories to use and how to define them. Many categorisations, and therefore multistate models with different states, may be possible. Different multistate models can show differences in the effects of covariates or in the time to events, such as death, hospitalisation, or disease progression. Furthermore, different categorisations contain different quantities of information, so that the corresponding likelihoods are on different scales, and standard, likelihood-based model comparison is not applicable. We adapt a recently developed modification of Akaike's criterion, and a cross-validatory criterion, to compare the predictive ability of multistate models on the information which they share. All the models we consider are fitted to data consisting of observations of the process at arbitrary times, often called 'panel' data. We develop an implementation of these criteria through Hidden Markov models and apply them to the comparison of multistate models for the Health Assessment Questionnaire score in psoriatic arthritis. This procedure is straightforward to implement in the R package 'msm'.

[Mathematical dynamical models for personalized medicine]

One of the necessary conditions to perform any personalized medicine is to obtain good individual predictions. In addition to the numerous markers available (omics data), the methods used to analyze the data are very important too. We are presenting an example of mathematical dynamical mechanistic model that could be used for adapting the antiretroviral treatment in patients infected by the human immunodeficiency virus. The interest of this type of approach is to build a model based on biological knowledge about the interaction between markers and therefore to allow for a better predictive power.

Quantifying and predicting the effect of exogenous interleukin-7 on CD4+ T cells in HIV-1 infection

Exogenous Interleukin-7 (IL-7), in supplement to antiretroviral therapy, leads to a substantial increase of all CD4⁺ T cell subsets in HIV-1 infected patients. However, the quantitative contribution of the several potential mechanisms of action of IL-7 is unknown. We have performed a mathematical analysis of repeated measurements of total and naive CD4⁺ T cells and their Ki67 expression from HIV-1 infected patients involved in three phase I/II studies (N = 53 patients). We show that, besides a transient increase of peripheral proliferation, IL-7 exerts additional effects that play a significant role in CD4⁺ T cell dynamics up to 52 weeks. A decrease of the loss rate of the total CD4⁺ T cell is the most probable explanation. If this effect could be maintained during repeated administration of IL-7, our simulation study shows that such a strategy may allow maintaining CD4⁺ T cell counts above 500 cells/µL with 4 cycles or fewer over a period of two years. This in-depth analysis of clinical data revealed the potential for IL-7 to achieve sustained CD4⁺ T cell restoration with limited IL-7 exposure in HIV-1 infected patients with immune failure despite antiretroviral therapy.

HIV infection is characterized by a decrease of CD4⁺ T-lymphocytes in the blood. Whereas antiretroviral treatment succeeds to control viral replication, some patients fail to reconstitute their CD4⁺ T cell count to normal value. IL-7 is a promising cytokine under evaluation for its use in HIV infection, in supplement to antiretroviral therapy, as it increases cell proliferation and survival. Here, we use data from three clinical trials testing the effect of IL-7 on CD4⁺ T-cell recovery in treated HIV-infected individuals and use a simple mathematical model to quantify IL-7 effects by estimating the biological parameters of the model. We show that the increase of peripheral proliferation could not explain alone the long-term dynamics of T cells after IL-7 injections underlining other important effects such as the improvement of cell survival. We also investigate the feasibility and the efficiency of repetitions of IL-7 cycles and argue for further evaluation through clinical trials.

NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations

Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients.

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.

Clonally diverse T cell homeostasis is maintained by a common program of cell-cycle control

Lymphopenia induces T cells to undergo cell divisions as part of a homeostatic response mechanism. The clonal response to lymphopenia is extremely diverse, and it is unknown whether this heterogeneity represents distinct mechanisms of cell-cycle control or whether a common mechanism can account for the diversity. We addressed this question by combining in vivo and mathematical modeling of lymphopenia-induced proliferation (LIP) of two distinct T cell clonotypes. OT-I T cells undergo rapid LIP accompanied by differentiation that superficially resembles Ag-induced proliferation, whereas F5 T cells divide slowly and remain naive. Both F5 and OT-I LIP responses were most accurately described by a single stochastic division model where the rate of cell division was exponentially decreased with increasing cell numbers. The model successfully identified key biological parameters of the response and accurately predicted the homeostatic set point of each clone. Significantly, the model was successful in predicting interclonal competition between OT-I and F5 T cells, consistent with competition for the same resource(s) required for homeostatic proliferation. Our results show that diverse and heterogeneous clonal T cell responses can be accounted for by a single common model of homeostasis.

Prevalence projections of chronic diseases and impact of public health intervention

The estimation of future prevalences of chronic diseases is essential for public health policy. Using incidence estimates from cohort data and demographic projections for general mortality and population sizes, we propose a method based on a general illness-death model to make prevalence projections for chronic diseases. In contrast to previously published methods, we account for differences between global mortality and mortality of healthy subjects and compare two assumptions regarding the secular trend for mortality of diseased subjects. Then we develop a methodology to estimate changes in future disease prevalences resulting from prevention campaign to reduce the frequency or the excess risk associated with a risk factor. The methods are applied for estimating dementia prevalence in France between 2010 and 2030.

Evidence synthesis through a degradation model applied to myocardial infarction

We propose an evidence synthesis approach through a degradation model to estimate causal influences of physiological factors on myocardial infarction (MI) and coronary heart disease (CHD). For instance several studies give incidences of MI and CHD for different age strata, other studies give relative or absolute risks for strata of main risk factors of MI or CHD. Evidence synthesis of several studies allows incorporating these disparate pieces of information into a single model. For doing this we need to develop a sufficiently general dynamical model; we also need to estimate the distribution of explanatory factors in the population. We develop a degradation model for both MI and CHD using a Brownian motion with drift, and the drift is modeled as a function of indicators of obesity, lipid profile, inflammation and blood pressure. Conditionally on these factors the times to MI or CHD have inverse Gaussian ([Formula: see text]) distributions. The results we want to fit are generally not conditional on all the factors and thus we need marginal distributions of the time of occurrence of MI and CHD; this leads us to manipulate the inverse Gaussian normal distribution ([Formula: see text]) (an [Formula: see text] whose drift parameter has a normal distribution). Another possible model arises if a factor modifies the threshold. This led us to define an extension of [Formula: see text] obtained when both drift and threshold parameters have normal distributions. We applied the model to results published in five important studies of MI and CHD and their risk factors. The fit of the model using the evidence synthesis approach was satisfactory and the effects of the four risk factors were highly significant.

Acute versus chronic partial sleep deprivation in middle-aged people: differential effect on performance and sleepiness

STUDY OBJECTIVE

To evaluate the effects of acute sleep deprivation and chronic sleep restriction on vigilance, performance, and self-perception of sleepiness.

DESIGN

Habitual night followed by 1 night of total sleep loss (acute sleep deprivation) or 5 consecutive nights of 4 hr of sleep (chronic sleep restriction) and recovery night.

PARTICIPANTS

Eighteen healthy middle-aged male participants (age [(± standard deviation] = 49.7 ± 2.6 yr, range 46-55 yr).

MEASUREMENTS

Multiple sleep latency test trials, Karolinska Sleepiness Scale scores, simple reaction time test (lapses and 10% fastest reaction times), and nocturnal polysomnography data were recorded.

RESULTS

Objective and subjective sleepiness increased immediately in response to sleep restriction. Sleep latencies after the second and third nights of sleep restriction reached levels equivalent to those observed after acute sleep deprivation, whereas Karolinska Sleepiness Scale scores did not reach these levels. Lapse occurrence increased after the second day of sleep restriction and reached levels equivalent to those observed after acute sleep deprivation. A statistical model revealed that sleepiness and lapses did not progressively worsen across days of sleep restriction. Ten percent fastest reaction times (i.e., optimal alertness) were not affected by acute or chronic sleep deprivation. Recovery to baseline levels of alertness and performance occurred after 8-hr recovery night.

CONCLUSIONS

In middle-aged study participants, sleep restriction induced a high increase in sleep propensity but adaptation to chronic sleep restriction occurred beyond day 3 of restriction. This sleepiness attenuation was underestimated by the participants. One recovery night restores daytime sleepiness and cognitive performance deficits induced by acute or chronic sleep deprivation.

CITATION

Philip P; Sagaspe P; Prague M; Tassi P; Capelli A; Bioulac B; Commenges D; Taillard J. Acute versus chronic partial sleep deprivation in middle-aged people: differential effect on performance and sleepiness. SLEEP 2012;35(7):997-1002.

Joint modeling of the clinical progression and of the biomarkers' dynamics using a mechanistic model

Joint models are used to rigorously explore the relationship between the dynamics of biomarkers and clinical events. In the context of HIV infection, where the multivariate dynamics of HIV-RNA and CD4 are complex, a mechanistic approach based on a system of nonlinear differential equations naturally takes into account the correlation between the biomarkers. Using data from a randomized clinical trial comparing dual antiretroviral therapy to a single drug regimen, a full maximum likelihood approach is proposed to explore the relationship between the evolution of the biomarkers and the time to a clinical event. The role of each marker as an independent predictor of disease progression is assessed. We show that the joint dynamics of HIV-RNA and CD4 captures the effect of antiretroviral treatment; the CD4 dynamics alone is found to capture most but not all of the treatment effect.

Score tests for exploring complex models: application to HIV dynamics models

In biostatistics, more and more complex models are being developed. This is particularly the case in system biology. Fitting complex models can be very time-consuming, since many models often have to be explored. Among the possibilities are the introduction of explanatory variables and the determination of random effects. The particularity of this use of the score test is that the null hypothesis is not itself very simple; typically, some random effects may be present under the null hypothesis. Moreover, the information matrix cannot be computed, but only an approximation based on the score. This article examines this situation with the specific example of HIV dynamics models. We examine the score test statistics for testing the effect of explanatory variables and the variance of random effect in this complex situation. We study type I errors and the statistical powers of this score test statistics and we apply the score test approach to a real data set of HIV-infected patients.

A general definition of influence between stochastic processes

We extend the study of weak local conditional independence (WCLI) based on a measurability condition made by (Commenges and Gégout-Petit J R Stat Soc B 71:1-18) to a larger class of processes that we call D'. We also give a definition related to the same concept based on certain likelihood processes, using the Girsanov theorem. Under certain conditions, the two definitions coincide on D'. These results may be used in causal models in that we define what may be the largest class of processes in which influences of one component of a stochastic process on another can be described without ambiguity. From WCLI we can construct a concept of strong local conditional independence (SCLI). When WCLI does not hold, there is a direct influence while when SCLI does not hold there is direct or indirect influence. We investigate whether WCLI and SCLI can be defined via conventional independence conditions and find that this is the case for the latter but not for the former. Finally we recall that causal interpretation does not follow from mere mathematical definitions, but requires working with a good system and with the true probability.

Estimating life expectancy of demented and institutionalized subjects from interval-censored observations of a multi-state model

We consider the problem of estimating life expectancy of demented and institutionalized subjects from interval-censored observations. A mixed discrete-continuous scheme of observation is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other events can be exactly observed. In this work, we jointly modelled dementia, institutionalization and death from data of a cohort study. Due to discrete time observations, it may happen that a subject developed dementia or was institutionalized between the last visit and the death. Consequently, there is an uncertainty about the precise number of diseased or institutionalized subjects. Moreover, the time of onset of dementia is interval censored. We use a penalized likelihood approach for estimating the transition intensities of the multi-state model. With these estimators, incidence and life expectancy can be computed easily. This approach deals with incomplete data due to the presence of left truncation and interval censoring. It can be generalized to take explanatory variables into account. We illustrate this approach by applying this model to the analysis of a large cohort study on cerebral ageing.

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.

Aluminum and silica in drinking water and the risk of Alzheimer's disease or cognitive decline: findings from 15-year follow-up of the PAQUID cohort

The authors examined associations between exposure to aluminum or silica from drinking water and risk of cognitive decline, dementia, and Alzheimer's disease among elderly subjects followed for 15 years (1988-2003). They actively searched for incident cases of dementia among persons aged 65 years or over living in 91 civil drinking-water areas in southern France. Two measures of exposure to aluminum were assessed: geographic exposure and individual exposure, taking into account daily consumption of tap water and bottled water. A total of 1,925 subjects who were free of dementia at baseline and had reliable water assessment data were analyzed. Using random-effects models, the authors found that cognitive decline with time was greater in subjects with a higher daily intake of aluminum from drinking water (>or=0.1 mg/day, P=0.005) or higher geographic exposure to aluminum. Using a Cox model, a high daily intake of aluminum was significantly associated with increased risk of dementia. Conversely, an increase of 10 mg/day in silica intake was associated with a reduced risk of dementia (adjusted relative risk =0.89, P=0.036). However, geographic exposure to aluminum or silica from tap water was not associated with dementia. High consumption of aluminum from drinking water may be a risk factor for Alzheimer's disease.

Alternative methods to analyse the impact of HIV mutations on virological response to antiviral therapy

Background

Principal component analysis (PCA) and partial least square (PLS) regression may be useful to summarize the HIV genotypic information. Without pre-selection each mutation presented in at least one patient is considered with a different weight. We compared these two strategies with the construction of a usual genotypic score.

Methods

We used data from the ANRS-CO3 Aquitaine Cohort Zephir sub-study. We used a subset of 87 patients with a complete baseline genotype and plasma HIV-1 RNA available at baseline and at week 12. PCA and PLS components were determined with all mutations that had prevalences >0. For the genotypic score, mutations were selected in two steps: 1) p-value < 0.01 in univariable analysis and prevalences between 10% and 90% and 2) backwards selection procedure based on the Cochran-Armitage Test. The predictive performances were compared by means of the cross-validated area under the receiver operating curve (AUC).

Results

Virological failure was observed in 46 (53%) patients at week 12. Principal components and PLS components showed a good performance for the prediction of virological response in HIV infected patients. The cross-validated AUCs for the PCA, PLS and genotypic score were 0.880, 0.868 and 0.863, respectively. The strength of the effect of each mutation could be considered through PCA and PLS components. In contrast, each selected mutation contributes with the same weight for the calculation of the genotypic score. Furthermore, PCA and PLS regression helped to describe mutation clusters (e.g. 10, 46, 90).

Conclusion

In this dataset, PCA and PLS showed a good performance but their predictive ability was not clinically superior to that of the genotypic score.

A latent process model for dementia and psychometric tests

We jointly model longitudinal values of a psychometric test and diagnosis of dementia. The model is based on a continuous-time latent process representing cognitive ability. The link between the latent process and the observations is modeled in two phases. Intermediate variables are noisy observations of the latent process; scores of the psychometric test and diagnosis of dementia are obtained by categorizing these intermediate variables. We propose maximum likelihood inference for this model and we propose algorithms for performing this task. We estimated the parameters of such a model using the data of the 5 year follow-up of the PAQUID study. In particular this analysis yielded interesting results about the effect of educational level on both latent cognitive ability and specific performance in the mini mental test examination. The predictive ability of the model is illustrated by predicting diagnosis of dementia at the 8 year follow-up of the PAQUID study based on the information from the first 5 years.

Practical identifiability of HIV dynamics models

We study the practical identifiability of parameters, i.e., the accuracy of the estimation that can be hoped, in a model of HIV dynamics based on a system of non-linear Ordinary Differential Equations (ODE). This depends on the available information such as the schedule of the measurements, the observed components, and the measurement precision. The number of patients is another way to increase it by introducing an appropriate statistical "population" framework. The impact of each improvement of the experimental condition is not known in advance but it can be evaluated via the Fisher Information Matrix (FIM). If the non-linearity of the biological model, as well as the complex statistical framework makes computation of the FIM challenging, we show that the particular structure of these models enables to compute it as precisely as wanted. In the HIV model, measuring HIV viral load and total CD4+ count were not enough to achieve identifiability of all the parameters involved. However, we show that an appropriate statistical approach together with the availability of additional markers such as infected cells or activated cells should considerably improve the identifiability and thus the usefulness of dynamical models of HIV.

Maximum likelihood estimation in dynamical models of HIV

The study of dynamical models of HIV infection, based on a system of nonlinear ordinary differential equations (ODE), has considerably improved the knowledge of its pathogenesis. While the first models used simplified ODE systems and analyzed each patient separately, recent works dealt with inference in non-simplified models borrowing strength from the whole sample. The complexity of these models leads to great difficulties for inference and only the Bayesian approach has been attempted by now. We propose a full likelihood inference, adapting a Newton-like algorithm for these particular models. We consider a relatively complex ODE model for HIV infection and a model for the observations including the issue of detection limits. We apply this approach to the analysis of a clinical trial of antiretroviral therapy (ALBI ANRS 070) and we show that the whole algorithm works well in a simulation study.

A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data

Cognition is not directly measurable. It is assessed using psychometric tests, which can be viewed as quantitative measures of cognition with error. The aim of this article is to propose a model to describe the evolution in continuous time of unobserved cognition in the elderly and assess the impact of covariates directly on it. The latent cognitive process is defined using a linear mixed model including a Brownian motion and time-dependent covariates. The observed psychometric tests are considered as the results of parameterized nonlinear transformations of the latent cognitive process at discrete occasions. Estimation of the parameters contained both in the transformations and in the linear mixed model is achieved by maximizing the observed likelihood and graphical methods are performed to assess the goodness of fit of the model. The method is applied to data from PAQUID, a French prospective cohort study of ageing.