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Maximum likelihood estimation of long-term HIV dynamic models and antiviral response.

ABSTRACT: HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short-term dynamic models, recent works considered more complex long-term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation-maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long-term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2-ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between-patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.

SUBMITTER: Lavielle M

PROVIDER: S-EPMC3173750 | biostudies-literature | 2011 Mar

REPOSITORIES: biostudies-literature

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Maximum likelihood estimation of long-term HIV dynamic models and antiviral response.

Lavielle Marc M Samson Adeline A Karina Fermin Ana A Mentré France F

Biometrics 20110301 1

HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short-term dynamic models, recent works considered more complex long-term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation ex ...[more]

PMID: 20486926

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Project description:This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart.

Project description:Longitudinal targeted maximum likelihood estimation (LTMLE) has very rarely been used to estimate dynamic treatment effects in the context of time-dependent confounding affected by prior treatment when faced with long follow-up times, multiple time-varying confounders, and complex associational relationships simultaneously. Reasons for this include the potential computational burden, technical challenges, restricted modeling options for long follow-up times, and limited practical guidance in the literature. However, LTMLE has desirable asymptotic properties, ie, it is doubly robust, and can yield valid inference when used in conjunction with machine learning. It also has the advantage of easy-to-calculate analytic standard errors in contrast to the g-formula, which requires bootstrapping. We use a topical and sophisticated question from HIV treatment research to show that LTMLE can be used successfully in complex realistic settings, and we compare results to competing estimators. Our example illustrates the following practical challenges common to many epidemiological studies: (1) long follow-up time (30 months); (2) gradually declining sample size; (3) limited support for some intervention rules of interest; (4) a high-dimensional set of potential adjustment variables, increasing both the need and the challenge of integrating appropriate machine learning methods; and (5) consideration of collider bias. Our analyses, as well as simulations, shed new light on the application of LTMLE in complex and realistic settings: We show that (1) LTMLE can yield stable and good estimates, even when confronted with small samples and limited modeling options; (2) machine learning utilized with a small set of simple learners (if more complex ones cannot be fitted) can outperform a single, complex model, which is tailored to incorporate prior clinical knowledge; and (3) performance can vary considerably depending on interventions and their support in the data, and therefore critical quality checks should accompany every LTMLE analysis. We provide guidance for the practical application of LTMLE.

Project description:Background Long-term effectiveness of asthma control medication has been shown in clinical trials but results from observational studies with children and adolescents are lacking. Marginal structural models estimated using targeted maximum likelihood methods are a novel statistiscal approach for such studies as it allows to account for time-varying confounders and time-varying treatment. Therefore, we aimed to calculate the long-term risk of reporting asthma symptoms in relation to control medication use in a real-life setting from childhood to adulthood applying targeted maximum likelihood estimation. Methods In the prospective cohort study SOLAR (Study on Occupational Allergy Risks) we followed a German subsample of 121 asthmatic children (9–11?years old) of the ISAAC II cohort (International Study of Asthma and Allergies in Childhood) until the age of 19 to 24. We obtained self-reported questionnaire data on asthma control medication use at baseline (1995–1996) and first follow-up (2002–2003) as well as self-reported asthma symptoms at baseline, first and second follow-up (2007–2009). Three hypothetical treatment scenarios were defined: early sustained intervention, early unsustained intervention and no treatment at all. We performed longitudinal targeted maximum likelihood estimation combined with Super Learner algorithm to estimate the relative risk (RR) to report asthma symptoms at SOLAR I and SOLAR II in relation to the different hypothetical scenarios. Results A hypothetical intervention of early sustained treatment was associated with a statistically significant risk increment of asthma symptoms at second follow-up when compared to no treatment at all (RR: 1.51, 95% CI: 1.19–1.83) or early unsustained intervention (RR:1.38, 95% CI: 1.11–1.65). Conclusions While we could confirm the tagerted maximum likelihood estimation to be a usable and robust statistical tool, we did not observe a beneficial effect of asthma control medication on asthma symptoms. Because of potential due to the small sample size, lack of data on disease severity and reverse causation our results should, however, be interpreted with caution.

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Maximum likelihood estimation of long-term HIV dynamic models and antiviral response.

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Maximum likelihood estimation of long-term HIV dynamic models and antiviral response.

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