A Flexible Semi-Parametric Approach to Estimating a Dose-Response Relationship: the Treatment of Childhood Amblyopia.

In a study of a dose-response relationship, flexibility in modelling is essential to capturing the treatment effect when the mean effect of other covariates is not fully understood, so that observed treatment effect is not due to the imposition of a rigid model for the relationship between response, treatment, and other variables. A semiparametric additive linear mixed (SPALM) model (Ruppert et al. 2003) provides a tractable and flexible approach to modelling the influence of potentially confounding variables. In this paper, we present pure likelihood and Bayesian versions of the SPALM model. Both methods of inference are readily implementable, but the Bayesian approach allows coherent propagation of uncertainty in the model, and, more importantly, allows prediction of future experimental results for as yet untreated individuals, thus allowing an assessment of the merits of different dosing strategies. We motivate the use of the methodology with the Monitored Occlusion Treatment of Amblyopia Study (MOTAS), which investigated the relationship between duration of occlusion and improvement in visual acuity

Effect of breastfeeding on gastrointestinal infection in infants: A targeted maximum likelihood approach for clustered longitudinal data

The PROmotion of Breastfeeding Intervention Trial (PROBIT) cluster-randomized a program encouraging breastfeeding to new mothers in hospital centers. The original studies indicated that this intervention successfully increased duration of breastfeeding and lowered rates of gastrointestinal tract infections in newborns. Additional scientific and popular interest lies in determining the causal effect of longer breastfeeding on gastrointestinal infection. In this study, we estimate the expected infection count under various lengths of breastfeeding in order to estimate the effect of breastfeeding duration on infection. Due to the presence of baseline and time-dependent confounding, specialized "causal" estimation methods are required. We demonstrate the double-robust method of Targeted Maximum Likelihood Estimation (TMLE) in the context of this application and review some related methods and the adjustments required to account for clustering. We compare TMLE (implemented both parametrically and using a data-adaptive algorithm) to other causal methods for this example. In addition, we conduct a simulation study to determine (1) the effectiveness of controlling for clustering indicators when cluster-specific confounders are unmeasured and (2) the importance of using data-adaptive TMLE.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS727 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The role of exchangeability in causal inference

The notion of exchangeability has been recognized in the causal inference literature in various guises, but only rarely in the original Bayesian meaning as a symmetry property between individual units in statistical inference. Since the latter is a standard ingredient in Bayesian inference, we argue that in Bayesian causal inference it is natural to link the causal model, including the notion of confounding and definition of causal contrasts of interest, to the concept of exchangeability. Here we relate the Bayesian notion of exchangeability to alternative conditions for unconfounded inferences, commonly stated using potential outcome variables, and define causal contrasts in the presence of exchangeability in terms of limits of posterior predictive expectations for further exchangeable units. We demonstrate that this reasoning also carries over to longitudinal settings where parametric inferences are susceptible to the so-called null paradox. We interpret the paradox in terms of an exchangeability assumption made on too coarse a scale

Is Antiretroviral Therapy Causing Long-Term Liver Damage? A Comparative Analysis of HIV-Mono-Infected and HIV/Hepatitis C Co-Infected Cohorts

The effects of highly active antiretroviral therapy (HAART) on progression of hepatic fibrosis in HIV-hepatitis C virus (HCV) co-infection are not well understood. Deaths from liver diseases have risen in the post-HAART era, yet some cross-sectional studies have suggested that HAART use is associated with improved fibrosis rates. In a retrospective cohort of 533 HIV mono-infected and 127 HIV/HCV co-infected patients, followed between January 1991 and July 2005 at a university-based HIV clinic, we investigated the relationship between cumulative HAART exposure and hepatic fibrosis, as measured by the aspartate aminotransferase-to-platelet ratio index (APRI). We used a novel methodological approach to estimate the dose-response relationship of the effect of HAART exposure on APRI. HAART was associated with increasing APRI over time in HIV/HCV co-infected patients suggesting that they may be experiencing cumulative hepatotoxicity from antiretrovirals. The estimated median change (95% confidence interval) in APRI per one year of HAART intake was of −0.46% (−1.61% to 0.71%) in HIV mono-infected compared to 2.54% (−1.77% to 7.03%) in HIV/HCV co-infected patients. Similar results were found when the direct effect of HAART intake since the last visit was estimated on the change in APRI. HAART use associated is with increased APRI in patients with HIV/HCV co-infection. Therefore treatment for HCV infection may be required to slow the growing epidemic of end-stage liver disease in this population

Bayesian inference for optimal dynamic treatment regimes in practice

In this work, we examine recently developed methods for Bayesian inference of optimal dynamic treatment regimes (DTRs). DTRs are a set of treatment decision rules aimed at tailoring patient care to patient-specific characteristics, thereby falling within the realm of precision medicine. In this field, researchers seek to tailor therapy with the intention of improving health outcomes; therefore, they are most interested in identifying optimal DTRs. Recent work has developed Bayesian methods for identifying optimal DTRs in a family indexed by $\psi$ via Bayesian dynamic marginal structural models (MSMs) (Rodriguez Duque et al., 2022a); we review the proposed estimation procedure and illustrate its use via the new BayesDTR R package. Although methods in (Rodriguez Duque et al., 2022a) can estimate optimal DTRs well, they may lead to biased estimators when the model for the expected outcome if everyone in a population were to follow a given treatment strategy, known as a value function, is misspecified or when a grid search for the optimum is employed. We describe recent work that uses a Gaussian process ($GP$) prior on the value function as a means to robustly identify optimal DTRs (Rodriguez Duque et al., 2022b). We demonstrate how a $GP$ approach may be implemented with the BayesDTR package and contrast it with other value-search approaches to identifying optimal DTRs. We use data from an HIV therapeutic trial in order to illustrate a standard analysis with these methods, using both the original observed trial data and an additional simulated component to showcase a longitudinal (two-stage DTR) analysis

Is Antiretroviral Therapy Causing Long-Term Liver Damage? A Comparative Analysis of HIV-Mono-Infected and HIV/Hepatitis C Co-Infected Cohorts

The effects of highly active antiretroviral therapy (HAART) on progression of hepatic fibrosis in HIV-hepatitis C virus (HCV) co-infection are not well understood. Deaths from liver diseases have risen in the post-HAART era, yet some cross-sectional studies have suggested that HAART use is associated with improved fibrosis rates. In a retrospective cohort of 533 HIV mono-infected and 127 HIV/HCV co-infected patients, followed between January 1991 and July 2005 at a university-based HIV clinic, we investigated the relationship between cumulative HAART exposure and hepatic fibrosis, as measured by the aspartate aminotransferase-to-platelet ratio index (APRI). We used a novel methodological approach to estimate the dose-response relationship of the effect of HAART exposure on APRI. HAART was associated with increasing APRI over time in HIV/HCV co-infected patients suggesting that they may be experiencing cumulative hepatotoxicity from antiretrovirals. The estimated median change (95% confidence interval) in APRI per one year of HAART intake was of −0.46% (−1.61% to 0.71%) in HIV mono-infected compared to 2.54% (−1.77% to 7.03%) in HIV/HCV co-infected patients. Similar results were found when the direct effect of HAART intake since the last visit was estimated on the change in APRI. HAART use associated is with increased APRI in patients with HIV/HCV co-infection. Therefore treatment for HCV infection may be required to slow the growing epidemic of end-stage liver disease in this population

Bayesian Optimization for Personalized Dose-Finding Trials with Combination Therapies

Identification of optimal dose combinations in early phase dose-finding trials is challenging, due to the trade-off between precisely estimating the many parameters required to flexibly model the dose-response surface, and the small sample sizes in early phase trials. Existing methods often restrict the search to pre-defined dose combinations, which may fail to identify regions of optimality in the dose combination space. These difficulties are even more pertinent in the context of personalized dose-finding, where patient characteristics are used to identify tailored optimal dose combinations. To overcome these challenges, we propose the use of Bayesian optimization for finding optimal dose combinations in standard ("one size fits all") and personalized multi-agent dose-finding trials. Bayesian optimization is a method for estimating the global optima of expensive-to-evaluate objective functions. The objective function is approximated by a surrogate model, commonly a Gaussian process, paired with a sequential design strategy to select the next point via an acquisition function. This work is motivated by an industry-sponsored problem, where focus is on optimizing a dual-agent therapy in a setting featuring minimal toxicity. To compare the performance of the standard and personalized methods under this setting, simulation studies are performed for a variety of scenarios. Our study concludes that taking a personalized approach is highly beneficial in the presence of heterogeneity.Comment: 26 pages, 4 figures, 1 tabl

Dynamic Treatment Regimen Estimation via Regression-Based Techniques: Introducing R Package DTRreg

Personalized medicine, whereby treatments are tailored to a specific patient rather than a general disease or condition, is an area of growing interest in the fields of biostatistics, epidemiology, and beyond. Dynamic treatment regimens (DTRs) are an integral part of this framework, allowing for personalized treatment of patients with long-term conditions while accounting for both their present circumstances and medical history. The identification of the optimal DTR in any given context, however, is a non-trivial problem, and so specialized methodologies have been developed for that purpose. Here we introduce the R package DTRreg which implements two regression-based approaches: G-estimation and dynamic weighted ordinary least squares regression. We outline the theory underlying these methods, discuss the implementation of DTRreg and demonstrate its use with hypothetical and real-world inspired simulated datasets