Bayesian set of best dynamic treatment regimes: Construction and sample size calculation for SMARTs with binary outcomes

Artman, William; Johnson, Brent A.; Lynch, Kevin G.; Ertefaie, Ashkan

doi:10.1002/sim.9323

Cited by 5 publications

(6 citation statements)

References 30 publications

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“…Next, we use the multiple comparisons with the best (MCB) 11,38,39 method to identify a set of optimal EDTRs compared to the best, described as follows. Suppose, Y (l) b denote the bth posterior draw for Y (l) , b ∈ {1, … , B}, l ∈ {1, … , L}, and L is the index of the estimated best EDTR.…”

Section: Resultsmentioning

confidence: 99%

“…Next, we use the multiple comparisons with the best (MCB) 11,38,39 method to identify a set of optimal EDTRs compared to the best, described as follows. Suppose,

{Y}_b^{(l)}

denote the

b

th posterior draw for

{Y}^{(l)}

b\in \left\{1,\dots, B\right\}

l\in \left\{1,\dots, L\right\}

, and

L

is the index of the estimated best EDTR.…”

Section: Resultsmentioning

confidence: 99%

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A non‐parametric Bayesian approach for adjusting partial compliance in sequential decision making

Bhattacharya

Johnson

Artman

et al. 2023

Statistics in Medicine

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Existing methods for estimating the mean outcome under a given sequential treatment rule often rely on intention‐to‐treat analyses, which estimate the effect of following a certain treatment rule regardless of compliance behavior of patients. There are two major concerns with intention‐to‐treat analyses: (1) the estimated effects are often biased toward the null effect; (2) the results are not generalizable and reproducible due to the potentially differential compliance behavior. These are particularly problematic in settings with a high level of non‐compliance, such as substance use disorder studies. Our work is motivated by the Adaptive Treatment for Alcohol and Cocaine Dependence study (ENGAGE), which is a multi‐stage trial that aimed to construct optimal treatment strategies to engage patients in therapy. Due to the relatively low level of compliance in this trial, intention‐to‐treat analyses essentially estimate the effect of being randomized to a certain treatment, instead of the actual effect of the treatment. We obviate this challenge by defining the target parameter as the mean outcome under a dynamic treatment regime conditional on a potential compliance stratum. We propose a flexible non‐parametric Bayesian approach based on principal stratification, which consists of a Gaussian copula model for the joint distribution of the potential compliances, and a Dirichlet process mixture model for the treatment sequence specific outcomes. We conduct extensive simulation studies which highlight the utility of our approach in the context of multi‐stage randomized trials. We show robustness of our estimator to non‐linear and non‐Gaussian settings as well.

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Section: Resultsmentioning

confidence: 99%

“…Next, we use the multiple comparisons with the best (MCB) 11,38,39 method to identify a set of optimal EDTRs compared to the best, described as follows. Suppose,

{Y}_b^{(l)}

denote the

b

th posterior draw for

{Y}^{(l)}

b\in \left\{1,\dots, B\right\}

l\in \left\{1,\dots, L\right\}

, and

L

is the index of the estimated best EDTR.…”

Section: Resultsmentioning

confidence: 99%

A non‐parametric Bayesian approach for adjusting partial compliance in sequential decision making

Bhattacharya

Johnson

Artman

et al. 2023

Statistics in Medicine

Self Cite

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“…Inference for Bayesian dynamic MSMs begins by considering a utility U (b, g ψ , β), with β being a parameter that we can use to maximize the utility; focus is on the negative squared error loss utility, U (b, g ψ , β) = −(y − h(β, ψ)) 2 , where h(β, ψ) models E E [Y |G = g ψ ], indexed by an unknown parameter β and where the expectation is taken with respect to the true data-generating distribution in the experimental world. For this specific choice of utility, which aims to minimize the square distance between observed outcomes and their marginal means, no other elements of b are required.…”

Section: Bayesian Dynamic Msms For Optimal Dynamic Regimesmentioning

confidence: 99%

“…There are several packages available in the Comprehensive R Archive Network (CRAN) that performs estimation or inference about DTRs. These include DTRreg which implements dynamic weighted least squares, g-estimation, and Q-learning [45], DTRlearn2 which performs outcome weighted learning [5], DynTxRegime which permits several methods including inverse probability weighting (IPW) and augmented IPW [14], and SMARTbayesR which allows for Bayesian inference of optimal DTRs with data arising from SMART designs with binary outcomes [2]. Currently, there are no packages that allow for Bayesian semiparametric inference of optimal DTRs, nor any that directly use GP optimization with estimators for the value of a DTR.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric Bayesian inference for optimal dynamic treatment regimes via dynamic marginal structural models

et al. 2022

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Summary Considerable statistical work done on dynamic treatment regimes (DTRs) is in the frequentist paradigm, but Bayesian methods may have much to offer in this setting as they allow for the appropriate representation and propagation of uncertainty, including at the individual level. In this work, we extend the use of recently developed Bayesian methods for Marginal Structural Models to arrive at inference of DTRs. We do this (i) by linking the observational world with a world in which all patients are randomized to a DTR, thereby allowing for causal inference and then (ii) by maximizing a posterior predictive utility, where the posterior distribution has been obtained from nonparametric prior assumptions on the observational world data-generating process. Our approach relies on Bayesian semiparametric inference, where inference about a finite-dimensional parameter is made all while working within an infinite-dimensional space of distributions. We further study Bayesian inference of DTRs in the double robust setting by using posterior predictive inference and the nonparametric Bayesian bootstrap. The proposed methods allow for uncertainty quantification at the individual level, thereby enabling personalized decision-making. We examine the performance of these methods via simulation and demonstrate their utility by exploring whether to adapt HIV therapy to a measure of patients’ liver health, in order to minimize liver scarring.

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“…(4) Which is the overall best ATS? Several sample size estimation methods for determining the overall optimal ATS have recently been introduced (Artman et al, 2020(Artman et al, , 2022Oetting et al, 2011;Rose et al, 2019), however, given the additional complexity induced by the multiple comparisons between all the embedded regimes in a SMART, the comparison of more than two strategies is currently mainly performed as a secondary analysis or in exploratory analyses aimed at generating hypotheses to be assessed in subsequent confirmatory trials. Most of the primary analyses performed on SMARTs are focused on the comparison between two means or two strategies, and given that the mean outcome of a strategy is a weighted mean across outcomes of individuals whose paths are consistent with the strategy, frequentist calculations for SMARTs sample sizes with continuous outcomes are similar to traditional randomized clinical trials (Kosorok & Moodie, 2015;Kidwell et al, 2018;Oetting et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Sample Size Calculations for Comparing Two Strategies in SMART Studies

Turchetta¹,

Moodie²,

Stephens

et al. 2022

Biometrics

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In the management of most chronic conditions characterized by the lack of universally effective treatments, adaptive treatment strategies (ATSs) have grown in popularity as they offer a more individualized approach. As a result, sequential multiple assignment randomized trials (SMARTs) have gained attention as the most suitable clinical trial design to formalize the study of these strategies. While the number of SMARTs has increased in recent years, sample size and design considerations have generally been carried out in frequentist settings. However, standard frequentist formulae require assumptions on interim response rates and variance components. Misspecifying these can lead to incorrect sample size calculations and correspondingly inadequate levels of power. The Bayesian framework offers a straightforward path to alleviate some of these concerns. In this paper, we provide calculations in a Bayesian setting to allow more realistic and robust estimates that account for uncertainty in inputs through the ‘two priors’ approach. Additionally, compared to the standard frequentist formulae, this methodology allows us to rely on fewer assumptions, integrate pre‐trial knowledge, and switch the focus from the standardized effect size to the MDD. The proposed methodology is evaluated in a thorough simulation study and is implemented to estimate the sample size for a full‐scale SMART of an internet‐based adaptive stress management intervention on cardiovascular disease patients using data from its pilot study conducted in two Canadian provinces.

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Bayesian set of best dynamic treatment regimes: Construction and sample size calculation for SMARTs with binary outcomes

Cited by 5 publications

References 30 publications

A non‐parametric Bayesian approach for adjusting partial compliance in sequential decision making

A non‐parametric Bayesian approach for adjusting partial compliance in sequential decision making

Semiparametric Bayesian inference for optimal dynamic treatment regimes via dynamic marginal structural models

Bayesian Sample Size Calculations for Comparing Two Strategies in SMART Studies

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