Efﬁcient and Robust Approaches for Analysis of SMARTs Illustration using the ADAPT-R Trial

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Efﬁcient and Robust Approaches for Analysis

of SMARTs: Illustration using the ADAPT-R

Trial

Lina M. Montoya *1, Michael R. Kosorok1, Elvin H. Geng2, Joshua

Schwab3, Thomas A. Odeny4, and Maya L. Petersen3

1Department of Biostatistics, University of North Carolina at

Chapel Hill, U.S.A.

2Division of Infectious Diseases, Washington University in St.

Louis, U.S.A.

3Division of Epidemiology and Biostatistics, University of

California, Berkeley, U.S.A.

4National Cancer Institute, National Institutes of Health, U.S.A.

October 2022

*Email address for correspondence: lmontoya@unc.edu

arXiv:2210.03316v1 [stat.ME] 7 Oct 2022

Abstract

Personalized intervention strategies, in particular those that modify treat-

ment based on a participant’s own response, are a core component of pre-

cision medicine approaches. Sequential Multiple Assignment Randomized

Trials (SMARTs) are growing in popularity and are speciﬁcally designed to

facilitate the evaluation of sequential adaptive strategies, in particular those

embedded within the SMART. Advances in efﬁcient estimation approaches

that are able to incorporate machine learning while retaining valid inference

can allow for more precise estimates of the effectiveness of these embedded

regimes. However, to the best of our knowledge, such approaches have not

yet been applied as the primary analysis in SMART trials. In this paper, we

present a robust and efﬁcient approach using Targeted Maximum Likelihood

Estimation (TMLE) for estimating and contrasting expected outcomes un-

der the dynamic regimes embedded in a SMART, together with generating

simultaneous conﬁdence intervals for the resulting estimates. We contrast

this method with two alternatives (G-computation and Inverse Probability

Weighting estimators). The precision gains and robust inference achievable

through the use of TMLE to evaluate the effects of embedded regimes are il-

lustrated using both outcome-blind simulations and a real data analysis from

the Adaptive Strategies for Preventing and Treating Lapses of Retention in

HIV Care (ADAPT-R) trial (NCT02338739), a SMART with a primary aim

of identifying strategies to improve retention in HIV care among people liv-

ing with HIV in sub-Saharan Africa.

1 Introduction

One question central to precision medicine and public health asks: “who should

get which intervention, and in what sequence?” For example, a wide class of se-

quenced strategies start with an initial intervention, and then switch to a new,

often higher intensity intervention based on participant response. These strategies

are personalized because both the decision to switch interventions and the timing

of the switch depend on an individual’s own response. Data generated from a

Sequential Multiple Assignment Randomized Trial (SMART) provide a straight-

forward way of evaluating the causal effects of such sequenced adaptive strategies

(or dynamic regimes). Often, participants are given treatment (either randomly

or deterministically) at pre-speciﬁed decision points based on their measured in-

formation (e.g., past treatments and/or intermediate covariates) up to that point.

Assigning treatment sequentially based on a participant’s measured past – includ-

ing commonly, a patient’s own response to earlier treatment – deﬁnes a SMART’s

embedded dynamic treatment regimes (or simply, embedded regimes; also known

as adaptive interventions or strategies). These embedded regimes correspond to

adaptive personalized strategies for assigning treatment, thus contributing to the

goals of precision health. Critically, by design, SMARTs allow the effects of these

embedded regimes (and others, such as optimal dynamic treatment regimes based

on covariates beyond those that deﬁne the trial design; [1]) to be identiﬁed and

estimated without risk of bias.

SMART designs are increasingly growing in popularity. For example, a re-

cent review by [2] cites 24 SMART protocol papers published since 2014. While

primary analyses for SMARTs sometimes aim to examine the single timepoint

static effects of the treatment options in the SMART’s nested trials, they increas-

ingly (in either primary or secondary aims) aim to evaluate the effects of embed-

ded regimes (e.g., [3, 4]) or additionally tailored individual interventions (e.g.,

[5]). When evaluating the SMART’s embedded regimes, common approaches for

estimating the expected counterfactual outcome (or “value”) of a given embed-

ded regime use inverse probability weighting (IPW) estimators, including weight-

ing and replicating approaches (introduced in [6, 7, 8]; see also [9]) and G-

computation approaches (introduced in [10, 11, 12, 13]). IPW estimators, and

some G-computation estimators (depending on how the sequential regressions are

estimated) will generally provide unbiased estimates of the value of the embed-

ded regime; however, they are inefﬁcient in that they do not make full use of

baseline and time-updated covariates to improve estimator precision. Advances

in semiparametric efﬁcient substitution estimators, such as longitudinal targeted

maximum likelihood estimation (TMLE), allow for the integration of machine

learning in the estimation process, enabling more precise estimates while retaining

valid inference (see [14] for a review in the context of SMARTs). Recent work has

documented the potential of ﬂexible covariate adjustment using machine learning,

and TMLE in particular, to improve precision in single timepoint individually ran-

domized trials (eg, [15]) and cluster randomized trials (eg, [16]). Simulations used

to inform the design of SMARTs (see, e.g., [14, 17]) further support the poten-

tial beneﬁts of longitudinal TMLE for the primary analysis of embedded regimes

in SMART studies. However, to the best of our knowledge, neither longitudinal

TMLE nor other semiparametric efﬁcient estimators have been implemented or

reported as the primary analysis method of a published SMART.

In this paper we ﬁrst review, using the “Causal Roadmap” [18], how SMART

designs can be used to identify the effects of embedded regimes, including the

expected counterfactual outcome (or value) of each regime had all participants in

the population followed it. We then describe an efﬁcient and robust approach to

estimating these counterfactual quantities without reliance on model assumptions,

beyond the assumption of sequential randomization known by design. Speciﬁ-

cally, we describe a longitudinal TMLE [19, 20] for estimating the values of these

embedded regimes. TMLE is a double robust, semi-parametric, efﬁcient, plug-in

estimator that incorporates machine learning to improve efﬁciency without sacri-

ﬁcing reliable inference. We review the assumptions needed for valid statistical

inference using this estimator, and we show how to construct individual and si-

multaneous conﬁdence intervals to evaluate multiple embedded regimes within a

SMART. Speciﬁcally, we illustrate the use of longitudinal TMLE as the primary

pre-speciﬁed analysis in the recently completed Adaptive Strategies for Preventing

and Treating Lapses of Retention in HIV Care (ADAPT-R) trial (NCT02338739).

We provide simulations to demonstrate the robustness of the approach, including

an illustration of how outcome-blind simulations based on real trial data can be

used to inform key decisions that must be pre-speciﬁed in a trial’s analysis plan,

such as speciﬁcation of the machine learning methods empoyed for nuisance pa-

rameter estimation. We further provide a comparison to the commonly used IPW

estimator. Using both simulations and analysis of the trial data, we illustrate how

the pre-speciﬁed use of TMLE integrating machine learning, in the analysis of the

ADAPT-R trial, resulted in substantial improvements in efﬁciency, and thereby

trial power, and discuss the interpretation of trial results.

The article is organized as follows: in Section 2, we provide background on

the ADAPT-R trial. In Section 3, we describe the causal model, deﬁne the causal

parameters corresponding to the value of each embedded regime, and identify

statistical parameters. In Section 4, we discuss estimation and inference of the

identiﬁed statistical parameters. In Section 5, we present two simulation studies,

with the dual objectives of illustrating the performance of these estimators and

demonstrating how outcome blind simulations can be used to fully pre-specify

a machine learning-based primary trial analysis using TMLE. In Section 6, we

apply these methods to the ADAPT-R study. We close with a discussion.

2 The ADAPT-R Trial

The ADAPT-R trial was a SMART carried out to evaluate individualized se-

quenced behavioral interventions to optimize successful HIV care outcomes in

Kenya. Up to 30% of persons receiving HIV care in this population experience at

least one lapse in HIV care; these lapses in retention can result in loss of viral sup-

pression. Importantly, patients that experience a retention lapse have a diversity

of characteristics and needs [21]. As a result, there is no “one-size-ﬁts-all” in-

centive or strategy to help patients stay in care and achieve virologic suppression,

demonstrating the need for effective personalized treatment regimes to increase

successful HIV care outcomes.

In ADAPT-R, 1,809 persons living with HIV and initiating antiretroviral treat-

ment (ART) in the Nyanza region of Kenya were randomized to one of three initial

interventions to prevent a lapse in care (short message service [SMS] text mes-

sages, conditional cash transfers [CCTs] in the form of transportation vouchers

for on-time visits, or standard of care [SOC] education and counseling). Patients

who had a lapse in care within the ﬁrst year of follow-up were re-randomized to a

more intensive intervention to facilitate return to care (SMS text messages paired

with CCTs, peer navigation, or SOC outreach); patients who did not have a lapse

in care during the ﬁrst year and who received SMS or CCTs in the ﬁrst randomiza-

tion were re-randomized to either continue or discontinue that intervention (study

design shown in Figure 1).

Thus, in ADAPT-R there were 15 embedded regimes (see Table 1 for the com-

plete list) that would have initially administered either SMS, CCTs, or SOC to all

patients starting ART, and then either a) SMS with CCTs, peer navigators, or

SOC in the second stage should a lapse occur, or b) for those on active ﬁrst line

treatment, a decision to continue or discontinue ﬁrst stage treatment should no

lapse occur. This article describes how to estimate the counterfactual probability

of having suppressed viral replication (plasma HIV RNA level <500 copies/ml)

two years after initial randomization, if a given embedded regime had been used

for the full study population.

Figure 1: The Adaptive Strategies for Preventing and Treating Lapses of Reten-

tion in HIV Care (ADAPT-R) study design, a Sequential Multiple Assignment

Randomized Trial (SMART). The circles with an “R” denote points of random-

ization.

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EfcientandRobustApproachesforAnalysisofSMARTs:IllustrationusingtheADAPT-RTrialLinaM.Montoya*1,MichaelR.Kosorok1,ElvinH.Geng2,JoshuaSchwab3,ThomasA.Odeny4,andMayaL.Petersen31DepartmentofBiostatistics,UniversityofNorthCarolinaatChapelHill,U.S.A.2DivisionofInfectiousDiseases,WashingtonUniversityinSt.L...

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