Instrumental variable estimation of the marginal structural Cox model for time-varying treatments

Robins (1998) introduced marginal structural models, a general class of counterfactual models for the joint effects of time-varying treatments in complex longitudinal studies subject to time-varying confounding. Robins (1998) established the identification of marginal structural model parameters under a sequential randomization assumption, which rules out unmeasured confounding of treatment assignment over time. The marginal structural Cox model is one of the most popular marginal structural models for evaluating the causal effect of time-varying treatments on a censored failure time outcome. In this paper, we establish sufficient conditions for identification of marginal structural Cox model parameters with the aid of a time-varying instrumental variable, in the case where sequential randomization fails to hold due to unmeasured confounding. Our instrumental variable identification condition rules out any interaction between an unmeasured confounder and the instrumental variable in its additive effects on the treatment process, the longitudinal generalization of the identifying condition of Wang & Tchetgen Tchetgen (2018). We describe a large class of weighted estimating equations that give rise to consistent and asymptotically normal estimators of the marginal structural Cox model, thereby extending the standard inverse probability of treatment weighted estimation of marginal structural models to the instrumental variable setting. Our approach is illustrated via extensive simulation studies and an application to estimating the effect of community antiretroviral therapy coverage on HIV incidence.

Association Between Telepsychiatry Capability and Treatment of Patients With Mental Illness in the Emergency Department

OBJECTIVE

Because of limited access to psychiatrists, patients with acute mental illness in some emergency departments (EDs) may wait days for a consultation in the ED or as a medical-surgical admission. The study assessed whether telepsychiatry improves access to care and decreases ED wait times and hospital admissions.

METHODS

ED visits with a primary diagnosis of mental illness were identified from 2010-2018 Medicare claims. A total of 134 EDs across 22 states that implemented telepsychiatry between 2013 and 2016 were matched 1:1 with control EDs without telepsychiatry on several characteristics, including availability of in-person psychiatrist consultations. Outcomes included patients' likelihood of admission to a medical-surgical or psychiatric bed, mental illness spending, prolonged ED length of stay (LOS) (two or more midnights in the ED), 90-day mortality, and outpatient follow-up care. Using a difference-in-difference design, changes in outcomes between the 3 years before telepsychiatry adoption and the 2 years after were examined.

RESULTS

There were 172,708 ED mental illness visits across the 134 matched ED pairs in the study period. Telepsychiatry adoption was associated with increased admissions to a psychiatric bed (differential increase, 4.3 percentage points; p<0.001), decreased admissions to a medical-surgical bed (differential decrease, 2.0 percentage points; p<0.001), increased likelihood of a prolonged ED LOS (differential increase, 3.0 percentage points; p<0.001), and increased mental illness spending (differential increase, $292; p<0.01).

CONCLUSIONS

Telepsychiatry adoption was associated with a lower likelihood of admission to a medical-surgical bed but an increased likelihood of admission to a psychiatric bed and a prolonged ED LOS.

Evaluating the heterogeneous effect of a modifiable risk factor on suicide: The case of vitamin D deficiency

OBJECTIVES

To illustrate the use of machine learning methods to search for heterogeneous effects of a target modifiable risk factor on suicide in observational studies. The illustration focuses on secondary analysis of a matched case-control study of vitamin D deficiency predicting subsequent suicide.

METHODS

We describe a variety of machine learning methods to search for prescriptive predictors; that is, predictors of significant variation in the association between a target risk factor and subsequent suicide. In each case, the purpose is to evaluate the potential value of selective intervention on the target risk factor to prevent the outcome based on the provisional assumption that the target risk factor is causal. The approaches illustrated include risk modeling based on the super learner ensemble machine learning method, Least Absolute Shrinkage and Selection Operator (Lasso) penalized regression, and the causal forest algorithm.

RESULTS

The logic of estimating heterogeneous intervention effects is exposited along with the illustration of some widely used methods for implementing this logic.

CONCLUSIONS

In addition to describing best practices in using the machine learning methods considered here, we close with a discussion of broader design and analysis issues in planning an observational study to investigate heterogeneous effects of a modifiable risk factor.

A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity

There is a fast-growing literature on estimating optimal treatment regimes based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a general instrumental variable approach to learning optimal treatment regimes under endogeneity. Specifically, we establish identification of both value function E [ Y D ( L ) ] for a given regime D and optimal regimes arg max D E [ Y D ( L ) ] with the aid of a binary instrumental variable, when no unmeasured confounding fails to hold. We also construct novel multiply robust classification-based estimators. Furthermore, we propose to identify and estimate optimal treatment regimes among those who would comply to the assigned treatment under a monotonicity assumption. In this latter case, we establish the somewhat surprising result that complier optimal regimes can be consistently estimated without directly collecting compliance information and therefore without the complier average treatment effect itself being identified. Our approach is illustrated via extensive simulation studies and a data application on the effect of child rearing on labor participation.

Machine learning methods for developing precision treatment rules with observational data

Clinical trials have identified a variety of predictor variables for use in precision treatment protocols, ranging from clinical biomarkers and symptom profiles to self-report measures of various sorts. Although such variables are informative collectively, none has proven sufficiently powerful to guide optimal treatment selection individually. This has prompted growing interest in the development of composite precision treatment rules (PTRs) that are constructed by combining information across a range of predictors. But this work has been hampered by the generally small samples in randomized clinical trials and the use of suboptimal analysis methods to analyze the resulting data. In this paper, we propose to address the sample size problem by: working with large observational electronic medical record databases rather than controlled clinical trials to develop preliminary PTRs; validating these preliminary PTRs in subsequent pragmatic trials; and using ensemble machine learning methods rather than individual algorithms to carry out statistical analyses to develop the PTRs. The major challenges in this proposed approach are that treatment are not randomly assigned in observational databases and that these databases often lack measures of key prescriptive predictors and mental disorder treatment outcomes. We proposed a tiered case-cohort design approach that uses innovative methods for measuring and balancing baseline covariates and estimating PTRs to address these challenges.

Strengthening Instrumental Variables Through Weighting

Instrumental variable (IV) methods are widely used to deal with the issue of unmeasured confounding and are becoming popular in health and medical research. IV models are able to obtain consistent estimates in the presence of unmeasured confounding, but rely on assumptions that are hard to verify and often criticized. An instrument is a variable that influences or encourages individuals toward a particular treatment without directly affecting the outcome. Estimates obtained using instruments with a weak influence over the treatment are known to have larger small-sample bias and to be less robust to the critical IV assumption that the instrument is randomly assigned. In this work, we propose a weighting procedure for strengthening the instrument while matching. Through simulations, weighting is shown to strengthen the instrument and improve robustness of resulting estimates. Unlike existing methods, weighting is shown to increase instrument strength without compromising match quality. We illustrate the method in a study comparing mortality between kidney dialysis patients receiving hemodialysis or peritoneal dialysis as treatment for end-stage renal disease.

Statistical Reasoning and Methods in Epidemiology to Promote Individualized Health: In Celebration of the 100th Anniversary of the Johns Hopkins Bloomberg School of Public Health

Epidemiology is concerned with determining the distribution and causes of disease. Throughout its history, epidemiology has drawn upon statistical ideas and methods to achieve its aims. Because of the exponential growth in our capacity to measure and analyze data on the underlying processes that define each person's state of health, there is an emerging opportunity for population-based epidemiologic studies to influence health decisions made by individuals in ways that take into account the individuals' characteristics, circumstances, and preferences. We refer to this endeavor as "individualized health." The present article comprises 2 sections. In the first, we describe how graphical, longitudinal, and hierarchical models can inform the project of individualized health. We propose a simple graphical model for informing individual health decisions using population-based data. In the second, we review selected topics in causal inference that we believe to be particularly useful for individualized health. Epidemiology and biostatistics were 2 of the 4 founding departments in the world's first graduate school of public health at Johns Hopkins University, the centennial of which we honor. This survey of a small part of the literature is intended to demonstrate that the 2 fields remain just as inextricably linked today as they were 100 years ago.