Doubly Robust Estimation of Optimal Dosing Strategies

Variable selection in high dimensions for discrete-outcome individualized treatment rules: Reducing severity of depression symptoms

Despite growing interest in estimating individualized treatment rules, little attention has been given the binary outcome setting. Estimation is challenging with nonlinear link functions, especially when variable selection is needed. We use a new computational approach to solve a recently proposed doubly robust regularized estimating equation to accomplish this difficult task in a case study of depression treatment. We demonstrate an application of this new approach in combination with a weighted and penalized estimating equation to this challenging binary outcome setting. We demonstrate the double robustness of the method and its effectiveness for variable selection. The work is motivated by and applied to an analysis of treatment for unipolar depression using a population of patients treated at Kaiser Permanente Washington.

Variable selection for individualised treatment rules with discrete outcomes

An individualised treatment rule (ITR) is a decision rule that aims to improve individuals' health outcomes by recommending treatments according to subject-specific information. In observational studies, collected data may contain many variables that are irrelevant to treatment decisions. Including all variables in an ITR could yield low efficiency and a complicated treatment rule that is difficult to implement. Thus, selecting variables to improve the treatment rule is crucial. We propose a doubly robust variable selection method for ITRs, and show that it compares favourably with competing approaches. We illustrate the proposed method on data from an adaptive, web-based stress management tool.

On "Reflections on the concept of optimality of single decision point treatment regimes"

This is a discussion of "Reflections on the concept of optimality of single decision point treatment regimes" by Trung Dung Tran, Ariel Alonso Abad, Geert Verbeke, Geert Molenberghs, and Iven Van Mechelen. The authors propose a thoughtful consideration of optimization targets and the implications of such targets for the resulting optimal treatment rule. However, we contest the assertation that targets of optimization have been overlooked and suggest additional considerations that researchers must contemplate as part of a complete framework for learning about optimal treatment regimes.

Double robust estimation of optimal partially adaptive treatment strategies: An application to breast cancer treatment using hormonal therapy

Precision medicine aims to tailor treatment decisions according to patients' characteristics. G-estimation and dynamic weighted ordinary least squares are double robust methods to identify optimal adaptive treatment strategies. It is underappreciated that they require modeling all existing treatment-confounder interactions to be consistent. Identifying optimal partially adaptive treatment strategies that tailor treatments according to only a few covariates, ignoring some interactions, may be preferable in practice. Building on G-estimation and dWOLS, we propose estimators of such partially adaptive strategies and demonstrate their double robustness. We investigate these estimators in a simulation study. Using data maintained by the Centre des Maladies du Sein, we estimate a partially adaptive treatment strategy for tailoring hormonal therapy use in breast cancer patients. R software implementing our estimators is provided.

Doubly robust estimation of optimal dynamic treatment regimes with multicategory treatments and survival outcomes

Patients with chronic diseases, such as cancer or epilepsy, are often followed through multiple stages of clinical interventions. Dynamic treatment regimes (DTRs) are sequences of decision rules that assign treatments at each stage based on measured covariates for each patient. A DTR is said to be optimal if the expectation of the desirable clinical benefit reaches a maximum when applied to a population. When there are three or more options for treatments at each decision point and the clinical outcome of interest is a time-to-event variable, estimating an optimal DTR can be complicated. We propose a doubly robust method to estimate optimal DTRs with multicategory treatments and survival outcomes. A novel blip function is defined to measure the difference in expected outcomes among treatments, and a doubly robust weighted least squares algorithm is designed for parameter estimation. Simulations using various weight functions and scenarios support the advantages of the proposed method in estimating optimal DTRs over existing approaches. We further illustrate the practical value of our method by applying it to data from the Standard and New Antiepileptic Drugs study. In this analysis, the proposed method supports the use of the new drug lamotrigine over the standard option carbamazepine. When the actual treatments match the estimated optimal treatments, survival outcomes tend to be better. The newly developed method provides a practical approach for clinicians that is not limited to cases of binary treatment options.

Privacy-preserving estimation of an optimal individualized treatment rule: a case study in maximizing time to severe depression-related outcomes

Estimating individualized treatment rules-particularly in the context of right-censored outcomes-is challenging because the treatment effect heterogeneity of interest is often small, thus difficult to detect. While this motivates the use of very large datasets such as those from multiple health systems or centres, data privacy may be of concern with participating data centres reluctant to share individual-level data. In this case study on the treatment of depression, we demonstrate an application of distributed regression for privacy protection used in combination with dynamic weighted survival modelling (DWSurv) to estimate an optimal individualized treatment rule whilst obscuring individual-level data. In simulations, we demonstrate the flexibility of this approach to address local treatment practices that may affect confounding, and show that DWSurv retains its double robustness even when performed through a (weighted) distributed regression approach. The work is motivated by, and illustrated with, an analysis of treatment for unipolar depression using the United Kingdom's Clinical Practice Research Datalink.

Preserving data privacy when using multi-site data to estimate individualized treatment rules

Precision medicine is a rapidly expanding area of health research wherein patient level information is used to inform treatment decisions. A statistical framework helps to formalize the individualization of treatment decisions that characterize personalized management plans. Numerous methods have been proposed to estimate individualized treatment rules that optimize expected patient outcomes, many of which have desirable properties such as robustness to model misspecification. However, while individual data are essential in this context, there may be concerns about data confidentiality, particularly in multi-center studies where data are shared externally. To address this issue, we compared two approaches to privacy preservation: (i) data pooling, which is a covariate microaggregation technique and (ii) distributed regression. These approaches were combined with the doubly robust yet user-friendly method of dynamic weighted ordinary least squares to estimate individualized treatment rules. In simulations, we extensively evaluated the performance of the methods in estimating the parameters of the decision rule under different assumptions. The results demonstrate that double robustness is not maintained in data pooling setting and that this can result in bias, whereas the distributed regression provides good performance. We illustrate the methods via an analysis of optimal Warfarin dosing using data from the International Warfarin Consortium.

Estimating the marginal effect of a continuous exposure on an ordinal outcome using data subject to covariate-driven treatment and visit processes

In the statistical literature, a number of methods have been proposed to ensure valid inference about marginal effects of variables on a longitudinal outcome in settings with irregular monitoring times. However, the potential biases due to covariate-driven monitoring times and confounding have rarely been considered simultaneously, and never in a setting with an ordinal outcome and a continuous exposure. In this work, we propose and demonstrate a methodology for causal inference in such a setting, relying on a proportional odds model to study the effect of the exposure on the outcome. Irregular observation times are considered via a proportional rate model, and a generalization of inverse probability of treatment weights is used to account for the continuous exposure. We motivate our methodology by the estimation of the marginal (causal) effect of the time spent on video or computer games on suicide attempts in the Add Health study, a longitudinal study in the United States. Although in the Add Health data, observation times are prespecified, our proposed approach is applicable even in more general settings such as when analyzing data from electronic health records where observations are highly irregular. In simulation studies, we let observation times vary across individuals and demonstrate that not accounting for biasing imbalances due to the monitoring and the exposure schemes can bias the estimate for the marginal odds ratio of exposure.

A single-index model with a surface-link for optimizing individualized dose rules

This paper focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression. The primary motivation is to estimate an optimal individualized dose rule and individualized treatment effects. To model possibly nonlinear interaction effects between patients' covariates and a continuous treatment variable, we employ a two-dimensional penalized spline regression on an index-treatment domain, where the index is defined as a linear projection of the covariates. The method is illustrated using two applications as well as simulation experiments. A unique contribution of this work is in the parsimonious (single-index) parametrization specifically defined for the interaction effect term.

Precision medicine: Statistical methods for estimating adaptive treatment strategies

SERIES EDITORS' NOTE

The beauty of science is that all the important things are unpredictable. Freeman Dyson In the typescript which follows, Moodie and Krakow tackle the topical issue of precision medicine and statistical methods for estimating adaptive treatment strategies. This may be the most difficult typescript in our series so far for non-statisticians to understand. It even has equations! But please bear with the authors and give it a chance. One needs not to understand the equations to get the thrust of the strategy.Precision medicine as we discuss elsewhere, is misnamed. In statistics and mathematics precision refers to getting the same answer again and again. It does not mean getting the correct answer, the term for which is accuracy, not precision. However, precision is the current buzz word so there's no point trying to get this straight. When we think about precision we need to consider two elements, reproducibility and replicability. Reproducibility means you give me your data and computer code and I come to the same conclusion you did. Replicability is another matter. I try to replicate your experiment and hopefully reach the same conclusion. In medicine, replicability is obviously more important than reproducibility but things which cannot be reproduced are unlikely to be replicated.As the authors discuss, one can think about precision medicine as one does a family vacation. A best vacation depends on several co-variates: where you live, your prior travel experiences, advice from family and friends, online reviews, Wikitravel, cost, your travel budget, if you have kids and many other co-variates. Consequently, there is unlikely to be a best vacation for everyone. Yours might be a week at the Ritz Carlton Cancun with dinner at Careyes and ours, a week at the Pfister Hotel in Milwaukee with dinner at Mader's German Restaurant (bring simvastatin). Similarly, it is unlikely there is a best therapy of acute myeloid leukemia, a best donor, a best conditioning regimen, a best posttransplant immune suppressive regimen etc. and certainly no best combination of these co-variates for your patient.The question Moodie and Krakow tackle is how we can determine the best therapy or combination of therapies for someone receiving a haematopoietic cell transplant. Although the default answer is typically: randomized clinical trials are the gold standard, these inform us of the outcome of a cohort of subjects, not individuals. In many instances, although a new therapy may be shown to be better than an old one in a controlled randomized trial the benefit is not uniformly distributed. Some subjects in the experimental cohort may do worse with the new therapy compared with controls, others better. The question is who are the winners and losers? We cannot do a controlled randomized trial of one person. Moodie and Krakow discuss statistical tools to help us sort this out.Again, please do not be put off by the equations; forgetaboutit. The overriding message is not so complex, and important. We are always standing by on twitter @BMTStats to help. But don't confuse us with Match.com. And, by the way, Freeman Dyson was a professor at the Institute for Advanced Studies at Princeton but never got his PhD.Robert Peter Gale, Imperial College London, and Mei-Jie Zhang, Medical College of Wisconsin, Center for International Blood and Marrow Research (CIBMTR).