An exponential bound for Cox regression

We present an asymptotic exponential bound for the deviation of the survival function estimator of the Cox model. We show that the bound holds even when the proportional hazards assumption does not hold

Stratification of the Risk of Bipolar Disorder Recurrences in Pregnancy and Postpartum

Background Pregnancy and childbirth are a period of high risk for women with bipolar disorder and involve difficult decisions particularly about continuing or stopping medications. Aims To explore what clinical predictors may help to individualise the risk of perinatal recurrence in women with bipolar disorder. Method Information was gathered retrospectively by semi-structured interview, questionnaires and case-note review from 887 women with bipolar disorder who have had children. Clinical predictors were selected using backwards stepwise logistic regression, conditional permutation random forests and reinforcement learning trees. Results Previous perinatal history of affective psychosis or depression was the most significant predictor of a perinatal recurrence (odds ratio (OR) = 8.5, 95% CI 5.04–14.82 and OR = 3.6, 95% CI 2.55–5.07 respectively) but even parous women with bipolar disorder without a previous perinatal mood episode were at risk following a subsequent pregnancy, with 7% developing postpartum psychosis. Conclusions Previous perinatal history of affective psychosis or depression is the most important predictor of perinatal recurrence in women with bipola

Rejoinder

We are very grateful for all of the discussants and their commentswhich have been constructive and idea-provoking.We are pleased that our work has been recognized as an important contribution to statistical methodology in personalized medicine research, and we are grateful for the opportunity to respond briefly to the comments of the discussants. We recognize that there are numerous important insights and questions raised by the discussants, and we regret that we are unable to adequately address each and everyone one of them. However, we have endeavored in what follows to highlight and provide meaningful responses to most of the main points raised. In Section 2, we respond to each of the discussion comments separately, and then we provide a few concluding thoughts in Section 3

Comment on “Dynamic treatment regimes: Technical challenges and applications”

Inference for parameters associated with optimal dynamic treatment regimes is challenging as these estimators are nonregular when there are non-responders to treatments. In this discussion, we comment on three aspects of alleviating this nonregularity. We first discuss an alternative approach for smoothing the quality functions. We then discuss some further details on our existing work to identify non-responders through penalization. Third, we propose a clinically meaningful value assessment whose estimator does not suffer from nonregularity

Goodness-of-fit test for nonparametric regression models: Smoothing spline ANOVA models as example

Nonparametric regression models do not require the specification of the functional form between the outcome and the covariates. Despite their popularity, the amount of diagnostic statistics, in comparison to their parametric counterparts, is small. We propose a goodness-of-fit test for nonparametric regression models with linear smoother form. In particular, we apply this testing framework to smoothing spline ANOVA models. The test can consider two sources of lack-of-fit: whether covariates that are not currently in the model need to be included, and whether the current model fits the data well. The proposed method derives estimated residuals from the model. Then, statistical dependence is assessed between the estimated residuals and the covariates using the HSIC. If dependence exists, the model does not capture all the variability in the outcome associated with the covariates, otherwise the model fits the data well. The bootstrap is used to obtain p-values. Application of the method is demonstrated with a neonatal mental development data analysis. We demonstrate correct type I error as well as power performance through simulations

Augmented outcome-weighted learning for estimating optimal dynamic treatment regimens

Dynamic treatment regimens (DTRs) are sequential treatment decisions tailored by patient's evolving features and intermediate outcomes at each treatment stage. Patient heterogeneity and the complexity and chronicity of many diseases call for learning optimal DTRs that can best tailor treatment according to each individual's time-varying characteristics (eg, intermediate response over time). In this paper, we propose a robust and efficient approach referred to as Augmented Outcome-weighted Learning (AOL) to identify optimal DTRs from sequential multiple assignment randomized trials. We improve previously proposed outcome-weighted learning to allow for negative weights. Furthermore, to reduce the variability of weights for numeric stability and improve estimation accuracy, in AOL, we propose a robust augmentation to the weights by making use of predicted pseudooutcomes from regression models for Q-functions. We show that AOL still yields Fisher-consistent DTRs even if the regression models are misspecified and that an appropriate choice of the augmentation guarantees smaller stochastic errors in value function estimation for AOL than the previous outcome-weighted learning. Finally, we establish the convergence rates for AOL. The comparative advantage of AOL over existing methods is demonstrated through extensive simulation studies and an application to a sequential multiple assignment randomized trial for major depressive disorder

Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

Comment

Xu, Müller, Wahed, and Thall proposed a Bayesian model to analyze an acute leukemia study involving multi-stage chemotherapy regimes. We discuss two alternative methods, Q-learning and O-learning, to solve the same problem from the machine learning point of view. The numerical studies show that these methods can be flexible and have advantages in some situations to handle treatment heterogeneity while being robust to model misspecification. © 2016 American Statistical Association

Impact of gonadectomy on maturational changes in brain volume in adolescent macaques

Adolescence is a transitional period between childhood and adulthood characterized by significant changes in global and regional brain tissue volumes. It is also a period of increasing vulnerability to psychiatric illness. The relationship between these patterns and increased levels of circulating sex steroids during adolescence remains unclear. The objective of the current study was to determine whether gonadectomy, prior to puberty, alters adolescent brain development in male rhesus macaques. Ninety-six structural MRI scans were acquired from 12 male rhesus macaques (8 time points per animal over a two-year period). Six animals underwent gonadectomy and 6 animals underwent a sham operation at 29 months of age. Mixed-effects models were used to determine whether gonadectomy altered developmental trajectories of global and regional brain tissue volumes. We observed a significant effect of gonadectomy on the developmental trajectory of prefrontal gray matter (GM), with intact males showing peak volumes around 3.5 years of age with a subsequent decline. In contrast, prefrontal GM volumes continued to increase in gonadectomized males until the end of the study. We did not observe a significant effect of gonadectomy on prefrontal white matter or on any other global or regional brain tissue volumes, though we cannot rule out that effects might be detected in a larger sample. Results suggest that the prefrontal cortex is more vulnerable to gonadectomy than other brain regions

Predicting Risk of Multidrug-Resistant Enterobacterales Infections Among People With HIV

Background: Medically vulnerable individuals are at increased risk of acquiring multidrug-resistant Enterobacterales (MDR-E) infections. People with HIV (PWH) experience a greater burden of comorbidities and may be more susceptible to MDR-E due to HIV-specific factors. Methods: We performed an observational study of PWH participating in an HIV clinical cohort and engaged in care at a tertiary care center in the Southeastern United States from 2000 to 2018. We evaluated demographic and clinical predictors of MDR-E by estimating prevalence ratios (PRs) and employing machine learning classification algorithms. In addition, we created a predictive model to estimate risk of MDR-E among PWH using a machine learning approach. Results: Among 4734 study participants, MDR-E was isolated from 1.6% (95% CI, 1.2%-2.1%). In unadjusted analyses, MDR-E was strongly associated with nadir CD4 cell count ≤200 cells/mm3 (PR, 4.0; 95% CI, 2.3-7.4), history of an AIDS-defining clinical condition (PR, 3.7; 95% CI, 2.3-6.2), and hospital admission in the prior 12 months (PR, 5.0; 95% CI, 3.2-7.9). With all variables included in machine learning algorithms, the most important clinical predictors of MDR-E were hospitalization, history of renal disease, history of an AIDS-defining clinical condition, CD4 cell count nadir ≤200 cells/mm3, and current CD4 cell count 201-500 cells/mm3. Female gender was the most important demographic predictor. Conclusions: PWH are at risk for MDR-E infection due to HIV-specific factors, in addition to established risk factors. Early HIV diagnosis, linkage to care, and antiretroviral therapy to prevent immunosuppression, comorbidities, and coinfections protect against antimicrobial-resistant bacterial infections