Set-regression with applications to subgroup analysis.

Regression is a commonly used statistical model. It is the conditional mean of the response given covariates µ(x)=E(Y|X=x) . However, in some practical problems, the interest is the conditional mean of the response given the covariates belonging to some set A. Notably, in precision medicine and subgroup analysis in clinical trials, the aim is to identify subjects who benefit the most from the treatment, or identify an optimal set in the covariate space which manifests treatment favoritism if a subject's covariates fall in this set and the subject is classified to the favorable treatment subgroup. Existing methods for subgroup analysis achieve this indirectly by using classical regression. This motivates us to develop a new type of regression: set-regression, defined as µ(A)=E(Y|X∈A) which directly addresses the subgroup analysis problem. This extends not only the classical regression model but also improves recursive partitioning and support vector machine approaches, and is particularly suitable for objectives involving optimization of the regression over sets, such as subgroup analysis. We show that the new versatile set-regression identifies the subgroup with increased accuracy. It is easy to use. Simulation studies also show superior performance of the proposed method in finite samples.

Analyzing Associations Between Chronic Disease Prevalence and Neighborhood Quality Through Google Street View Images.

Deep learning and, specifically, convoltional neural networks (CNN) represent a class of powerful models that facilitate the understanding of many problems in computer vision. When combined with a reasonable amount of data, CNNs can outperform traditional models for many tasks, including image classification. In this work, we utilize these powerful tools with imagery data collected through Google Street View images to perform virtual audits of neighborhood characteristics. We further investigate different architectures for chronic disease prevalence regression through networks that are applied to sets of images rather than single images. We show quantitative results and demonstrate that our proposed architectures outperform the traditional regression approaches.

Survival analysis with functions of mismeasured covariate histories: the case of chronic air pollution exposure in relation to mortality in the nurses' health study.

Environmental epidemiologists are often interested in estimating the effect of functions of time-varying exposure histories, such as the 12-month moving average, in relation to chronic disease incidence or mortality. The individual exposure measurements that comprise such an exposure history are usually mis-measured, at least moderately, and, often, more substantially. To obtain unbiased estimates of Cox model hazard ratios for these complex mis-measured exposure functions, an extended risk set regression calibration method for Cox models is developed and applied to a study of long-term exposure to the fine particulate matter (PM2.5) component of air pollution in relation to all-cause mortality in the Nurses' Health Study. Simulation studies under several realistic assumptions about the measurement error model and about the correlation structure of the repeated exposure measurements were conducted to assess the finite sample properties of this new method, and found that the method has good performance in terms of finite sample bias reduction and nominal confidence interval coverage.