Journal of Data Science

Linear regression models are widely used in empirical studies. When serial correlation is present in the residuals, generalized least squares (GLS) estimation is commonly used to improve estimation efficiency. This paper proposes the use of an alternative estimator, the approximate generalized least squares estimators based on high-order AR(p) processes (GLS-AR). We show that GLS-AR estimators are asymptotically efficient as GLS estimators, as both the number of AR lag, p, and the number of observations, n, increase together so that $p=o({n^{1/4}})$ in the limit. The proposed GLS-AR estimators do not require the identification of the residual serial autocorrelation structure and perform more robust in finite samples than the conventional FGLS-based tests. Finally, we illustrate the usefulness of GLS-AR method by applying it to the global warming data from 1850–2012.

Statistical learning methods have been growing in popularity in recent years. Many of these procedures have parameters that must be tuned for models to perform well. Research has been extensive in neural networks, but not for many other learning methods. We looked at the behavior of tuning parameters for support vector machines, gradient boosting machines, and adaboost in both a classification and regression setting. We used grid search to identify ranges of tuning parameters where good models can be found across many different datasets. We then explored different optimization algorithms to select a model across the tuning parameter space. Models selected by the optimization algorithm were compared to the best models obtained through grid search to select well performing algorithms. This information was used to create an R package, EZtune, that automatically tunes support vector machines and boosted trees.

Identifying treatment effect modifiers (i.e., moderators) plays an essential role in improving treatment efficacy when substantial treatment heterogeneity exists. However, studies are often underpowered for detecting treatment effect modifiers, and exploratory analyses that examine one moderator per statistical model often yield spurious interactions. Therefore, in this work, we focus on creating an intuitive and readily implementable framework to facilitate the discovery of treatment effect modifiers and to make treatment recommendations for time-to-event outcomes. To minimize the impact of a misspecified main effect and avoid complex modeling, we construct the framework by matching the treated with the controls and modeling the conditional average treatment effect via regressing the difference in the observed outcomes of a matched pair on the averaged moderators. Inverse-probability-of-censoring weighting is used to handle censored observations. As matching is the foundation of the proposed methods, we explore different matching metrics and recommend the use of Mahalanobis distance when both continuous and categorical moderators are present. After matching, the proposed framework can be flexibly combined with popular variable selection and prediction methods such as linear regression, least absolute shrinkage and selection operator (Lasso), and random forest to create different combinations of potential moderators. The optimal combination is determined by the out-of-bag prediction error and the area under the receiver operating characteristic curve in making correct treatment recommendations. We compare the performance of various combined moderators through extensive simulations and the analysis of real trial data. Our approach can be easily implemented using existing R packages, resulting in a straightforward optimal combined moderator to make treatment recommendations.