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The use of surrogate markers to examine the effectiveness of a treatment has the potential to decrease study length and identify effective treatments more quickly. Most available methods to investigate the usefulness of a surrogate marker involve restrictive parametric assumptions and tend to focus on settings where the surrogate is measured at a single point in time. However, in many clinical settings, the potential surrogate marker is often measured repeatedly over time, and thus, the surrogate marker information is a trajectory of measurements. In addition, it is often difficult in practice to correctly specify the relationship between a treatment, primary outcome, and surrogate marker trajectory. In this paper, we propose a model-free definition for the proportion of the treatment effect on the primary outcome that is explained by the treatment effect on the longitudinal surrogate markers. We propose three novel flexible methods to estimate this proportion, develop the asymptotic properties of our estimators, and investigate the robustness of the estimators under multiple settings via a simulation study. We apply our proposed procedures to an AIDS clinical trial dataset to examine a trajectory of CD4 counts as a potential surrogate.

Valid estimation of treatment effects from observational data requires proper control of confounding. If the number of covariates is large relative to the number of observations, then controlling for all available covariates is infeasible. In cases where a sparsity condition holds, variable selection or penalization can reduce the dimension of the covariate space in a manner that allows for valid estimation of treatment effects. In this article, we propose matching on both the estimated propensity score and the estimated prognostic scores when the number of covariates is large relative to the number of observations. We derive asymptotic results for the matching estimator and show that it is doubly robust, in the sense that only one of the two score models need be correct to obtain a consistent estimator. We show via simulation its effectiveness in controlling for confounding and highlight its potential to address nonlinear confounding. Finally, we apply the proposed procedure to analyze the effect of gender on prescription opioid use using insurance claims data.

Studying multiple outcomes simultaneously allows researchers to begin to identify underlying factors that affect all of a set of diseases (i.e., shared etiology) and what may give rise to differences in disorders between patients (i.e., disease subtypes). In this work, our goal is to build risk scores that are predictive of multiple phenotypes simultaneously and identify subpopulations at high risk of multiple phenotypes. Such analyses could yield insight into etiology or point to treatment and prevention strategies. The standard canonical correlation analysis (CCA) can be used to relate multiple continuous outcomes to multiple predictors. However, in order to capture the full complexity of a disorder, phenotypes may include a diverse range of data types, including binary, continuous, ordinal, and censored variables. When phenotypes are diverse in this way, standard CCA is not possible and no methods currently exist to model them jointly. In the presence of such complications, we propose a semi-parametric CCA method to develop risk scores that are predictive of multiple phenotypes. To guard against potential model mis-specification, we also propose a nonparametric calibration method to identify subgroups that are at high risk of multiple disorders. A resampling procedure is also developed to account for the variability in these estimates. Our method opens the door to synthesizing a wide array of data sources for the purposes of joint prediction.