Evaluating subject-level incremental values of new markers for risk classification rule

Estimation of treatment policies based on functional predictors

Biosignatures such as brain scans, mass spectrometry, or gene expression profiles might one day be used to guide treatment selection and improve outcomes. This article develops a way of estimating optimal treatment policies based on data from randomized clinical trials by interpreting patient biosignatures as functional predictors. A flexible functional regression model is used to represent the treatment effect and construct the estimated policy. The effectiveness of the estimated policy is assessed by furnishing prediction intervals for the mean outcome when all patients follow the policy. The validity of these prediction intervals is established under mild regularity conditions on the functional regression model. The performance of the proposed approach is evaluated in numerical studies.

PERFORMANCE GUARANTEES FOR INDIVIDUALIZED TREATMENT RULES

Because many illnesses show heterogeneous response to treatment, there is increasing interest in individualizing treatment to patients [11]. An individualized treatment rule is a decision rule that recommends treatment according to patient characteristics. We consider the use of clinical trial data in the construction of an individualized treatment rule leading to highest mean response. This is a difficult computational problem because the objective function is the expectation of a weighted indicator function that is non-concave in the parameters. Furthermore there are frequently many pretreatment variables that may or may not be useful in constructing an optimal individualized treatment rule yet cost and interpretability considerations imply that only a few variables should be used by the individualized treatment rule. To address these challenges we consider estimation based on l(1) penalized least squares. This approach is justified via a finite sample upper bound on the difference between the mean response due to the estimated individualized treatment rule and the mean response due to the optimal individualized treatment rule.

On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data

For modern evidence-based medicine, a well thought-out risk scoring system for predicting the occurrence of a clinical event plays an important role in selecting prevention and treatment strategies. Such an index system is often established based on the subject's 'baseline' genetic or clinical markers via a working parametric or semi-parametric model. To evaluate the adequacy of such a system, C-statistics are routinely used in the medical literature to quantify the capacity of the estimated risk score in discriminating among subjects with different event times. The C-statistic provides a global assessment of a fitted survival model for the continuous event time rather than focussing on the prediction of bit-year survival for a fixed time. When the event time is possibly censored, however, the population parameters corresponding to the commonly used C-statistics may depend on the study-specific censoring distribution. In this article, we present a simple C-statistic without this shortcoming. The new procedure consistently estimates a conventional concordance measure which is free of censoring. We provide a large sample approximation to the distribution of this estimator for making inferences about the concordance measure. Results from numerical studies suggest that the new procedure performs well in finite sample.