Semiparametric Estimation of Time-Dependent: ROC Curves for Longitudinal Marker Data

One approach to evaluating the strength of association between a longitudinal marker process and a key clinical event time is through predictive regression methods such as a time-dependent covariate hazard model. For example, a time-varying covariate Cox model specifies the instantaneous risk of the event as a function of the time-varying marker and additional covariates. In this manuscript we explore a second complementary approach which characterizes the distribution of the marker as a function of both the measurement time and the ultimate event time. Our goal is to flexibly extend the standard diagnostic accuracy concepts of sensitivity and specificity to explicitly recognize both the timing of the marker measurement and the timing of disease. The accuracy of a longitudinal marker can be fully characterized using time-dependent receiver operating characteristic (ROC) curves. We detail a semiparametric estimation method for time-dependent ROC curves that adopts a regression quantile approach for longitudinal data introduced by Heagerty and Pepe (1999}. We extend the work of Heagerty and Pepe (1999} by developing asymptotic distribution theory for the ROC estimators where the distributional shape for the marker is allowed to depend on covariates. To illustrate our method, we analyze pulmonary function measurements among cystic fibrosis subjects to assemble a case-control study and estimate ROC curves that assess how well the pulmonary function measurement can distinguish subjects that progress to death from subjects that remain alive. Comparing the results from our semiparametric analysis to a fully parametric method discussed by Etzioni and Pepe (1999} suggests that the ability to relax distributional assumptions may be important in practice

Marginal Modeling of Multilevel Binary Data with Time-Varying Covariates

We propose and compare two approaches for regression analysis of multilevel binary data when clusters are not necessarily nested: a GEE method that relies on a working independence assumption coupled with a three-step method for obtaining empirical standard errors; and a likelihood-based method implemented using Bayesian computational techniques. Implications of time-varying endogenous covariates are addressed. The methods are illustrated using data from the Breast Cancer Surveillance Consortium to estimate mammography accuracy from a repeatedly screened population

Survival Model Predictive Accuracy and ROC Curves

The predictive accuracy of a survival model can be summarized using extensions of the proportion of variation explained by the model, or R^2, commonly used for continuous response models, or using extensions of sensitivity and specificity which are commonly used for binary response models. In this manuscript we propose new time-dependent accuracy summaries based on time-specific versions of sensitivity and specificity calculated over risk sets. We connect the accuracy summaries to a previously proposed global concordance measure which is a variant of Kendall\u27s tau. In addition, we show how standard Cox regression output can be used to obtain estimates of time-dependent sensitivity and specificity, and time-dependent reciever operating characteristic (ROC) curves. Semi-parametric estimation methods appropriate for both proportional hazards and non-proportional hazards data are introduced, evaluated in simulations, and illustrated using two familiar survival data sets

Partly Conditional Survival Models for Longitudinal Data

It is common in longitudinal studies to collect information on the time until a key clinical event, such as death, and to measure markers of patient health at multiple follow-up times. One approach to the joint analysis of survival and repeated measures data adopts a time-varying covariate regression model for the event time hazard. Using this standard approach the instantaneous risk of death at time t is specified as a possibly semi-parametric function of covariate information that has accrued through time t. In this manuscript we decouple the time scale for modeling the hazard from the time scale for accrual of available longitudinal covariate information. Specifically, we propose a class of models that condition on the covariate information through time s and then specifies the conditional hazard for times t where t \u3e s. Our approach parallels the “partly conditional” models proposed by Pepe and Couper (1997} for pure repeated measures applications. Estimation is based on the use of estimating equations applied to clusters of data formed through the creation of derived survival times that measure the time from measurement of covariates to the end of follow-up. Patient follow-up may be terminated either by the occurrence of the event or by censoring. The proposed methods allow a flexible characterization of the association between a longitudinal covariate process and a survival time, and facilitate the direct prediction of survival probabilities in the time-varying covariate setting

Robust Inference for the Stepped Wedge Design

Based on a permutation argument, we derive a closed form expression for an estimate of the treatment effect, along with its standard error, in a stepped wedge design. We show that these estimates are robust to misspecification of both the mean and covariance structure of the underlying data-generating mechanism, thereby providing a robust approach to inference for the treatment effect in stepped wedge designs. We use simulations to evaluate the type I error and power of the proposed estimate and to compare the performance of the proposed estimate to the optimal estimate when the correct model specification is known. The limitations, possible extensions, and open problems regarding the method are discussed

Motor cortex organization after stroke is related to side of stroke and level of recovery.

The present study hypothesized that side of stroke and level of recovery influence motor system organization after stroke.Functional MRI was performed on 14 control subjects and 21 patients with chronic stroke during index finger tapping (control subjects, right; patients, recovered side).On functional MRI, stroke patients with right arm involvement showed (1) significantly smaller activation in contralateral motor cortexes compared with control subjects; (2) smaller ipsilateral (nonstroke) premotor and larger contralateral (stroke-side) sensorimotor activation compared with patients with left arm involvement, although electromyogram across groups was similar; and (3) 2.7-fold-larger contralateral sensorimotor cortex activation, ventrally, in those with full recovery compared with those with partial recovery, despite similar tapping force, frequency, range of motion, and electromyogram between groups. Supplementary motor area activation was unrelated to level of recovery.After stroke that causes mild to moderate initial impairment and mild residual hand weakness, cortical organization varies with side of injury and with final motor status. The findings may have implications for treatment after stroke