Obese children under three years of age without obese parents are at low risk for obesity in adulthood, but among older children, obesity is an increasingly important predictor of adult obesity, regardless of whether the parents are obese. Parental obesity more than doubles the risk of adult obesity among both obese and nonobese children under 10 years of age.

ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials.

This paper looks at a new approach to the design and analysis of Phase 1 clinical trials in cancer. The basic idea and motivation behind the approach stem from an attempt to reconcile the needs of dose-finding experimentation with the ethical demands of established medical practice. It is argued that for these trials the particular shape of the dose toxicity curve is of little interest. Attention focuses rather on identifying a dose with a given targeted toxicity level and on concentrating experimentation at that which all current available evidence indicates to be the best estimate of this level. Such an approach not only makes an explicit attempt to meet ethical requirements but also enables the use of models whose only requirements are that locally (i.e., around the dose corresponding to the targeted toxicity level) they reasonably well approximate the true probability of toxic response. Although a large number of models could be contemplated, we look at a particularly simple one. Extensive simulations show the model to have real promise.