Limitations of the Odds Ratio in Gauging the Performance of a Diagnostic or Prognostic Marker

A marker that is strongly associated with outcome (or disease) is often assumed to be effective for classifying individuals according to their current or future outcome. However, for this to be true, the associated odds ratio must be of a magnitude rarely seen in epidemiological studies. An illustration of the relationship between odds ratios and receiver operating characteristic (ROC) curves shows, for example, that a marker with an odds ratio as high as 3 is in fact a very poor classification tool. If a marker identifies 10 percent of controls as positive (false positives) and has an odds ratio of 3, then it will only correctly identify 25 percent of cases as positive (true positives). Moreover, the authors illustrate that a single measure of association such as an odds ratio does not meaningfully describe a marker’s ability to classify subjects. Appropriate statistical methods for assessing and reporting the classification power of a marker are described. The serious pitfalls of using more traditional methods based on parameters in logistic regression models are illustrated.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

Analyzing Bivariate Survival Data with Interval Sampling and Application to Cancer Epidemiology

In medical follow-up studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as the outcomes to identify the progression of a disease. In cancer studies interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme where the first failure event (cancer onset) is identified within a calendar time interval, the time of the initiating event (birth) can be retrospectively confirmed, and the occurrence of the second event (death) is observed sub ject to right censoring. To analyze this type of bivariate failure time data, it is important to recognize the presence of bias arising due to interval sampling. In this paper, nonparametric and semiparametric methods are developed to analyze the bivariate survival data with interval sampling under stationary and semi-stationary conditions. Numerical studies demonstrate the proposed estimating approaches perform well with practical sample sizes in different simulated models. We apply the proposed methods to SEER ovarian cancer registry data for illustration of the methods and theory.