Bayesian Inference for the Lead Time in Periodic Cancer Screening

Abstract

This article develops a probability distribution for the lead time in periodic cancer screening examinations. The general aim is to allow statistical inference for a screening program's lead time, the length of time the diagnosis is advanced by screening. The program's lead time is distributed as a mixture of a point mass and a piecewise continuous distribution. Simulation studies using the HIP (Health Insurance Plan for Greater New York) study's data provide estimates of different characteristics of a screening program under different screening frequencies. The components of this mixture represent two aspects of screening's benefit, namely, a reduction in the number of interval cases and the extent by which screening advanced the age of diagnosis. We present estimates of these two measures for participants in a breast cancer screening program. We also provide the mean, mode, variance, and density curve of the program's lead time. The model can provide policy makers with important information regarding the screening period, frequency, and the endpoints that may serve as surrogates for the benefit to women who take part in a periodic screening program. Though the study focuses on breast cancer screening, it is also applicable to other kinds of chronic disease.

The Lead Time Distribution When Lifetime is Subject to Competing Risks in Cancer Screening

“…Throughout this paper, the time variable t represents the participating individual's age; the random variable T represents human lifetime. We briefly review the probability model in Wu et al 2007, but with new notation, which allows a clearer presentation for the new model in Section 3.…”

“…For policy purposes, it is important to estimate how large this proportion may be. Wu et al (2007) derived the probability distribution of lead time for the whole diseased cohort, including both screen-detected cases and intervalincident cases, when the human lifetime was treated as a fixed value. The model includes Prorok's result as a special case (no interval cases).…”

“…In this paper, we first review briefly the method for deriving lead time distribution developed by Wu et al 2007 (Section 2). We then extend the method by allowing the lifetime T , and the number of screens to be random variables.…”

Modelling and Inference in Screening: Exemplification with the Faecal Occult Blood Test

“…We will briefly review the probability distribution of the lead time derived under a progressive disease model (Wu et al, 2007(Wu et al, , 2009a as in Section 2.1. The distribution for the lead time was derived and presented in equation 6 (Wu et al, 2007(Wu et al, , 2009a.…”

“…Prevention efforts in the population requires reliable estimates of the sensitivity of the test, the sojourn time of the disease, the transition probabilities from the disease-free state to the preclinical state, the lead time of the disease and the indirect effects in the screening per se in the estimates of rates of the disease. The aim of this chapter is to introduce the concept of probability modelling in colorectal cancer screening, and the statistical methods developed by the authors in this area (Wu et al, 2005(Wu et al, , 2007(Wu et al, , 2009a(Wu et al, , 2009b. We will estimate these essential components from a population based perspective.…”