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

Abstract

This paper extends the previous probability model for the distribution of lead time in periodic cancer screening exams, namely, in that the lifetime T is treated as a random variable, instead of a fixed value. Hence the number of screens for a given individual is a random variable as well. We use the actuarial life table from the Social Security Administration to obtain the lifetime distribution, and then use this information to project the lead time distribution for someone with a future screening schedule. Simulation studies using the HIP study group data provide estimates of the lead time under different screening frequencies. The projected lead time has two components: a point mass at zero (corresponding to interval cases detected between screening exams) and a continuous probability density. We present estimates of the projected lead time for participants in a breast cancer screening program. The model is more realistic and can inform optimal screening frequency. This study focuses on breast cancer screening, but is applicable to other kinds of cancer screening also.

Inference of Long-Term Screening Outcomes for Individuals with Screening Histories

“…(21) For the lifetime distribution, we used the conditional lifetime density for females, currently aged 60, 70, and 80, using the actuarial life table from the Social Security Administration (SSA) website (see the beginning of this section). The derivation of the conditional probability density function (pdf) is given in Wu et al (2012). The marginal probabilities of each of the four cases P(Case i|H K 1 , T ≥ t K 1 , HIP) with standard errors are reported in Table 1.…”

“…We applied our model to the Health Insurance Plan of the Greater New York (HIP) breast cancer screening data (Shapiro et al 1988), using for a lifetime distribution that derived from the actuarial lifetable on the Social Security Administration (SSA) website 3 ; see Wu et al (2012) for a detailed procedure on using this lifetime distribution.…”

Over Diagnosis in Screening: Does It Make Sense?

“…This is because over diagnosis means those patients whose clinical symptoms would not have appeared before death. The probability of over diagnosis can be expressed mathematically as a function of the three key parameters, the (future) screening schedule or frequency, and the expected lifetime of patients at their current age [4][5][6][7]. This approach builds up a strict probability formula for the estimation or prediction of over diagnosis.…”

“…b). the expected lifetime needs to be estimated accurately [6]. Much research has been done to estimate the three key parameters, and new approaches still appear constantly these days [5].…”

“…Much research has been done to estimate the three key parameters, and new approaches still appear constantly these days [5]. The expected lifetime distribution for males and females can be derived from the actuarial life table in the US Government Social Security Administration's website [6]. The estimated probability of over diagnosis for breast cancer is about 6-9%, very close to the results in the cumulative incidence study by Zackrisson, et al [1], showing that the probability modeling is correct besides theoretical proof.…”