MLE and Bayesian Inference of Age‐Dependent Sensitivity and Transition Probability in Periodic Screening

Abstract

SummaryThis article extends previous probability models for periodic breast cancer screening examinations. The specific aim is to provide statistical inference for age dependence of sensitivity and the transition probability from the disease free to the preclinical state. The setting is a periodic screening program in which a cohort of initially asymptomatic women undergo a sequence of breast cancer screening exams. We use age as a covariate in the estimation of screening sensitivity and the transition probability simultaneously, both from a frequentist point of view and within a Bayesian framework. We apply our method to the Health Insurance Plan of Greater New York study of female breast cancer and give age-dependent sensitivity and transition probability density estimates. The inferential methodology we develop is also applicable when analyzing studies of modalities for early detection of other types of progressive chronic diseases.

A limited review of over diagnosis methods and long-term effects in breast cancer screening

“…We first get the information of the sensitivity, the transition probability density and the sojourn time distribution from the HIP data by using the likelihood model we developed with a Bayesian inference. These three key parameters were reported through the 2000 Bayesian posterior samples [12]. Then we substitute in these 2000 posterior samples into the four probability formulae to estimate the probabilities of each category under different screening frequencies and different initial ages.…”

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

“…Thus inference on the lead time distribution requires estimates of β(t), w(t) and q(x), which are available from the Health Insurance Plan for Greater New York (HIP) study using likelihoods and Bayesian inference (Wu et al 2005). The parametric model was:…”

When Sensitivity is a Function of Age and Time Spent in the Preclinical State in Periodic Cancer Screening

“…The screening sensitivity may depend on a variety of factors, including age, position, location and size of the tumor, the experience of the radiologist, etc. For example, recent studies indicate that the sensitivity of mammography increases with age at diagnosis (Wu et al, 2005;Shapiro et al, 1988;Miller et al, 1992aMiller et al, , 1992b, attributable to the fact that breast tissue tends to be more dense and fibrous in younger women, and more soft and fatty in older women (Kerlikowske, et al, 1996).…”

“…In Wu, et al (2005), the sensitivity was modeled as a function of age, while transition probability is agedependent as well. Previous result are extended by investigating changes in the sensitivity from simultaneous variation of age and time spent in the preclinical stage.…”

“…Wu et al (2005) showed that sensitivity is monotone increasing with age, but intuitively, sensitivity is also a function of the time one has spent in the preclinical stage. This allows us to infer sensitivity at a late stage, just before symptoms manifest.…”