A note on the catch-up time method for estimating lead or sojourn time in prostate cancer screening

Abstract

Models of cancer screening assume that cancers are detectable by screening before being diagnosed clinically through symptoms. The duration of this preclinical phase is called sojourn time, and it determines how much diagnosis might be advanced in time by the screening test (lead time). In the catch-up time method, mean sojourn time or lead time are estimated as the time needed for cumulative incidence in an unscreened population to catch up with the detection rate (prevalence) at a first screening test. The method has been proposed as a substitute of the prevalence/incidence ratio in the case of prostate cancer where incidence cannot be treated as a constant. A model is proposed to justify this estimator. It is shown that this model is different from classic Markov-type models developed for breast cancer screening. In both models, the catch-up time method results in biased estimates of mean sojourn time.

Keywords: cancer screening; lead time; prostate cancer; sojourn time.

Figure 1

The catch-up time estimate for mean sojourn time. The graph shows the cumulative incidence of prostate cancer in the control arm from study entry in the Rotterdam section of ERSPC. The horizontal line represents the prevalence (4%) of preclinical prostate cancer at the first screening test. Cumulative incidence in the control arm catches up with prevalence after 8.16 years. The dashed line represents the quadratic approximation of cumulative incidence, 0.0034342704x + 0.0001796227x² used in the numerical example. Figure adapted from Finne et al. .

Figure 2

Relevant variables in screening models. Screening at time t may detect cancers with time of clinical diagnosis X > t and sojourn time Y > X − t, that is, with onset of preclinical disease Z < t. In case of detection, diagnosis has been advanced with lead time L.

Figure 3

Prostate cancer incidence after a screening test with sensitivity 1.0 as predicted by the classic model (13) with μ = 11.64 and the catch-up time model (14) with mean sojourn time μ = 6.80 compared with background incidence without screening. Background incidence as given in Figure 1.