Lead time and overdiagnosis.

In this issue of the Journal, Etzioni et al. (1) suggest a novel approach to estimating overdiagnosis in breast cancer. However, there is a key assumption in their method regarding the nature of overdiagnosis that is unlikely to hold and leads to an underestimate of the overdiagnosis rate. To understand this assumption, we need to go back to basic definitions. Lead time is the time from detection of preclinical cancer by screening to detection of clinical (symptomatic) cancer in the absence of screening. An overdiagnosed cancer is a cancer detected by screening that would not have presented clinically during that person’s lifetime in the absence of screening. We define two types of preclinical cancer detected on screening, progressive and nonprogressive, which are linked to two types of overdiagnosis described by Welch and Black (2). A progressive preclinical cancer would present as clinical cancer in the person’s lifetime in the absence of both screening and death from a competing risk. A person with progressive preclinical cancer is overdiagnosed if the person dies from a competing risk before the cancer presents clinically. In contrast, a nonprogressive preclinical cancer would not present as clinical cancer in a person’s lifetime in the absence of both screening and death from a competing risk. A person with nonprogressive preclinical cancer is always overdiagnosed because the cancer never progresses to a clinical state, or even regresses. (Spontaneous breast cancer regression has been observed [3] and could result from a variety of mechanisms, including normalization of disrupted signals from adjacent tissues [4].) Importantly, only progressive preclinical cancers are related to lead time, because the definition of lead time requires clinical presentation of cancer in the absence of screening. In computing the overdiagnosis rate, Etzioni et al. (1) use estimates of mean lead time based on models that assume that all preclinical cancers are progressive. (Technically these models allow for an infinite lead time, which could, in theory, capture nonprogressive preclinical cancer; however, in practice, the usual lead time distributions, such as exponential, have little probability mass in the upper tails, so practically the preclinical cancers under these models are progressive.) Although Etzioni et al. recognize this limitation, they do not acknowledge that it could potentially yield a large bias. To quantitatively investigate this bias, we extended the classic mathematical model for cancer development in three screening states (healthy, progressive preclinical, and clinical) (5,6) to include progressive and nonprogressive preclinical states. We generated hypothetical data under this model, and then we fit the model under the assumption of only progressive preclinical cancer. Let w(x) = κ x4 denote the probability of entering the preclinical state at age x. Let λ exp(–λ u) denote the distribution of time u in the progressive preclinical state; this is an exponential distribution, so the mean lead time in the progressive preclinical state is 1/ λ. Let π denote the probability a preclinical cancer is nonprogressive. Let β denote the probability of detecting preclinical cancer on the screening. For simplicity we consider a single screening of a crosssection of persons ages a = 50, 55, 60, 65 with follow-up for five years after screening. Under our model, the probability that screening at age a detects preclinical cancer is: