Estimating lead‐time bias in lung cancer diagnosis of patients with previous cancers

Surprisingly, survival from a diagnosis of lung cancer has been found to be longer for those who experienced a previous cancer than for those with no previous cancer. A possible explanation is lead‐time bias, which, by advancing the time of diagnosis, apparently extends survival among those with a previous cancer even when they enjoy no real clinical advantage. We propose a discrete parametric model to jointly describe survival in a no‐previous‐cancer group (where, by definition, lead‐time bias cannot exist) and in a previous‐cancer group (where lead‐time bias is possible). We model the lead time with a negative binomial distribution and the post–lead‐time survival with a linear spline on the logit hazard scale, which allows for survival to differ between groups even in the absence of bias; we denote our model Logit‐Spline/Negative Binomial. We fit Logit‐Spline/Negative Binomial to a propensity‐score matched subset of the Surveillance, Epidemiology, and End Results–Medicare linked data set, conducting sensitivity analyses to assess the effects of key assumptions. With lung cancer–specific death as the end point, the estimated mean lead time is roughly 11 months for stage I&II patients; with overall survival, it is roughly 3.4 months in stage I&II. For patients with higher‐stage lung cancers, the mean lead time is 1 month or less for both outcomes. Accounting for lead‐time bias reduces the survival advantage of the previous‐cancer group when one exists, but it does not nullify it in all cases.