Estimating the cumulative risk of false positive cancer screenings

When evaluating cancer screening it is important to estimate the cumulative risk of false positives from periodic screening. Because the data typically come from studies in which the number of screenings varies by subject, estimation must take into account dropouts. A previous approach to estimate the probability of at least one false positive in n screenings unrealistically assumed that the probability of dropout does not depend on prior false positives.

By redefining the random variables, we obviate the unrealistic dropout assumption. We also propose a relatively simple logistic regression and extend estimation to the expected number of false positives in n screenings.

We illustrate our methodology using data from women ages 40 to 64 who received up to four annual breast cancer screenings in the Health Insurance Program of Greater New York study, which began in 1963. Covariates were age, time since previous screening, screening number, and whether or not a previous false positive occurred. Defining a false positive as an unnecessary biopsy, the only statistically significant covariate was whether or not a previous false positive occurred. Because the effect of screening number was not statistically significant, extrapolation beyond 4 screenings was reasonable. The estimated mean number of unnecessary biopsies in 10 years per woman screened is.11 with 95% confidence interval of (.10,.12). Defining a false positive as an unnecessary work-up, all the covariates were statistically significant and the estimated mean number of unnecessary work-ups in 4 years per woman screened is.34 with 95% confidence interval (.32,.36).

Using data from multiple cancer screenings with dropouts, and allowing dropout to depend on previous history of false positives, we propose a logistic regression model to estimate both the probability of at least one false positive and the expected number of false positives associated with n cancer screenings. The methodology can be used for both informed decision making at the individual level, as well as planning of health services.