James Hanley, Ph.D.
Department of Epidemiology, Biostatistics and Occupational Health
McGill University, Montreal, Canada
In cancer screening trials, or comparisons involving regions that did/did not introduce population-based screening programs, the mortality reductions are usually summarized by an overall (single-number) mortality reduction. But this overall mortality reduction is a combination of minimal reductions in the first years, larger ones after some years, and waning ones starting some years after the last screen. Because it involves differing ages and years at cohort-entry, it also averages smaller reductions among those screened a few times and larger ones among those screened several times. Age at the first screen may also matter.
Statistical models—albeit over-simplistic and over-parametrized—that used convolutions of the impacts of successive rounds of screening were proposed in the 1960s, and extended in the 1990s to help plan screening trials. However, their central principles—derived from the very concept of early detection—have not been used in the analysis—or re-analysis—of the data from early/more recent screening trials. The prevailing study-design and data-analysis practices still use the same test statistics and single-summary estimates that were used in 1972. Even today, trialists cling to the—logically untenable—assumption that a successful screening program will produce proportional hazards, even though the only screening that can generate proportional hazards is the one that is so ineffective that the hazard ratio is 1 over all follow-up time from year 1 through year 30 of follow-up.
Liu et al. (IntStatRev2015) developed a model for the expected reductions in each (Age,Year) cell of a Lexis diagram. It describes the effect of one round of screening with 3 parameters (1) when in follow-up time the reduction produced by this one round is maximal (2) how large this reduction is and (3) how dispersed in follow-up time the reductions are. Using the screening history in each (Age,Year) cell as a design matrix, reductions from previous screens are combined. Ultimately (if follow-up extends far enough beyond the last screen) the resulting hazard ratio curves have bathtub shapes that are modulated by the screening histories. Used with follow-up-year-specific data, this model considerably refined the results in various screening trials.
We illustrate this model using data from screening trials in prostate, colon, lung, and ovarian cancer, and—for breast cancer—using population data from Denmark (Njor, JMedScr2015). We show how analyses of such screening data can be extended/refined to incorporate the numbers and timing of screening invitations in relation to where in the Lexis diagram the deaths do/do not occur.
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