Proportional hazards models and age-period-cohort analysis of cancer rates

Abstract

Age-period-cohort (APC) analysis is widely used in cancer epidemiology to model trends in cancer rates. We develop methods for comparative APC analysis of two independent cause-specific hazard rates assuming that an APC model holds for each one. We construct linear hypothesis tests to determine whether the two hazards are absolutely proportional or proportional after stratification by cohort, period, or age. When a given proportional hazards model appears adequate, we derive simple expressions for the relative hazards using identifiable APC parameters. To demonstrate the utility of these new methods, we analyze cancer incidence rates in the United States in blacks versus whites for selected cancers, using data from the National Cancer Institute's Surveillance, Epidemiology, and End Results Program. The examples illustrate that each type of proportionality may be encountered in practice.

Figure 1

Descriptive analysis of cancer incidence rates in blacks and whites, for selected cancers, using data from the NCI SEER database. A) Female bladder cancer; data for APC analysis included all 2186 cases in blacks and 29,148 cases in whites; panel shows age-specific rates over time for two selected age groups. B) Female colorectal cancer; APC analysis included 17,460 cases in blacks and 129,975 cases in whites; panel shows longitudinal age-specific incidence rates for three selected birth cohorts. C) Male kidney cancer; APC analysis included 5,161 cases in blacks and 44,050 cases in whites; panel shows age-specific rates over time for two selected age groups. D) Female pancreas cancer; APC analysis included 4,316 cases in blacks and 28,463 cases in whites; panel shows cross-sectional age-specific rates for two selected calendar periods.

Figure 2

Black-versus-white incidence rate ratios and 95% point-wise confidence limits for selected cancers, estimated from SEER using comparative APC analysis. Models were fitted to data summarized in Figure 1. A) Female bladder cancer; panel shows fitted rate ratio from PH-A model. B) Female colorectal cancer, fitted rate ratios from PH-L model versus birth cohort. C) Male kidney cancer, fitted rate ratios from PH-T model versus age at diagnosis. D) Female pancreas cancer, fitted rate ratios from PH-X model versus period of diagnosis.

Figure 3

Black-versus white incidence rates and incidence rate ratios for oral cancer in males, by age and calendar year, based on 5,516 cases in blacks and 42,468 cases in whites in SEER, using comparative APC analysis. A) Observed rates by age for two selected calendar periods. B) Fitted rate ratios, with corresponding 95% point-wise confidence limits, derived using separate APC models. Estimates are shown for the first and last calendar periods included in the analyses.

Figure 4

The model selection problem in comparative APC analysis.