Efficient interval estimation for age-adjusted cancer rates

Abstract

The age-adjusted cancer rates are defined as the weighted average of the age-specific cancer rates, where the weights are positive, known, and normalized so that their sum is 1. Fay and Feuer developed a confidence interval for a single age-adjusted rate based on the gamma approximation. Fay used the gamma approximations to construct an F interval for the ratio of two age-adjusted rates. Modifications of the gamma and F intervals are proposed and a simulation study is carried out to show that these modified gamma and modified F intervals are more efficient than the gamma and F intervals, respectively, in the sense that the proposed intervals have empirical coverage probabilities less than or equal to their counterparts, and that they also retain the nominal level. The normal and beta confidence intervals for a single age-adjusted rate are also provided, but they are shown to be slightly liberal. Finally, for comparing two correlated age-adjusted rates, the confidence intervals for the difference and for the ratio of the two age-adjusted rates are derived incorporating the correlation between the two rates. The proposed gamma and F intervals and the normal intervals for the correlated age-adjusted rates are recommended to be implemented in the Surveillance, Epidemiology and End Results Program of the National Cancer Institute.

Paranasal sinus squamous cell carcinoma incidence and survival based on Surveillance, Epidemiology, and End Results data, 1973 to 2009

“…The differences in rates between men and women and among whites, African Americans, and individuals of all other racial groups were examined by calculating rate ratios (RRs) and the corresponding 95% CIs, as described by Tiwari et al 17 Changes in incidence over time were expressed as the annual percentage change (APC) and were examined further using the Joinpoint Regression Program (Control and Population Sciences, National Cancer Institute, Bethesda, Md). The APC was calculated by fitting a least-squares regression line to the natural logarithm of the rates using the calendar year as a regressor variable.…”

Burden of cervical cancer in the United States, 1998-2003

“…We did not examine in situ cervical tumors, which have not been reportable to NPCR and SEER since 1996. All analyses were limited to cervical carcinomas by using specific histologies defined in Table 1 18 Rates were calculated in SEER*Stat, standardized to the 2000 US Standard Population, and expressed per 100,000 women; limits of confidence intervals were 95% and were based on the Gamma method using the modification described by Tiwari et al 19 Age-adjusted rates of invasive cervical carcinoma incidence are reported for race, Hispanic ethnicity, histology, stage, and US census region. Racial groups examined include white, black, and Asian-Pacific Islander (API); 'all races' also includes other and unknown categories.…”

Breast cancer incidence among American Indian and Alaska Native women: US, 1999-2004

“…Rates and 95% modified g confidence intervals (CIs) were generated by using SEER*Stat software version 6.3.6. 24,25 Percentage distributions also were age-adjusted. Rate ratios with 95% CIs were provided for regional comparisons of incidence rates between AI/AN and NHW populations ( Table 1).…”