Estimating key parameters in periodic breast cancer screening—Application to the Canadian National Breast Screening Study data

Abstract

Problem statement: Breast cancer screening in women of younger age has been controversial. The screening sensitivities, transition probabilities and sojourn time distributions are estimated for females aged 40–49 years and 50–59 years separately, using the Canadian National Breast Screening Study (CNBSS) data. The purpose is to estimate the lead time distribution and the probability of not detecting the cancer early. Approach: Within the 40–49-year-old and 50–59-year-old cohorts separately, the age-independent statistical model was applied. Bayesian estimators along with 95% highest probability density (HPD) credible intervals (CI) were calculated. Bayesian hypothesis testing was used to compare the parameter estimates of the two cohorts. The lead time density was also estimated for both the 40–49 and 50–59-year-old cohorts. Results: The screening sensitivity, transition probability of the disease, and mean sojourn time were all found to increase with age. For the 40–49-year-old and 50–59-year-old cohorts, the posterior mean sensitivities were 0.70 (95% HPD-CI: 0.46, 0.93) and 0.77 (0.61, 0.93), respectively. The posterior mean transition probabilities were 0.0023 (0.0018, 0.0027) and 0.0031 (0.0024, 0.0038), while the posterior mean sojourn times were 2.55 (1.56, 4.26) years and 3.15 (2.12, 4.96) years. Bayes factors for the ratio of posterior probabilities that the respective parameter was larger vs. smaller in the 50–59-year-old cohort were estimated to be 2.09, 40.8 and 3.0 for the sensitivity, transition probability, and mean sojourn time, respectively. All three Bayes factors were larger than two, indicating greater than 2:1 odds in favor of the hypothesis that each of these parameters was greater in the 50–59-year-old cohort. The estimated mean lead times were 0.83 years and 0.96 years if the two cohorts were screened annually. Conclusions: The increase in sensitivity corresponds to an increase in the mean sojourn time. Breast cancer in younger women is more difficult to detect by screening tests and is more aggressive than breast cancer in older women. Women aged 50–59 tend to benefit more from screening compared with women aged 40–49.