A Stochastic Model for Calibrating the Survival Benefit of Screen-Detected Cancers

Abstract

Comparison of the survival of clinically detected and screen-detected cancer cases from either population-based service screening programs or opportunistic screening is often distorted by both lead-time and length biases. Both are correlated with each other and are also affected by measurement errors and tumor attributes such as regional lymph node spread. We propose a general stochastic approach to calibrate the survival benefit of screen-detected cancers related to both biases, measurement errors, and tumor attributes. We apply our proposed method to breast cancer screening data from one arm of the Swedish Two-County trial in the trial period together with the subsequent service screening for the same cohort. When there is no calibration, the results—assuming a constant (exponentially distributed) post-lead-time hazard rate (i.e., a homogeneous stochastic process)—show a 57% reduction in breast cancer death over 25 years. After correction, the reduction was 30%, with approximately 12% of the overestimation being due to lead-time bias and 15% due to length bias. The additional impacts of measurement errors (sensitivity and specificity) depend on the type of the proposed model and follow-up time. The corresponding analysis when the Weibull distribution was applied—relaxing the assumption of a constant hazard rate—yielded similar findings and lacked statistical significance compared with the exponential model. The proposed calibration approach allows the benefit of a service cancer screening program to be fairly evaluated. This article has supplementary materials online.

Keywords:

• Calibration
• Lead-time bias
• Length bias
• Screening
• Survival

Acknowledgments

We would like to thank Dr. Jane Warwick, senior statistician at the Centre for Cancer Prevention, Wolfson Institute of Preventive Medicine, Queen Mary University of London, for help with technical English editing. This work was financially supported by the grants from National Science Council (NSC 97-2314-B-002-019-MY3).