[Paper Review] A Millennium Bug Still Bites Public Health - An Illustration Using Cancer Mortality

Martina Fu, David Todem+2 more|arXiv (Cornell University)|Jan 29, 2014

Global Cancer Incidence and Screening8 references4 citations

TL;DR

This paper identifies significant bias in cancer mortality rate comparisons caused by the U.S. Year 2000 Population Standard in age-standardization, overestimating prostate cancer mortality by 12–91% and underestimating case fatality by 9–78%. It proposes a novel mean reference population method using mathematical optimization to minimize squared bias, offering a more accurate, universally applicable alternative to arbitrary standard populations.

ABSTRACT

Accurate estimation of cancer mortality rates and the comparison across cancer sites, populations or time periods is crucial to public health, as identification of vulnerable groups who suffer the most from these diseases may lead to efficient cancer care and control with timely treatment. Because cancer mortality rate varies with age, comparisons require age-standardization using a reference population. The current method of using the Year 2000 Population Standard is standard practice, but serious concerns have been raised about its lack of justification. We have found that using the US Year 2000 Population Standard as reference overestimates prostate cancer mortality rates by 12-91% during the period 1970-2009 across all six sampled U.S. states, and also underestimates case fatality rates by 9-78% across six cancer sites, including female breast, cervix, prostate, lung, leukemia and colon-rectum. We develop a mean reference population method to minimize the bias using mathematical optimization theory and statistical modeling. The method corrects the bias to the largest extent in terms of squared loss and can be applied broadly to studies of many diseases.

Motivation & Objective

• To investigate the impact of using the U.S. Year 2000 Population Standard as a reference in age-standardization on cancer mortality rate estimation.
• To identify systematic bias introduced by this standard, particularly in prostate cancer and case fatality rate comparisons.
• To develop a statistically principled method that minimizes overall squared bias in age-adjusted rate estimation across populations.
• To provide a universally applicable, theoretically justified alternative to the arbitrary choice of standard reference populations in public health reporting.

Proposed method

• The paper formulates an optimization problem to find a reference population that minimizes the sum of squared deviations between age-adjusted rates and crude rates across all populations.
• It uses quadratic programming to solve the constrained optimization problem, deriving a system of equations involving Lagrange multipliers to estimate optimal weights for the reference population.
• The method constructs a mean reference population as a convex combination of observed population age structures, ensuring it reflects the central tendency of the compared populations.
• It proves that the optimal solution is unique and globally minimal under convexity assumptions, avoiding local minima.
• A statistical sampling approach is also proposed to numerically approximate the optimal weights, especially useful when analytical solutions are intractable.
• The method is validated using SEER data from six U.S. states and case fatality data from six cancer sites, comparing results against the Year 2000 Standard and crude rates.

Experimental results

Research questions

• RQ1 Does the use of the U.S. Year 2000 Population Standard as a reference population introduce systematic bias in age-standardized cancer mortality rates?
• RQ2 How does the choice of reference population affect the ranking and interpretation of cancer mortality and case fatality rates across different populations?
• RQ3 Can a mathematically optimal reference population be constructed to minimize overall bias in age-adjusted rate estimation?
• RQ4 To what extent does the proposed mean reference population method reduce bias compared to the current standard practice?
• RQ5 Is the proposed method robust and generalizable across different diseases and population groups?

Key findings

• The use of the U.S. Year 2000 Population Standard overestimates prostate cancer mortality rates by 12–91% across six U.S. states from 1970 to 2009.
• The same standard underestimates case fatality rates by 9–78% across six cancer sites, including female breast, cervix, prostate, lung, leukemia, and colon-rectum.
• The proposed mean reference population method minimizes the overall squared bias among all convex linear combinations of the compared populations.
• The method produces a unique, globally optimal reference population that is statistically and mathematically justified, avoiding the arbitrariness of existing standards.
• The mean reference population closely resembles the age profiles of all populations in the comparison, enhancing interpretability and fairness.
• The method is broadly applicable to disease rate comparisons beyond cancer, offering a more reliable foundation for public health policy and health disparities research.