Bias in the proportionate mortality ratio analysis of small study populations: a case on analyses of radiation and mesothelioma

Our plain-English summary of Bias in the proportionate mortality ratio analysis of small study populations: a case on analyses of radiation and mesothelioma, by J.Y. Zhou (International Journal of Radiation Biology, 2014).

The study

• Author: J.Y. Zhou
• Journal: International Journal of Radiation Biology
• Published: 2014;90(11):1075-9
• Cited by: 9 articles, as counted by NIH iCite
• Read it: PubMed · Publisher

Abstract

Unlabelled: Abstract Purpose: To quantify bias in the proportionate mortality ratio (PMR) analysis of small study populations and develop a bias correction methodology.

Materials And Methods: Bias in the PMR analysis of small study populations is quantified through algebraic derivation. A simulation procedure is developed to evaluate the relationship between bias and study population size. A recently published PMR analysis of radiation and mesothelioma among 329 deceased registrants in the United States Transuranium and Uranium Registries (USTUR) is used as an illustrated example.

Results: The proportionate mortality ratios are biased and overestimated in small population studies; the smaller the study population, the larger the overestimation. As such, the average overestimation of PMR for mesothelioma in the analyses of radiation and mesothelioma in USTUR is 7.2% (95% confidence interval = 5.1%, 9.7%); the PMR overestimation is 22.5% (95% confidence interval = 16.8%, 29.1%) when stratified by quartiles of radiation doses.

Conclusions: The degree of PMR small sample bias is mainly determined by the sample size ratio, which is defined as the ratio of the sample size to the number of disease categories in the reference population. Correction for the bias is recommended when the sample size ratio is less than 5. The quantification and correction algorithm of the PMR small sample bias developed in this research supplements the PMR methodology.

In plain English

This single-author methods paper examined the proportionate mortality ratio (PMR), which compares the share of deaths from one cause in a study group with that share in a reference population. Using algebra and simulation, the author argued that PMRs are overestimated in small groups, where many disease categories have no deaths. As an example, the author reanalyzed Gibb et al. (2013), a study of 329 deceased registrants of the United States Transuranium and Uranium Registries with seven mesothelioma deaths. There, 64 of 119 disease categories had no deaths. Simulations for the 293 deaths with dose data estimated an average PMR overestimation of 7.2% (95% CI 5.1% to 9.7%), and 22.5% (95% CI 16.8% to 29.1%) for dose-quartile-sized groups. After the author's small-sample correction, the mesothelioma PMR changed from 62.40 (95% CI 25.09 to 128.75) to 56.35 (95% CI 22.66 to 116.26). The all-cancer and the biliary, liver and gall bladder cancer PMRs were no longer statistically significant. The author recommended correction when the number of deaths divided by the number of reference-population disease categories is below 5.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Methodological study: algebraic derivation and computer simulation of bias in proportionate mortality ratios, applied as a reanalysis of a previously published PMR study (Gibb et al. 2013)
• Who was studied: Data from the Gibb et al. 2013 study: 329 deceased registrants of the United States Transuranium and Uranium Registries (USTUR), with seven mesothelioma deaths. Of these, 293 had cumulative external radiation dose data. USTUR registrants are volunteer body donors, typically former U.S. Department of Energy nuclear workers.
• Exposure: The reanalyzed data concern cumulative external radiation dose, grouped into low and high doses and into quartiles. This article did not study asbestos exposure.
• Main results:
  • In the reanalyzed USTUR data, 64 of the 119 disease categories (54%) had no observed deaths.
  • In simulations (5,000 simulated datasets per sample size) for a sample of 293 deaths, the average PMR overestimation was 7.2% (95% CI 5.1% to 9.7%).
  • In simulations for low and high cumulative external radiation dose groups (147 cases in each), the average PMR overestimation was 13.2% (95% CI 9.4% to 17.7%).
  • In simulations for dose-quartile groups (fewer than 74 cases in each, as printed), the average PMR overestimation was 22.5% (95% CI 16.8% to 29.1%).
  • The mesothelioma PMR reported by Gibb et al., based on 7 deaths (62.40; 95% CI 25.09 to 128.75), became 56.35 (95% CI 22.66 to 116.26) after the author's small-sample bias correction.
  • The Gibb et al. PMR for biliary, liver and gall bladder cancer (2.94; 95% CI 1.08 to 6.39) became 2.66 (95% CI 0.98 to 5.77) after correction, which was not statistically significant.
  • The Gibb et al. all-cancers PMR (1.33; 95% CI 1.09 to 1.60) became 1.20 (95% CI 0.98 to 1.45) after correction, which was not statistically significant.
  • The Gibb et al. asbestosis PMR (23.22; 95% CI 2.81 to 83.90) became 20.97 (95% CI 2.54 to 75.76) after correction.
  • In simulations for the 114 cancer deaths, the average overestimation of the proportionate cancer mortality ratio (PCMR) was 5.5% (95% CI 2.4% to 10.1%).
  • The sample size ratio of the Gibb study population was 2.46 (293/119) for PMR and 3.08 (114/37) for PCMR.
• The authors' conclusion: The author concluded that PMRs are overestimated in small study populations. The author recommended correcting for this bias when the sample size ratio (sample size divided by the number of disease categories in the reference population) is less than 5. The author stated that the paper's algorithm to quantify and correct the bias supplements the PMR methodology.
• Limitations the authors state:
  • The author stated that USTUR registrants are not a representative sample of all nuclear workers, and that the small, non-representative population limits its value for epidemiological analysis.

Topics

The National Library of Medicine indexes this study under subjects our site covers: Mesothelioma.

Medical terms in this study, explained in our Lexicon: Mesothelioma, confidence interval.

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