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

Our plain-English summary of Re: Bias in the proportionate mortality ratio analysis of small study populations: A case on analyses of radiation and mesothelioma, by M.J. Hein, M.K. Schubauer-Berigan (International Journal of Radiation Biology, 2015).

The study

• Authors: M.J. Hein, M.K. Schubauer-Berigan
• Journal: International Journal of Radiation Biology
• Published: 2015;91(11):908-10
• Type of article: Letter, Comment
• Read it: PubMed · Publisher

In plain English

This letter to the editor concerned a statistical method, not people exposed to asbestos or radiation. The authors responded to Zhou (2014), who used a small study of radiation and mesothelioma (Gibb et al. 2013) as an example. Zhou had claimed that the NIOSH LTAS.NET software gives biased proportionate mortality ratios (PMRs) when few deaths are spread across many cause-of-death categories. With a worked example, the authors called Zhou's proposal a logical fallacy: combining categories should not change other categories' PMRs, and under the usual method it did not. They then simulated 10,000 samples of 128 deaths across 46 causes. The usual PMR averaged around 1 for every cause, as expected of an unbiased method. Zhou's method averaged below 1 for common causes (0.903, versus 0.999 for the usual method, for the commonest) and above 1 for rare causes, but those rare-cause averages excluded samples with zero deaths, where it gives no PMR. The authors concluded that LTAS.NET PMRs are not biased and suggested that Zhou's approach introduces a downward bias. They noted that small groups analysed with many cause categories give very wide confidence intervals.

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: Letter to the editor responding to Zhou (2014), with a worked numerical example and a computer (statistical) simulation
• Who was studied: Simulated data only: a standard population of 10 million deaths assigned to 46 causes, and 10,000 random samples of 128 decedents. The ratio of deaths to causes was matched to a small study (Gibb et al. 2013) that Zhou had used as an example.
• Main results:
  • In the authors' worked example, combining cause categories 4 and 5 (zero study deaths) with category 3 left the usual PMRs for categories 1 and 2 unchanged. The combined category 3 to 5 had a PMR of 0.42, a weighted average of the original PMRs. The authors stated that combining categories should not change the PMRs for other categories, and called Zhou's proposal a logical fallacy.
  • In the simulation, the usual PMR averaged around 1 for all 46 causes of death.
  • Zhou's proposed PMR averaged below 1 (downwardly biased) for causes 1 to 6, where zero-death samples were absent or rare. For cause 1 (population proportion 0.25), the mean usual PMR was 0.999 and the mean Zhou PMR was 0.903.
  • Zhou's proposed PMR averaged above 1 for the rarer causes 17 to 46, where zero-death samples were common. Zhou's method gives no PMR for a sample with zero deaths from a cause, so its averages for rarer causes are based on fewer than 10,000 samples. The usual method counts those samples as PMR 0.
  • For the rarest causes (27 to 46), more than half of the 10,000 simulated samples had zero deaths.
  • Wherever both methods could be calculated, the mean ratio of Zhou's PMR to the usual PMR was always below one.
• The authors' conclusion: The authors concluded that PMR estimates from LTAS.NET are not biased. They suggested that Zhou's approach of analysing only causes with deaths, chosen after looking at the data, introduces a downward bias in PMR estimates.
• Limitations the authors state:
  • The authors noted that a PMR for one cause depends on the other categories: an excess in one cause must be offset by a deficit in another.
  • The authors noted that when small study groups are analysed with large numbers of categories, confidence intervals are very wide and PMRs may often be zero.

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.

Related studies

• Bias in the proportionate mortality ratio analysis of small study populations: a case on analyses of radiation and mesothelioma — J.Y. Zhou (2014)
• Analyses of radiation and mesothelioma in the US Transuranium and Uranium Registries — H. Gibb, K. Fulcher, et al. (2013)
• Evaluation of Confounding and Selection Bias in Epidemiological Studies of Populations Exposed to Low-Dose, High-Energy Photon Radiation — M.K. Schubauer-Berigan, A. Berrington de Gonzalez, et al. (2020)
• Solid cancer mortality associated with chronic external radiation exposure at the French atomic energy commission and nuclear fuel company — C. Metz-Flamant, E. Samson, et al. (2011)
• Risk of cancer from occupational exposure to ionising radiation: retrospective cohort study of workers in France, the United Kingdom, and the United States (INWORKS) — D.B. Richardson, E. Cardis, et al. (2015)
• Inter-rater agreement for a retrospective exposure assessment of asbestos, chromium, nickel and welding fumes in a study of lung cancer and ionizing radiation — E.A. Seel, D.D. Zaebst, et al. (2007)

Browse more research in International Journal of Radiation Biology, or return to medical research.