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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Regul Toxicol Pharmacol. Author manuscript; available in PMC 2009 April 1.
Published in final edited form as:
PMCID: PMC2423201

MtBE and cancer in animals: Statistical issues with Poly-3 survival adjustments for lifetime studies

Dear Sir

Goodman, et al. (2007) implemented the poly-3 survival adjustment based on maximum lifetime, discounting significant tumor findings in Sprague-Dawley rats exposed to the oxygenated gasoline additive, methyl-tertiary-butyl ether (MtBE) (Belpoggi et al., 1995, 1997, 1998). The poly-3 survival adjustment (Bailer and Portier, 1988; Portier and Bailer, 1989) was empirically derived from spontaneous tumor data using a series of 2-year studies in F344 rats and B6C3F1 mice (Portier, Hedges, Hoel, 1986), adhering to the National Toxicology Program’s carcinogenesis bioassay protocol (Bucher, 2002). The operating characteristics of the poly-3 adjustment beyond a two-year time frame have never been validated. Therefore, implementation of this approach to studies longer than two years must be carefully considered. Importantly, it can be shown that applying the poly-3 adjustment to longer term studies without proper regard for its assumptions and limitations may result in erroneous conclusions.

Based on a Weibull distribution for tumor onset, the poly-3 survival adjustment for animal i is

(ti/T)3if animal i was free of the tumor and died before the end of the study
1if animal i had the tumor or survived to the end of the study

where ti is the time at death from study start and T is the length of the study. Survival adjustment terms are summed within each dose group to give the effective number of animals at risk. While Portier et al. (1986) showed that tumor onset could be modeled well by the Weibull distribution up to 118 weeks of age, there is no evidence that tumors occurring beyond 2 years on study follow this distribution. In lifetime studies that exceed two years, such as the MtBE study and others conducted by the Ramazzini Foundation (Soffritti et al., 2002), using T=maximum lifetime rather than two years dramatically reduces the contribution of tumor-free animals to the effective number of animals at risk. If the control group, in particular, contains more tumor-free animals than do the treated groups, this may lead to failure to detect a significant increase in tumors, as we show below. Furthermore, when T=maximum lifetime, the poly-3 weights and the resulting analyses are highly influenced by the longest living animal; this animal may have lived substantially longer than all of the others in the study.

The authors used T=174 weeks – much longer than 2 years (T=104 weeks) – in three separate cases, dealing with the timing of when Leydig cell tumors (LCTs) occurred in the test animals. Using the same three cases, we explored using T=104 weeks in the poly-3 adjustment. We assigned a poly-3 survival adjustment of 1 to each animal that died free of LCTs after two years. Results for Case 1 are presented in Table 1.

Table 1
A Poly-3 adjusted Analysis of Leydig Cell Tumors (LCTs) With T=104 Using the Data for Case 1 from Goodman et al. (2007).

In our reanalysis, both the high-exposure group comparison with the control group and the trend test were significant (pH=0.026 and pT=0.008, respectively). Our reanalyses of Cases 2 and 3 yielded nearly identical results (Case 2: pH=0.023 and pT=0.007; Case 3: pH=0.024 and pT=0.008). In the Table 6 analysis for Case 1 presented by Goodman et al. (2007), neither the individual pairwise p-values (pL=0.41 and pH=0.19) nor the test for trend (pT=0.17) were significant; Cases 2 and 3 were similar.

The discrepancies between our analyses and the authors’ analyses are a direct result of the poly-3 weights assigned to animals dying without an LCT. For example, in our analyses, an animal dying at 2 years without an LCT receives a weight of 1; the animal is assumed to have lived long enough to contribute fully to the evaluation. The authors would assign that same animal a weight of (104/174)3=0.21; the animal contributes 1/5 as much to the risk of developing an LCT as an animal dying at 174 weeks. To illustrate the impact, in Case 1, the effective number of animals at risk in the control, 250 mg/kg, and 1000 mg/kg groups in our analyses are 37.8, 37.6, and 40.4, respectively, whereas they are 11.6, 13.1 and 22.7 in the authors’ analyses. Because the tumor-free animals were assigned relatively small weights in the authors’ analyses, the effective numbers of animals at risk were reduced, increasing the poly-3 LCT incidences. There were more tumor-free animals in the control group than in the 1000 mg/kg group, so the poly-3 incidence in the control group was increased proportionately more than, and closer to, that in the 1000 mg/kg group. Thus, the authors did not detect a significant increase or trend.

We also note that p-values in Table 6 of Goodman et al. (2007) appear to be two-sided, even though the authors stated that they were one-sided.

After contacting Dr. Belpoggi, we analyzed the data using the exact death times and the poly-3 test as outlined above, resulting in pL=0.39, pH=0.03 and pT=0.01; these numbers do not fall within the range of p-values seen for the “extreme” cases chosen by Goodman et al. Incidentally, Portier, Hedges and Hoel (1986) evaluated the lethality and appropriate poly-k adjustment for interstitial cell tumors of the testes in Fischer 344 rats and found them to be clearly non-lethal with an estimated Weibull shape parameter of 4.1; hence a poly-4 test may be more appropriate here.

Finally, we are surprised that the authors were not able to obtain the death times from Dr. Belpoggi or from the Ramazzini Foundation web site, and we are equally surprised that the Journal of Regulatory Toxicology and Pharmacology would accept this article without the correct data included in the analysis.


Grace E. Kissling, PhD.

Biostatistics Branch, NIEHS

Chief Statistician for the NTP

Christopher J. Portier, PhD.

Associate Director, NIEHS

Director, Office of Risk Assessment Research

James Huff, PhD.

Associate Director for Chemical Carcinogenesis, NIEHS


This research was supported by the Intramural Research Program of the NIH, National Institute of Environmental Health Sciences.


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Contributor Information

Grace E. Kissling, Biostatistics Branch, NIEHS, Chief Statistician for the NTP.

Christopher J. Portier, Associate Director, NIEHS, Director, Office of Risk Assessment Research.

James Huff, Associate Director for Chemical Carcinogenesis, NIEHS.


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