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Quantitative estimates of cancer risk generally involve low-dose extrapolation based on an exponential dose-response model for dichotomous response data. Frequently more than one data set is available. If a careful analysis of the biological issues indicates that more than one of the available data sets could be used in the quantitative estimate of cancer risk, it is reasonable to think of combining the data. Before combining data, however, it would be prudent to test whether the data sets are compatible with a common dose-response model. If they are not, it could be concluded that an underlying biological factor is responsible. If they are statistically compatible, the decision to combine data sets based on biological issues would be reinforced. A statistical test based on the generalized likelihood ratio method is proposed for evaluating the compatibility of different data sets with a common dose-response model. This method of constructing a statistical test and the associated asymptotic theory is consistent with the approach used by GLOBAL86 (R. B. Howe, K. S. Crump, and C. Van Landingham, GLOBAL86: A Computer Program to Extrapolate Quantal Animal Toxicity Data to Low Doses, K. S. Crump & Co., Ruston, LA, 1986) for estimating the confidence limits that are used as a basis for quantitative estimates.