According to current policy, chemicals are evaluated for possible cancer risk to humans at low dose by testing in bioassays, where high doses of the chemical are given to rodents. Thus, risk is extrapolated from high dose in rodents to low dose in humans. The accuracy of these extrapolations is generally unverifiable, since data on humans is limited. However, it is feasible to examine the accuracy of extrapolations from mice to rats. If mice and rats are similar in respect to carcinogenesis, this provides some evidence in favor of inter-species extrapolations; conversely, if mice and rats are different, this casts doubt on the validity of extrapolations from mice to humans. Once measure of inter-species agreement is concordance, the percentage of chemicals that are classified the same way as to carcinogenicity in mice and rats. Observed concordance in NCI/NTP bioassays is around 75%, which may seem on the low side -- because mice and rats are closely related species tested under the same experimental conditions. Theoretically, observed concondance could under-estimate true concordance, due to measurement error in bioassays. Thus, bias in concordance is of policy interest. Expanding on previous work by Piegorsh et. al. (1992), we show that the bias in observed concordance can be either positive or negative: an observed concordance of 75% can arise if the true concordance is anything between 20% and 100%. In particular, observed concordance can seriously overestimate true concordance. A variety of models more or less fit the data, with quite different implications for bias. Therefore, given our present state of knowledge, it seems quite unlikely that true concordance can be determined from bioassay data.