Animals are still widely used in drug development and safety tests, despite evidence for their lack of predictive value. In this regard, we recently showed, by producing Likelihood Ratios (LRs) for an extensive data set of over 3,000 drugs with both animal and human data, that the absence of toxicity in animals provides little or virtually no evidential weight that adverse drug reactions will also be absent in humans. While our analyses suggest that the presence of toxicity in one species may sometimes add evidential weight for risk of toxicity in another, the LRs are extremely inconsistent, varying substantially for different classes of drugs. Here, we present further data from analyses of other species pairs, including non-human primates (NHPs), which support our previous conclusions, and also show in particular that test results inferring an absence of toxicity in one species provide no evidential weight with regard to toxicity in any other species, even when data from NHPs and humans are compared. Our results for species including humans, NHPs, dogs, mice, rabbits, and rats, have major implications for the value of animal tests in predicting human toxicity, and demand that human-focused alternative methods are adopted in their place as a matter of urgency.