Special Considerations

Test for Combining Two Datasets for the Same Endpoint

BMDS does not include a formal test for similarity of dose response across covariate values (e.g., across class variables like species or sex). EPA’s categorical regression software, CatReg, has that capability.

However, the following procedure can be used in BMDS if there are dose-response data for two experiments that the user is considering combining (e.g., for the two sexes within a species, or two species, etc.).

  1. Choose a single model to consider for both datasets.

  2. Model the two datasets separately. For each run, record the following:

    • Maximum log-likelihood for each dataset. Add the two log-likelihoods (one from each dataset) to get the summed log-likelihood. The fitted model log-likelihoods are reported in the Analysis of Deviance (dichotomous endpoints) or Likelihoods of Interest (continuous endpoints) tables.

    • The number of unconstrained parameters for each dataset. Add those numbers from each run to get the summed unconstrained parameters.

  3. Combine the data from the two experiments and model them together. Record the following:

    • The maximum log-likelihood for the combined dataset. This will be the combined log-likelihood. The fitted model log-likelihoods are reported in the Analysis of Deviance (dichotomous endpoints) or Likelihoods of Interest (continuous endpoints) tables.

    • The number of unconstrained parameters for the combined dataset. This will be the combined unconstrained parameters.

  4. Subtract the combined log-likelihood from the summed log-likelihood. Then, multiply the difference by 2.

  5. Compare the value from Step 4 to a Chi-square distribution. The degrees of freedom for that Chi-square distribution will be the difference between the summed unconstrained parameters (Step 2) and the combined unconstrained parameters (Step 3).

If the value from Step 4 is in the tail (say, greater than the 95th percentile) of the Chi-square distribution in question, then reject the null hypothesis that the two sets have the same dose-response relationship. If rejection occurs, then infer that it is not proper to combine the two datasets.