Population physiologically-based pharmacokinetic (PBPK) models have come to play a key role in toxicological dose-response assessments, but can be computationally intensive to calibrate. The purpose of this study is to apply global sensitivity analysis (GSA) to ascertain which PBPK model parameters are nonidentifiable, and therefore can be assigned fixed values in Bayesian parameter estimation, increasing computational efficiency with minimal bias. We illustrate this approach using a published human population PBPK model for acetaminophen (APAP) and its two major metabolites APAP-glucuronide and APAP-sulfate. The Morris Elementary Effects method and variance-based Sobol indices (estimated using three different algorithms) were used to determine the sensitivity of parameters in the original model. Unsupervised hierarchical clustering was used to distinguish between sensitive and insensitive parameters. We compared Bayesian model calibration results using the “original” versus “original sensitive” parameters. We then expanded our GSA to encompass all PBPK parameters, including those fixed in the published model, comparing the model calibration results using “all” versus “all sensitive” parameters. The three variance-based GSA estimators gave similar results, which different from the results of the Morris method. We found that 12 of the 21 original parameters have low sensitivity, and could be fixed to improve computational efficiency without discernable changes in prediction accuracy or precision. We further found 10 additional sensitive parameters among the parameters that were previously fixed in the published PBPK model. Adding these additional sensitive parameters improved model performance beyond that of the original publication, while maintaining similar computational efficiency. We conclude that GSA provides an objective, transparent, and reproducible approach to improve the performance and computational efficiency of PBPK models.