dOFV distribution plot (left panel, Fig. 2)

dOFV quantile distributions were suggested as a method to diagnose the appropriateness of bootstrap uncertainty distributions [15] and were applied to SIR. The principle behind this diagnostic is that if the parameter vectors resampled by SIR were the true uncertainty, the difference between their OFV and the OFV obtained at the final parameter estimates of the model should follow a Chi square distribution. The degrees of freedom (df) of this distribution is equal to the number of estimated parameters for an unconstrained fixed effects model [30], but the exact df is unknown for NLMEM. Indeed, it is expected to be equal to or below the number of estimated parameters, notably due to the estimation of random effects and other bounded parameters, which may not account for full degrees of freedom [31]. Plotting the dOFV distributions obtained from the M proposal samples and from the m SIR resamples against a Chi square distribution with degrees of freedom equal to the number of estimated parameters informs about the adequacy of the proposal distribution and M/m. If the dOFV distribution obtained from the M samples is at or close to the Chi square distribution, it means that the proposal distribution is close to the true distribution; if it is far above or below, it means that it is quite different from the true distribution. If the dOFV distribution obtained from the m SIR resamples is at or below the Chi square distribution, M/m may have been sufficient and should be further investigated with the temporal trends plot; if the distribution is above the Chi square distribution, M/m was not sufficient. The mean of the dOFV distribution can be used to quantitatively compare the distributions; it corresponds to the degrees of freedom if the distribution is a Chi square distribution.