**Accelerating Monte-Carlo Power Studies through Parametric Power Estimation**

Sebastian Ueckert, Mats O. Karlsson, Andrew C. Hooker

Pharmacometrics Research Group, Dept. Pharmaceutical Biosciences, Uppsala University, Sweden

**Objectives:** To evaluate the performance of a novel algorithm for faster sample size calculations and compare it to sample size calculations through standard Monte-Carlo simulations and estimations.

**Methods: **Power versus sample size curves for 3 different pharmacometric models (disease progression, PK auto-induction and count) were calculated with 2 different methods: (i) an algorithm using pure Monte-Carlo simulations and estimations (MC) and (ii) a novel parametric power estimation (PPE) algorithm. All calculations were repeated for a differing number of Monte-Carlo samples (100, 200, 300, 400 and 500) and the power estimates from both algorithms were evaluated for accuracy and precision. Power estimates obtained with the MC algorithm and 10,000 Monte-Carlo samples served as a reference.

*MC algorithm:* For each sample size, N datasets are simulated, re-estimated with a full and reduced model and the log-likelihood ratio test is carried out. The power estimate for a specific sample size is the number of dataset where the null hypothesis was rejected.

*PPE algorithm:* For a complete power versus sample size curve, N dataset are simulated and re-estimated with full and reduced model. The resulting N log-likelihood ratios are used to estimate the non-centrality parameter of the theoretical non-central chi-square distribution [1] and the power for a specific sample size is determined from the cumulative distribution function. Simple scaling of the non-centrality parameter yields the full power curve.

**Results:** For all 3 examples investigated the median power estimates from both algorithms were in good agreement with the reference. However, the power estimates from the PPE algorithm displayed a small bias between 0 and minus 2%.

For one sample size the PPE algorithm required about 50% fewer Monte-Carlo samples to achieve the same precision of the power estimates. More importantly, the full power versus sample size curve was derived from one single non-centrality parameter estimate. Thus, compared to a power curve calculated with the MC algorithm at 8 grid points, the PPE algorithm reduces the number of required Monte-Carlo samples by a factor of 16.

**Conclusions:** The PPE algorithm can obtain full power versus sample size curves with drastically reduced computational effort than through pure Monte-Carlo simulations and estimations.

**Acknowledgements:** This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under Grant Agreement no 602552.

**References:**

[1] R. F. Engle, “Wald, likelihood ratio, and Lagrange multiplier tests in econometrics,” in Handbook of Econometrics, vol. Volume 2, Zvi Griliches and Michael D. Intriligator, Ed. Elsevier, 1984, pp. 775–826.