Evaluation of a Random Sparse Sampling Design: An Assessment of Power and Bias Using Simulation

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Evaluation of a Random Sparse Sampling Design: An Assessment of Power and Bias Using Simulation

K. Kowalski (1), M. Hutmacher (2)

(1) Pfizer, Inc., Statistical Research Center, Ann Arbor, MI, USA; (2) Pfizer, Inc., Statistics, Skokie, IL, USA
oral presentation

Objectives: Assess power and sample size requirements for a population pharmacokinetic (PK) substudy of a phase III clinical trial using simulation.

Methods: A simulation study was conducted to determine the sample size (number of patients) that would achieve adequate power (i.e., >80%) to detect a 40% difference in oral drug clearance (CL) in a subpopulation of 5-10% of the total population. The simulations were based on a population PK model developed from phase I healthy volunteer data. The simulation model was a two-compartment model with first-order absorption. A sparse sampling design was proposed based on practical considerations and clinical convenience. It was anticipated that the sparse sampling design would not support fitting a two-compartment model. Thus, simulations were also conducted to assess bias in CL and the apparent steady-state volume of distribution (Vss) estimated from fitting a one-compartment model. The power and type I error rates for a likelihood ratio test on subpopulation differences in CL based on the one-compartment model were also assessed.

Results: The proposed design fitting a one-compartment model can provide accurate mean estimates of CL and Vss when the true underlying model is a two-compartment model. However, the size and power of the likelihood ratio test for subpopulation differences in CL are inflated when using the one-compartment model. The simulation results suggest that an approximate 9-point change in the objective function value corresponds to the 5% significance level rather than the commonly used c 2(1) critical value of 3.84.

Conclusions: In the presence of known model misspecification, likelihood ratio tests can be anti-conservative (inflated type I error rates) even when the analysis model provides a good fit and accurate estimates of the fixed effects (including covariate effects). Simulations can be used to assess whether sparse data can support fitting all the parameters of the assumed (simulation) model or whether a simpler (analysis) model may suffice. When a simpler (misspecified) model is considered for the analysis, simulations should be performed to assess bias in the key parameter estimates (e.g., covariate effects on CL). Furthermore, simulations should also be conducted under the null model (no covariate effects) to characterize the distribution of the likelihood ratio test as the type I error rates can be substantially inflated. Moreover, the power of the likelihood ratio test may also be inflated and can be adjusted based on the empirical distribution of the likelihood ratio test obtained from simulations under the null model.

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