Sample size for detection of drug effect using item level and total score models for Unified Parkinson’s Disease Rating Scale data
Siv Jönsson (1), Shuying Yang (2), Chao Chen (2), Elodie L. Plan (1), Mats O. Karlsson (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden. (2) GlaxoSmithKline, London, UK
Objectives: The aim of this investigation was to estimate the sample size required to reach 80% power for detection of a drug effect using an item response model (IRM) and a total score model (TSM), both describing longitudinal 44-item Unified Parkinson’s Disease Rating Scale (UPDRS) data in advanced Parkinson’s disease (PD) patients.
Methods: A longitudinal IRM [1] based on data in early and advanced PD was the starting point. The IRM contains 3 latent variables, for each latent variable a placebo time course described with an exponential model estimating the extent (Extent) and onset rate (Onset) of symptom relief over time, and for all a joint exposure independent symptomatic (SY) drug effect: Baseline+(Extent+SY)·(1-exp[-Onset·time]). In this investigation, the IRM was re-estimated for data from advanced PD patients only, comprising of baseline and longitudinal UPDRS recordings collected in a randomized study comparing ropinirole to placebo as adjunct therapy to L-dopa over 24 weeks at individually titrated doses between 6 and 24 mg/day [2]. For the corresponding data a TSM was developed based on patients with complete records of the 44 UPDRS items. Model estimations were performed using NONMEM 7.3. The Monte-Carlo Mapped Power (MCMP) method [3] implemented in PsN was used for power calculations as follows: both models were re-estimated excluding the SY drug effect, and the individual difference in objective function values between the full (with drug effect) and reduced (without drug effect) models (iΔOFV) were extracted. The observed iΔOFVs were employed in the MCMP. The MCMP was stratified based on treatment, a 5% significance level was applied for 1 degree of freedom (ΔOFV 3.84) and 10,000 Monte Carlo samples were drawn. To support the ΔOFV cut-off used in the MCMP approach, a randomisation test [4] was performed for TSM using PsN: based on only placebo or combined placebo and ropinirole data, 1000 data sets were generated, each with a randomly assigned treatment indicator, i.e. placebo or ropinirole on a 1:1 basis, and for each data set the full and reduced model was estimated.
Results: In total 31,212 (190 patients) and 33,951 (201 patients) UPDRS records from placebo and ropinirole treatment, respectively, were used for the IRM. For the TSM corresponding numbers were 663 (189 patients) and 727 (200 patients) records from placebo and ropinirole treatment, respectively. The newly developed TSM was in agreement with the previous IRM, i.e. exponential placebo time course and an exposure independent SY drug effect. The drug effect was statistically significant (p<0.001) with ΔOFVs of -210 and -37 for IRM and TSM, respectively. Type I error rates based on the randomisation test employing sampling from only placebo and combined placebo and ropinirole treated patients were similar, and sampling from all patients indicated that using a ΔOFV cut-off of 3.84 would be appropriate. At the 3.84 cut-off the sample size required for 80% power in detecting a drug effect was 54% lower using IRM compared with TSM. The reduction in required sample size tended to be larger when applying a higher cut-off value, with a sample size reduction of 69% at ΔOFV of 10.8.
Conclusions: The results show that employing IRM in the analysis of UPDRS data is clearly beneficial from a study size perspective compared with a TSM analysis, pointing toward a sample size reduction of approximately 50% for detection of a drug effect with 80% power using the current data set. Previous investigations where IRM has been compared with alternative models in PD and other disease areas reported reductions in sample size varying from 18% to 49% [5-8]. The special MCMP approach taken here is beneficial given the use of observed iΔOFVs, but due to the low number of patients the estimated sample size is expected to be less precise [3].
References:
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