Thao-Nguyen Pham (1),(2), John Maringwa (1), Maria Luisa Sardu (1), Richard C Franzese (1), Anna Largajolli(1), S Y Amy Cheung (1)
(1) Certara, Integrated Drug Development, Princeton, NJ, USA (2) Normandie Univ, UNICAEN, CNRS, ISTCT, GIP CYCERON, 14000 Caen, France
Objectives:
A conventional model-based meta-analysis (MBMA) integrates aggregate data (AD) from multiple studies and may provide more power to detect small, but clinically significant, effects than an individual clinical trial alone [1]. At the same time, MBMA using only AD might be sometimes subject to bias, as it is not able to fully capture the influences of patient/subject level covariates [2].
Meta-Analysis using individual patient/subject data (IPD) combines raw data from different studies and is considered the “gold standard” [3]. Including IPD in MBMA may facilitate more complex modeling structures by informing the understanding of inter-subject variability and the impact of patient/subject-level covariates on the endpoint. However, IPD for historical literature trial or competitor data is not always accessible, potentially leading to biased results in case of IPD-only meta-analysis [3]. Therefore, supplementing the available IPD with AD for those studies where IPD is not available may help [3]. We evaluate the practical statistical question of how to appropriately combine IPD and AD, focusing on the implementation of such models using the gnls function in the nlme statistical R package [4]. To our best knowledge, there are limited examples of applications of this approach in literature.
Methods:
Four studies investigating the effect of tofacitinib in rheumatoid arthritis (RA) were selected [5] and used as the basis for illustrating the proposed approach. Each study comprised a placebo arm and four dose levels: 2, 6, 10 and 20 mg/day enrolling 20 to 60 patients in each arm. The outcome of interest was the (mean) Disease Activity Score (DAS) change from baseline at the primary time point. Reported standard deviations (SDs), as measures of precision associated with the mean change from baseline, were also available.
For these four studies, there was no IPD reported in the literature hence simulated IPD was generated assuming a normal distribution of the change from baseline in DAS score based on reported mean and SDs for each dose level of each study.
AD from three studies was combined with IPD from one other study (all four permutations were investigated). First, we fitted a typical regression Emax model to the single study IPD and estimated the residual error variance from this model (Step 1). In the second, validation step, an MBMA based on the three AD studies was developed (Step 2). In the third and final step we then combined the single IPD study and three AD studies and fitted an integrated model in which the residual error variance associated with IPD was fixed to the value obtained in Step 1. The residual error variance for the AD was fixed to the reported measures of precision as is typically done in MBMA. To validate the approach, we compared the estimated variance components (weights) in Step 3 with those obtained in Steps 1 and 2. R package nlme (version 3.1-153) was used for model fitting in R (version 4.1.1) [4].
Results:
The R package nlme was successfully applied to combine IPD and AD in one common model. The results indicated that the estimated variance components associated with IPD and AD in the composite model in which both types of data were combined (Step 3), were the same as the variance components when IPD and AD were analyzed separately in Steps 1 and 2 respectively. This demonstrates that the combined model could reflect the appropriate weighting associated with each of these two different levels of information.
All the four permutations using one study with IPD and the remaining three studies with AD showed consistent results in terms of parameter estimates. The results were also in agreement with the conventional MBMA based on all studies AD.
Conclusions:
An integrated MBMA combining IPD and AD using a three-step approach was successfully developed with the nlme package in R. This procedure could be expanded to include more studies and to investigate more complex scenarios such as cases where covariates are incorporated, inter-study variability components are added, or when structural components of the models differ between IPD and AD. Furthermore, the additional benefit of combining IPD and AD may be evaluated through simulations by adjusting different parameters such as number of subjects in IPD study, magnitude of residual error, or ratio of studies with IPD and AD information.
References:
[1] Mould DR. Model-based meta-analysis: an important tool for making quantitative decisions during drug development. Clin Pharmacol Ther. 2012 Sep;92(3):283-6. doi: 10.1038/clpt.2012.122. PMID: 22910485.
[2] Gillespie WR, MBMA of combined individual and aggregate data: strategies and issues, 7th American Conference on Pharmacometrics 2016
[3] Riley RD, Lambert PC, Staessen JA, Wang J, Gueyffier F, Thijs L, Boutitie F. Meta-analysis of continuous outcomes combining individual patient data and aggregate data. Stat Med. 2008 May 20;27(11):1870-93. doi: 10.1002/sim.3165. PMID: 18069721.
[4] R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/ 2021
[5] Home – ClinicalTrials.gov
[6] Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team. nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-155 2022
Reference: PAGE 30 (2022) Abstr 10088 [www.page-meeting.org/?abstract=10088]
Poster: Methodology - Other topics