A Combined Model-Based Meta-Analysis of Aggregated and Individual FEV1 Data From Randomized COPD Trials

Abstract

Model-based meta-analysis allows integration of aggregated-level data (AD) from different clinical trials in one model to assess population efficacy/safety. However, AD is limited in individual-level information, while individual-patient-level data (IPD) are hard to obtain. Combined modeling may take advantage of both sources. Chronic obstructive pulmonary disease (COPD) is a leading cause of poor health and death. This study established a combined ADIPD model of COPD clinical trials with forced expiratory volume in 1 s (FEV1) as an endpoint and explored methods for estimating interstudy variability (ISV), interindividual variability (IIV), and aggregation bias. Stochastic simulation and estimations (SSE) showed the best method in NONMEM to estimate ISV/IIV: using $LEVEL with equal weight of studies; for the AD part, ISVs from the AD model were fixed, estimating IIV with separate ETAs for each arm; the IPD part shared the fixed ISV and estimated IIV. An approximated normal distribution was derived for lognormal IIV to avoid aggregation bias. Covariate correlations were different at aggregated and individual levels, but did not introduce aggregation bias according to SSE. A separate AD model (published) and IPD model were built, then combined to form the ADIPD model. The ADIPD model included FEV1 baseline, disease progression, placebo effect, and Emax/constant dose-responses for 23 compounds. Identified covariate relationships: higher age, female, higher disease severity, non-current smoker related to lower baseline; higher baseline related to faster disease progression and higher drug effects. Covariate coefficients were estimated more precisely in the ADIPD model than the AD model. ADIPD modeling allows more informed clinical trial simulations for study design. Trial Registration: ClinicalTrials.gov identifier: NCT01053988 and NCT01054885.

Keywords: COPD; aggregated data; aggregation bias; combined modeling; individual‐patient data.

FIGURE 1

Comparison of different methods to estimate ISV/IIV in the combined model. SSE was repeated 100 times. The parameter estimates of different methods are shown in different colors. The notation in the figure: B: baseline; DPS: disease progression slope; OM: omega, random effect parameter for ISV/IIV; PMX: maximal placebo effect; PT50: time when placebo effect reaches 50%; SI: sigma, random effect for residual error model; TH: theta, fixed effect parameter; The method of best performance is highlighted in red rectangle. The version without y‐scale truncation of this figure is shown in Figure S2.

FIGURE 2

Simulations of distributions of individual parameter and aggregated parameter, use FEV1 baseline as an example for illustration. The individual parameter baseline was simulated following a lognormal distribution 1000 times with different sample sizes per arm, and the individual parameter distributions across all 1000 simulations are shown (left column). The distribution of the parameter mean was simulated by three ways: calculation of mean (the true distribution, red curve); same lognormal distribution as the individual parameter with scaled SD = (individual SD)/√N (green curve); and the approximate normal distribution (blue curve). The sample size of each arm was set as 20, 200, 1000, 5000.

FIGURE 3

(A) SSE results of aggregation bias caused by the lognormal distribution of IIV assumption. IPD model (red) and two AD models were applied to estimate parameters of baseline (lognormal IIV distribution) and disease progression slope (normal IIV distribution) using 100 simulated datasets. The simulated datasets of AD were obtained by averaging the simulated datasets of IPD. The two AD models were applied to the lognormal distribution (green) and the approximated normal distribution (blue) of baseline. The final panel (black bar) showed the difference in OFVs of the two AD models. (B) SSE results of aggregation bias caused by covariate correlation. The IPD model (red) and the AD model (green) were applied to estimate parameters of baseline (normal IIV distribution) and disease progression slope and covariates on baseline of 100 simulated datasets. The simulated datasets of AD were obtained by averaging the simulated datasets of IPD. TH_BAGE1 and TH_BSEX were covariate coefficients of age and sex on baseline respectively.

FIGURE 4

The simulation from the combined ADIPD model with two treatments (vilanterol 25 μg, vilanterol/fluticasone furoate 25/200 μg). The two treatments were applied to the same virtual population of 100 studies, 200 patients per study. The distributions of FEV1 on the 24th week were plotted. The black dashed lines are the density plots of the simulated overall populations across all the studies in each panel. The vertical lines represent the means of the simulated overall populations across all the studies in each panel, and the values of mean and variance of the simulated overall population were noted for each panel. Curves of different colors represent different studies. The figure was facet by sex and treatments. The blue dashed lines are the density plots of the observed FEV1 at 24 weeks from study NCT01054885, and patient numbers were: VIL 25 μg: 35 for female and 116 for male, VIL/FF 25/200 μg: 53 for female and 110 for male.