Kohei Yamaguchi 1,2, Hisashi Noma 1,3
1 The Graduate Institute for Advanced Studies, The Graduate University for Advanced Studies (SOKENDAI) (, Japan), 2 Clinical Pharmacology & Translational Research, Eisai Co., Ltd (, Japan), 3 Department of Interdisciplinary Statistical Mathematics, The Institute of Statistical Mathematics (, Japan)
Introduction and Objectives:
Dose-response meta-analysis (DRMA) has gained considerable attention as an effective approach to synthesize the dose-response relationships reported across multiple studies. In DRMA, dose-response relationships are combined under a random-effects model, which accounts for potential heterogeneity between studies [1]. Nevertheless, when subgroups exhibit markedly different dose-response profiles, careful consideration should be given to their synthesis. We previously proposed methods for outlier detection and influence diagnostics for DRMA, based on studentized residuals or generalized variance statistics [2]. However, these methods were intended to identify a single or a small number of outliers, and may not perform adequately when studies are divided into subgroups with different profiles.
Dette et al. proposed methods for assessing the equivalence of two regression curves using distance measures [3]. Hagemann and Möllenhoff recently extended these methods based on the duality between hypothesis testing and confidence intervals (CIs), and introduced methods for testing the similarity of dose-response curves based on CIs for distance measures [4]. We extend their approach to the statistical model for DRMA and develop methods for similarity assessment of subgroups in DRMA.
Methods:
We adopted the one-stage procedure of DRMA introduced by Crippa et al. and implemented in dosresmeta R package [5,6]. This approach estimates the hierarchical variance structure within and between studies using linear mixed-effects models to synthesize dose-response relationships across multiple studies. To assess similarity between two subgroups, maximum deviation distance of the estimated dose-response curves is used as the similarity measure. If the hypothesis that the maximum deviation is less than the predefined similarity threshold (Δ) is accepted, similarity is considered demonstrated. The maximum deviation estimate (MDE) is obtained from the dose-response curves estimated by DRMA for the two subgroups. The distribution of the MDE is complicated, and determining critical values for hypothesis testing is challenging. Therefore, two types of CIs for the MDE, obtained via parametric bootstrap approach proposed by Hagemann and Möllenhoff [4], are used for the similarity test. One approach constructs the CI based on the percentiles of the bootstrap distribution of the MDE (Percentile CI). The other is a hybrid approach, where the standard error of the MDE is estimated via bootstrap, and the CI is constructed based on the asymptotic normality (Hybrid CI). To evaluate the performance of the similarity tests based on two CIs, simulations were conducted using the alcohol_cvd dataset in dosresmeta R package as the basis for the simulation design [6]. This dataset is derived from a meta-analysis of the dose-response relationship between alcohol intake (mL/day) and cardiovascular disease risk (log relative risk [logRR]) reported by Liu et al. [7]. A dose-response model estimated by applying a quadratic model to the original dataset was treated as the reference model. Deviation models were constructed with nominal maximum deviations (NMD) of 0, 0.5, 1, and 2 in the outcome variable (logRR of cardiovascular disease) relative to the reference model. As part of the Monte Carlo experiment, simulated datasets were generated for both the reference and deviation models to represent two subgroups. The thresholds (Δ) were set to 0.5, 1, 1.5, and 2, and similarity tests were conducted on the simulated datasets to evaluate the detection rates by Percentile CI and Hybrid CI in each scenario. A significance level of α = 0.05 was used for the CIs.
Results:
In scenarios where NMD ≥ Δ, Type I error rates were assessed and were controlled below the nominal level (α = 0.05) for both Percentile CI and Hybrid CI. In contrast, in scenarios where NMD < Δ, power was assessed, and Hybrid CI consistently yielded higher power than Percentile CI. Considering that Type I errors were appropriately controlled in both CIs, Hybrid CI, which demonstrated higher power, may be preferable in practice.
Conclusion:
We propose test methods to assess the similarity between two subgroups in DRMA using CIs for the MDE between dose-response curves obtained via a bootstrap approach. Since the power of the test is influenced by the threshold, it should be predefined considering domain knowledge or regulatory requirements.
References:
References:
[1] Orsini N and Spiegelman D. Meta-Analysis of Dose-Response Relationships. In: Handbook of Meta-Analysis (2020) CRC Press.
[2] Yamaguchi K et al. Biostatistics & Epidemiology (2026) 10(1), e2604384.
[3] Dette H et al. Journal of the American Statistical Association (2018) 113(522), 711-729.
[4] Hagemann N and Möllenhoff K. Statistics in Medicine (2025) 44(6), e10309.
[5] Crippa A et al. Statistical Methods in Medical Research (2019) 28(5), 1579-1596.
[6] Crippa A and Orsini N. Journal of Statistical Software (2016) 72(1), 1-15.
[7] Liu Q et al. Computational Statistics & Data Analysis (2009) 53(12), 4157-4167.
Reference: PAGE 34 (2026) Abstr 11969 [www.page-meeting.org/?abstract=11969]
Poster: Methodology - Other topics