Speaker
Description
In epidemiology dose-response meta analysis often refers to fitting a meta regression model that describes a linear trend in the outcome ("response") as a function of the exposure ("dose"), based on aggregated data from a number of studies.
Fixed- and random-effects extensions for handling nonlinear dose-response for odds ratios, relative risks and differences in means through the use of fractional polynomial models and cubic spline models have been proposed (e.g., Crippa & Orsini, 2016). Multiple correlated estimates from the same studies are handled through derivation of explicit formulas for the corresponding variance-covariance matrix. A related approach, which also involves semi-parametric modelling, has been proposed by Xu & Doi (2020) who proposed the use of a robust sandwich-type variance-covariance estimator as an alternative means for handling correlated estimates.
In some cases it may, however, be desirable to be able impose more structure on the nonlinear dose-response trend through the use of a parametric nonlinear function. One key advantage of parametric modelling is that interpretable quantities are more readily available, possibly shifting the focus of nonlinear dose-response meta analysis further away from being mostly used for descriptive and graphical purposes and more towards inference useful for informing public health decision making. There has been surprisingly little methodological work on parametric modelling of nonlinear dose-response trends in a meta-analytic context. In one study, a parametric three-parameter sigmoidal log-logistic dose-response model, often referred to as the Emax model, was fitted by means of four different fixed-effects meta-analytic approaches (Langford et al., 2018).
The aim of this study is to outline a general methodology for fitting a wide range of parametric nonlinear dose-response meta regression models that also include study-specific random effects. Estimation will involve a combination of nonlinear least squares estimation and a profile likelihood approach. Both simulations and data examples will be used to demonstrate the usefulness of the methodology.
References
Crippa, A., Orsini, N. (2016). Dose-response meta-analysis of differences in means. BMC Medical Research Methodology, 2, 91.
doi: 10.1177/0962280218773122
Langford, O., Aronson, J. K., van Valkenhoef, G., Stevens, R. J. (2018). Methods for meta-analysis of pharmacodynamic dose-response data with application to multi-arm studies of alogliptin. Statistical Methods in Medical Research, 27, 564-578.
doi: 10.1177/0962280216637093
Xu, C., Doi, S. A. R. (2020). Dose-Response Meta-Analysis. Chapter 13 in Meta-Analysis: Methods for Health and Experimental Studies (pp. 267-283). Springer: Singapore.
doi: 10.1007/978-981-15-5032-4_13
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