Re-expressing coefficients from regression models for inclusion in a meta-analysis

Table 1 Values of parameters used in the simulation and rationale for their choice. Number of simulations = 2000

Parameter	Possible values	Rationale for the choice
n_obs	162, 8474	Quantiles (10th, 90th) of the distribution of sample sizes for the 15 real data examples
e	Selected from a normal distribution with mean = 0 and SD = SD_e^a	Standard deviation selected to result in an R² ~ 0.2, to make realistic models (Aslibekyan et al., 2014) [17]
β_DGM	-15, 0.5, 1, 10, 30	Broad range of effect sizes encompassing those in the real data examples
Logbase	2, e, 10	Log bases used in the 15 real data examples
σ	0.25, 0.45, 0.65, 0.85	Selected values cover the approximate range of σ values in the 15 real data examples
Median (µ = log(median))	0.25, 0.5, 1, 2, 4, 8, 16, 32	Selected values cover the range of median exposure in the 15 real data examples

^aSD_e was calculated using the following method: SD_e =|β_DGM * log(median + 2) * Mult_SD| where β_DGM and median are from the table above and Mult_SD is a multiplier to prevent extremely large variability. For each median, the Mult_SD was as follows: median 0.25, Mult_SD 1; 0.5, 0.886; 1, 0.771; 2, 0.657; 4, 0.543; 8, 0.429; 16, 0.315; 32, 0.120). Mult_SD was selected based on values that will introduce enough error to result in r² values around 0.2 (similar to many epidemiological studies) for estimation of β_Estimand

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