M_inf_sigc: Optimization function for the SIGC(M) prior: Adjust the prior...
In ra4bayesmeta: Reference Analysis for Bayesian Meta-Analysis

Description Usage Arguments Details Value Warning References See Also Examples

Computes the parameter value M=M_{inf} of the SIGC(M) prior, such that the relative latent model complexity (RLMC) with respect to the reference threshold is approximately rlmc. The reference threshold is chosen as the (1-alpha)-quantile of the SIGC(M_{inf}) prior.

1	M_inf_sigc(rlmc, df, alpha=0.5, truncation=5*10^6)

`rlmc`	target RLMC value. Real number in (0,1).
`df`	data frame with one column "sigma" containing the standard errors of the estimates for the individual studies.
`alpha`	determines the (1-`alpha`)-quantile of the SIGC(M) prior, which is used as reference threshold. Defaults to 0.5 (i.e. the median).
`truncation`	upper bound for the parameter value M. Defaults to the empirically determined value 5*10^6.

See the Supplementary Material of Ott et al. (2021), Section 2.3.2, for the formulas and explanations. Note that the parameter value M_{inf} does depend on the data set considered.

Parameter value M=M_{inf} of the SIGC(M) prior. Real number > 1.

Occasionally, the formula for M_{inf} given in the Supplementary Material of Ott et al. (2021, Section 2.3.2) yields values larger than 5*10^6. This can cause numerical problems in the bayesmeta function. Therefore, we truncate the parameter value at the empirically determined threshold 5*10^6 by default.

Ott, M., Plummer, M., Roos, M. Supplementary Material: How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Revised for Statistics in Medicine. 2021.

m_inf_sgc

# extreme RLMC target value close to 1 used in Ott et al. (2021)
# for the aurigular acupuncture (AA) data set
data(aa)
M_inf_sigc(df=aa, rlmc=0.9999)
# for the respiratory tract infections (RTI) data set
data(rti)
M_inf_sigc(df=rti, rlmc=0.9999)

# 75% quantile instead of the median as ref. threshold
M_inf_sigc(df=rti, rlmc=0.9999, alpha=0.25)