R: Fit the alternative model for bivariate random-effects...
rileyES
R Documentation
Fit the alternative model for bivariate random-effects meta-analysis (Riley)
Description
This function fits the alternative model for bivariate random-effects meta-analysis on effect size data when the within-study correlations are unknown. This bivariate model was proposed by Riley et al. (2008) and is similar to the bivariate random-effects model from Reitsma et al. (2005), but includes an overall correlation parameter rather than separating the (usually unknown) within- and between-study correlation. As a consequence, the alternative model is not fully hierarchical, and estimates of additional variation beyond sampling error (psi) are not directly equivalent to the between-study variation (tau) from the general model. Furthermore, it has been argumented that assuming zero within-study correlations (i.e. applying Reitsma's approach) is reasonable when summarizing the sensitivities and false positive rates of a diagnostic test (Reitsma et al. 2005, Daniels and Hughes 1997, Korn et al. 2005, Thompson et al. 2005, Van Houwelingen et al. 2002). The alternative model for bivariate random-effects meta-analysis may, however, be useful when there is large within-study variability, few primary studies are available or the general model estimates the between-study correlation as 1 or -1.
any object that can be converted to a data frame with integer variables Y1, vars1, Y2 and vars2.
Y1
vector of numerics representing the effect sizes of outcome 1, ignored if X is not NULL
vars1
vector of numerics representing the error variances of Y1, ignored if X is not NULL
Y2
vector of numerics representing the effect sizes of outcome 2, ignored if X is not NULL
vars2
vector of numerics representing the error variances of Y2, ignored if X is not NULL
optimization
The optimization method that should be used for minimizing the negative (restricted) log-likelihood function. The default method is an implementation of that of Nelder and Mead (1965), that uses only function values and is robust but relatively slow. Other methods are described in optim.
control
A list of control parameters to pass to optim.
...
arguments to be passed on to other functions, currently ignored
Details
The following parameters are estimated by iteratively maximizing the restriced log-likelihood using the Newton-Raphson procedure: pooled effect size for outcome 1 (beta1), pooled effect size for outcome 2 (beta2), additional variation of beta1 beyond sampling error (psi1), additional variation of beta2 beyond sampling error (psi2) and a transformation of the correlation between psi1 and psi2 (rhoT). The original correlation is given as inv.logit(rhoT)*2-1. The results from a univariate random-effects meta-analysis with a method-of-moments estimator are used as starting values for beta1, beta2, psi1 and psi2 in the optim command. The starting value for rhoT is 0. Standard errors for all parameters are obtained from the inverse Hessian matrix.
Value
An object of the class riley for which many standard methods are available. A warning message is casted when the Hessian matrix contains negative eigenvalues, which implies that the identified solution is a saddle point and thus not optimal.
Author(s)
Thomas Debray <thomas.debray@gmail.com>
References
Nelder JA, Mead R. A simplex algorithm for function minimization. Computer Journal (1965); 7: 308–313.
Daniels MJ, Hughes MD. Meta-analysis for the evaluation of potential surrogate markers. Statistics in Medicine 1997; 16: 1965–1982.
van Houwelingen HC, Arends LR, Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression. Statistics in Medicine 2002; 21: 589–624.
Reitsma J, Glas A, Rutjes A, Scholten R, Bossuyt P, Zwinderman A. Bivariate analysis of sensitivity and specificity produces informative summary
measures in diagnostic reviews. Journal of Clinical Epidemiology 2005; 58: 982–990.
Korn EL, Albert PS, McShane LM. Assessing surrogates as trial endpoints using mixed models. Statistics in Medicine 2005; 24: 163–182.
Thompson JR, Minelli C, Abrams KR, Tobin MD, Riley RD. Meta-analysis of genetic studies using mendelian randomization–a multivariate approach. Statistics in Medicine 2005; 24: 2241–2254.
Riley RD, Thompson JR, Abrams KR. An alternative model for bivariate random-effects meta-analysis when the within-study correlations are unknown. Biostatistics 2008; 9: 172–186.
providing 
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