# test.metaLik: Hypothesis testing on a scalar fixed-effect component in... In metaLik: Likelihood Inference in Meta-Analysis and Meta-Regression Models

## Description

Performs hypothesis testing on a scalar component of the fixed-effects vector in meta-analysis and meta-regression models, using the signed profile log-likelihood ratio test and its higher-order Skovgaard's adjustment (Skovgaard, 1996), as described in Guolo (2012). See Guolo and Varin (2012) for illustrative examples about the usage of metaLik package.

## Usage

 1 2 test.metaLik(object, param=1, value=0, alternative=c("two.sided", "less", "greater"), print=TRUE) 

## Arguments

 object an object of class "metaLik". param a specification of which parameter is to be given confidence interval, either a number or a name. Default is 1 corresponding to the intercept. value a single number indicating the value of the fixed-effect parameter under the null hypothesis. Default is 0. alternative a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". Just the initial letter can be specified. print logical, whether output information should be printed or not; default is TRUE.

## Details

test.metaLik allows hypothesis testing on a scalar component of interest in the fixed-effects vector. The signed profile log-likelihood ratio statistic for inference on scalar component β of θ is

r(β) = sign(\hat{β}-β)√{2 \{l(\hat{θ})-l(θ)\} },

where l is the log-likelihood function and \hat{θ} is the maximum likelihood estimate of θ. The Skovgaard's adjustment is defined as

\overline r(β) = r(β) + \frac{1}{r(β)}\log\frac{u(β)}{r(β)},

where u(β) is a correction term involving the observed and the expected information matrix and covariances of likelihood quantities, as described in Guolo (2012). Skovgaard's statistic has a second-order accuracy in approximating the standard normal distribution. In the rare case of equal within-study variances, Skovgaard's statistic reaches third-order accuracy.

## Value

A list with the following components:

 r the value of the signed profile log-likelihood ratio statistic. pvalue.r the p-value of the signed profile log-likelihood ratio test. rskov the value of the Skovgaard's statistic. pvalue.rskov the p-value of the Skovgaard's test.

## Author(s)

Annamaria Guolo and Cristiano Varin.

## References

Guolo, A. (2012). Higher-Order Likelihood Inference in Meta-Analysis and Meta-Regression. Statistics in Medicine 31, 313–327.

Guolo, A. and Varin, C. (2012). The R Package metaLik for Likelihood Inference in Meta-Analysis. Journal of Statistical Software 50 (7), 1–14. http://www.jstatsoft.org/v50/i07/.

Skovgaard, I. M. (1996). An Explicit Large-Deviation Approximation to One-Parameter Tests. Bernoulli 2, 145–165.

Function metaLik for fitting meta-analysis and meta-regression models. Function summary.metaLik for summaries.
 1 2 3 4 5 6 7 8 data(vaccine) m <- metaLik(y~latitude, data=vaccine, sigma2=sigma2) ## significance test for the intercept coefficient test.metaLik(m) ## significance test for the 'latitude' coefficient test.metaLik(m, param=2) ## testing for the 'latitude' coefficient less than 0 test.metaLik(m, param=2, value=0, alternative='less')