Title: Synthesizing Correlations with Computational Likelihood Approach: Vitamin C Data,
Abstract: It is known that the primary source of dietary vitamin C is fruit and
vegetables and the plasma level of vitamin C has been considered a good
surrogate biomarker of vitamin C intake by fruit and vegetable consumption. To
combine the information about association between vitamin C intake and the
plasma level of vitamin C, numerical approximation methods for likelihood
function of correlation coefficient are studied. The least squares approach is
used to estimate a log-likelihood function by a function from a space of
B-splines having desirable mathematical properties. The likelihood interval
from the Highest Likelihood Regions (HLR) is used for further inference. This
approach can be easily extended to the realm of meta-analysis involving sample
correlations from different studies by use of an approximated combined
likelihood function. The sample correlations between vitamin C intake and serum
level of vitamin C from many studies are used to illustrate application of this
approach.