Synthesizing Correlations with Computational Likelihood Approach: Vitamin C Data

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.