# Synthesizing Correlations with Computational Likelihood Approach: Vitamin C Data

## TL;DR

This paper introduces a likelihood-based method using B-splines to estimate correlations between vitamin C intake and plasma levels, facilitating meta-analyses and providing a robust statistical inference framework.

## Contribution

It develops a novel likelihood approximation approach for correlation estimation using B-splines, enabling meta-analysis of correlation data across multiple studies.

## Key findings

- Effective estimation of correlation coefficients from multiple studies.
- Construction of likelihood intervals for correlation inference.
- Extension of method to meta-analysis scenarios.

## 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.

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Source: https://tomesphere.com/paper/1701.08145