An introduction to new robust linear and monotonic correlation coefficients

Area of Science:

• Statistics
• Genomics
• Biostatistics

Background:

• Pearson correlation is standard but sensitive to outliers.
• Robust statistical measures are needed for accurate association analysis.
• Introduces three novel robust correlation estimators: Taba (T), TabWil (TW), and TabWil rank (TWR).

Purpose of the Study:

• To introduce and evaluate new robust correlation measures.
• To compare the performance of T, TW, and TWR against existing classical and robust methods.
• To identify genes associated with Williams Syndrome using Taba distance.

Main Methods:

• Simulation studies to assess robustness and performance (RMSE, bias).
• Comparison with Pearson (P), Spearman (S), Quadrant (Q), Median (M), and Minimum Covariance Determinant (MCD).
• Application of Taba distance and statistical tests for gene association analysis in Williams Syndrome.

Main Results:

• Proposed measures (T, TW, TWR) are competitive with classical (P, S) and robust (Q, M, MCD) methods.
• TBL2 identified as the most significant gene in Williams Syndrome patients, showing reduced expression (P value = 6.37E-05).

Conclusions:

• TWR and T perform best for bias and RMSE, respectively, under specific bivariate distributions (Log-Normal, Weibull).
• MCD shows good performance under Normal distribution; other methods are comparable.
• TBL2 gene expression may serve as a diagnostic marker for Williams Syndrome.
• A Taba R package is available for implementing the proposed methods.