Censored correlated cytokine concentrations: multivariate Tobit regression using clustered variance estimation

Area of Science:

• Immunology
• Biostatistics

Background:

• Cytokine measurements are crucial for understanding immune system function.
• Quantification methods often yield censored data due to detection limits, complicating statistical analysis.
• Geometric mean ratios (GMRs) and GMR ratios (GMRRs) are valuable for comparing cytokine concentrations between groups.

Purpose of the Study:

• To evaluate methods for estimating GMRRs from censored cytokine concentration data.
• To propose and assess novel Tobit stacking methods (Stackc, Stackh) for handling censored distributions.

Main Methods:

• Comparison of deletion, substitution, direct Tobit (Diff), multiple imputation, bivariate Tobit (Bitobit), and Tobit stacking (Stackc, Stackh).
• Evaluation using simulated and real-world immune marker data.
• Assessment of sensitivity to non-normality and variance inhomogeneity.

Main Results:

• Deletion and substitution methods showed empirical bias.
• The direct Tobit method (Diff) exhibited bias that increased with decreasing correlation between log-concentrations.
• Multiple imputation, Stackh, and Bitobit provided nearly identical, minimally biased estimates across various distributions, especially with <30% censoring.

Conclusions:

• Tobit stacking (Stackh) and multiple imputation are recommended for accurately estimating GMRRs from censored cytokine data.
• These robust methods provide reliable comparisons of immune marker concentrations between groups.
• Availability in common statistical software (Stata, R, SAS) facilitates their application.