Evaluation of regression methods when immunological measurements are constrained by detection limits

Area of Science:

• Immunological data analysis
• Statistical methods for censored data

Background:

• Immunological data often contains nondetects (values below detection limits), referred to as left-censored data.
• Nondetects cannot be treated as missing at random, complicating statistical analysis.
• Current common practice involves imputing nondetects with a single value (e.g., half the detection limit) and using ordinary regression.

Purpose of the Study:

• To provide an overview of methods for analyzing left-censored immunological data.
• To introduce new methods for handling censored data beyond ordinary linear regression.
• To compare various statistical methods through simulation studies using real data.

Main Methods:

• Comparison of six methods: deletion, single substitution, regression on order statistics, multiple imputation, tobit regression, and logistic regression.
• Simulation studies were conducted to evaluate method performance.
• Analysis focused on parameter estimation accuracy and variance under different censoring proportions.

Main Results:

• Deletion and regression on order statistics yielded biased parameter estimates.
• Single substitution underestimated variances, and logistic regression showed reduced statistical power.
• Tobit regression performed well with less than 30% nondetects.
• Multiple imputation demonstrated the best overall performance.

Conclusions:

• Multiple imputation is a robust method for analyzing left-censored immunological data.
• This method performs consistently well across various proportions of nondetects, sample sizes, and error structures (including heteroscedasticity).