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

The statistical analysis of immunological data may be complicated because precise quantitative levels cannot always be determined. Values below a given detection limit may not be observed (nondetects), and data with nondetects are called left-censored. Since nondetects cannot be considered as missing at random, a statistician faced with data containing these nondetects must decide how to combine nondetects with detects. Till now, the common practice is to impute each nondetect with a single value such as a half of the detection limit, and to conduct ordinary regression analysis. The first aim of this paper is to give an overview of methods to analyze, and to provide new methods handling censored data other than an (ordinary) linear regression. The second aim is to compare these methods by simulation studies based on real data.

We compared six new and existing methods: deletion of nondetects, single substitution, extrapolation by regression on order statistics, multiple imputation using maximum likelihood estimation, tobit regression, and logistic regression. The deletion and extrapolation by regression on order statistics methods gave biased parameter estimates. The single substitution method underestimated variances, and logistic regression suffered loss of power. Based on simulation studies, we found that tobit regression performed well when the proportion of nondetects was less than 30%, and that taken together the multiple imputation method performed best.

Based on simulation studies, the newly developed multiple imputation method performed consistently well under different scenarios of various proportion of nondetects, sample sizes and even in the presence of heteroscedastic errors.