Modeling Variables with a Detection Limit using a Truncated Normal Distribution with Censoring

Abstract

Background: When data are collected subject to a detection limit, observations below the detection limit may be considered censored. In addition, the domain of such observations may be restricted; for example, values may be required to be non-negative. Methods We propose a regression method for censored observations that also accounts for domain restriction. The method finds maximum likelihood estimates assuming an underlying truncated normal distribution. Results: We show that our method, tcensReg, outperforms other methods commonly used for data with detection limits such as Tobit regression and single imputation of the detection limit or half detection limit with respect to bias and mean squared error under a range of simulation settings. We apply our method to analyze vision quality data collected from ophthalmology clinical trials comparing different types of intraocular lenses implanted during cataract surgery. All methods tested returned similar conclusions for non-inferiority testing, but estimates from the tcensReg method suggest that there may be greater mean differences and overall variability. Conclusions: In the presence of detection limits, our new method tcensReg provides a way to incorporate known domain restrictions when modeling limited dependent variables that substantially improves inferences.