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When data are collected subject to a detection limit, observations below thedetection limit may be considered censored. In addition, the domain of suchobservations may be restricted; for example, values may be required to benon-negative. We propose a regression method for censored observations thatalso accounts for domain restriction. The method finds maximum likelihoodestimates assuming an underlying truncated normal distribution. We show thatour method, tcensReg, outperforms other methods commonly used for data withdetection limits such as Tobit regression and single imputation of thedetection limit or half detection limit with respect to bias and mean squarederror under a range of simulation settings. We apply our method to analyzevision quality data collected from ophthalmology clinical trials comparingdifferent types of intraocular lenses implanted during cataract surgery.

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