  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. 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. 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.
