Abstract
BackgroundWhen 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.MethodsWe propose a method for estimating population mean and variance from censored observations that accounts for known domain restriction. The method finds maximum likelihood estimates assuming an underlying truncated normal distribution.ResultsWe show that our method, tcensReg, has lower bias, Type I error rates, and mean squared error than other methods commonly used for data with detection limits such as Tobit regression and single imputation under a range of simulation settings from mild to heavy censoring and truncation. We further demonstrate the consistency of the maximum likelihood estimators. 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 of the methods yield similar conclusions regarding non-inferiority, but estimates from the tcensReg method suggest that there may be greater mean differences and overall variability.ConclusionsIn the presence of detection limits, our new method tcensReg provides a way to incorporate known domain restrictions in dependent variables that substantially improves inferences.
Highlights
When data are collected subject to a detection limit, observations below the detection limit may be considered censored
Simulation study We conducted a simulation study to compare the performance of our method to that of five methods of estimating the mean and standard deviation from a truncated normal distribution with censored observations
3 imputes all censored values with the detection limit and uses maximum likelihood estimation with a normal distribution likelihood, while Method 4 imputes all values as half of the detection limit and uses normal maximum likelihood estimation
Summary
When data are collected subject to a detection limit, observations below the detection limit may be considered censored. In which the value of an observation is not known exactly but rather is only known to be above or below a specific value, is prevalent in many data settings. Censoring occurs with time-to-event data, but can occur when measurements are subject to a detection limit (DL). A detection limit is defined as the lowest quantity or concentration of a compound that can be reliably detected with a given analytical method [1]. Detection limits and the Estimation of the parameters of a normal distribution based on a sample with censored observations has a long history of investigation. [9] was one of the first authors to develop maximum likelihood estimation methods for this data setting.
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