Re: [R] Left censored responses in mixed effects models

From: Richard Cotton <>
Date: Tue, 13 May 2008 03:29:41 -0700 (PDT)

Bert Gunter wrote:
> What is your recommended way of dealing with a left-censored response
> (non-detects) in (linear Gaussian) mixed effects models?
> Specifics: Response is a numeric positive measurement (of volume,
> actually);
> but when it falls below some unknown and slightly random value (depending
> on
> how the sample is prepared and measured), it cannot be measured and is
> recorded as 0.
> There is some statistical literature on this, but I was unable to find
> anything that appeared to me to implement a strategy in any R package. If
> it
> matters, I am less interested in inference than in removing possible bias
> in
> estimation.

The simplest way is to substitute some number for the nondetects, typically half the limit of detection. This method is usually fine if you have less than about 10% nondetects, but can lead to big biases with larger numbers of nondetects.

Denis Helsel has written fairly extensively on this topic, and is the author of the book "Nondetects and data analysis", which the NADA R package is

based upon.  He discusses it here: 

Possibly the best option is to use OpenBUGS to run an MCMC model. It has a nice interface with R using the R2WinBUGS package. Be warned though, this option does require some understanding of Bayesian stats.


Mathematical Sciences Unit

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