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From |
Dr Murray Finkelstein <murray.finkelstein@utoronto.ca> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: how to deal with censoring at zero (a lot of zeroes) fora laboratory result which I would like to log transform |

Date |
Wed, 15 Jun 2005 19:57:54 -0400 |

I've published a paper that shows how to use Excel to make maximum likelihood estimates of the parameters of a distribution with "below detection limit" values.

See:

Finkelstein MM, Verma D: Exposure Estimation in the Presence of Nondetectable Values: Another Look. Am Ind Hyg Assoc J 2001; 62:195-198.

Daniel Waxman wrote:

Svend,

Thanks. I did indeed look extensively as the predictor as a categorical

variable and as a predictor when .005 is used. My dataset is large enough,

and events common enough, that the confidence intervals are quite small at

the .01 level. There is a threshold, but it is below .01. In other words,

there is no measurable change in outcome between .01 and .02, but there is

one between 'undetectable' and .01.

Zero could be .005, but it could be .0005 or .00005. (biologically speaking

as well) I suppose this becomes irrelevant very soon though if it can't be

measured. However, the logistic equation suggests (given the measured # of

deaths at the zero value) that the zero should be approximately .001.

It seems that this is a common issue in the environmental literature, where

people care a lot about very small concentrations of things (lead, arsenic,

etc.) I have found various sources that suggest that the method of Cohen

(mentioned below) of estimating the entire distribution curve by using the

available points and the known or assumed shape can be preferable to picking

half of the lower limit arbitrarily.

Daniel

-----Original Message-----

From: owner-statalist@hsphsun2.harvard.edu

[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Svend Juul

Sent: Sunday, June 05, 2005 9:47 AM

To: statalist@hsphsun2.harvard.edu

Subject: RE: st: how to deal with censoring at zero (a lot of zeroes) for a

laboratory result which I would like to log transform

Daniel,

You wonder how to handle zero values in a predictor you have good reasons to log-transform.

For a first look I would make a reasonable categorization of the predictor, e.g. five categories (0, 0.01-0.09, 0.10-0.99, 1-10, 10+) and use -xi: logistic- to see the pattern. This analysis might also give an idea whether there is some threshold.

If this justifies using a log-transform, I think you almost give

the answer yourself: zero means a result somewhere between 0 and

0.01. So why not select 0.005, log-transform, and run -logistic-

using the log-transformed predictor.

The idea to let the data determine the "best" value that the zeros

represent has its problems: The confidence interval for the odds

ratio estimate becomes too small.

Hope this helps

Svend

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-- Murray M. Finkelstein PhD MD CCFP Department of Family and Community Medicine Mt Sinai Hospital, Suite 413 600 University Avenue Toronto, Ontario, Canada M5G 1X5 Phone: 416-326-7879 Fax: 416-326-7761 E-Mail: murray.finkelstein@utoronto.ca * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: how to deal with censoring at zero (a lot of zeroes) for a laboratory result which I would like to log transform***From:*"Daniel Waxman" <dan@amplecat.com>

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