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From |
"Kevin Boudreau" <boudreau@MIT.EDU> |

To |
<statalist@hsphsun2.harvard.edu> |

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

Date |
Sun, 5 Jun 2005 12:08:44 -0400 |

Dear Daniel: I also wonder whether you could model the data as a truncated ("left-censored") continuous distribution, where you cannot observe observe the values "below zero." This might help simplify the challenge of getting distributional assumptions right when assuming the variable is strictly non-negative. Kevin. -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Daniel Waxman Sent: Saturday, June 04, 2005 8:53 PM To: statalist@hsphsun2.harvard.edu Cc: 'Gregg Husk' Subject: st: how to deal with censoring at zero (a lot of zeroes) for a laboratory result which I would like to log transform Hello, I have a problem which I believe must be commonly encountered, and which must have a simple solution in Stata, but I just can't see it. I am modeling a laboratory test (Troponin I) as an independent (continuous) predictor of in-hospital mortality in a sample of >10,000 subjects. A simple model seems to fit well: In a logistic model, the odds ratio for the log-transformed result (dropping the zeroes, or making something up) remains relatively constant with whatever I throw in with it. The problem is the zero values, what they represent, and what to do with them. The distribution of results ranges from the minimal detectable level of .01 mcg/L to 94 mcg/L, with results markedly skewed to the left (nearly half the results are zero; 90% are < .20. results are given in increments of .01). Of course, zero is a censored value which represents a distribution of results between zero and somewhere below .01. I noted that plotting N vs. log(troponin) is for all practical purposes linear at the lowest measurable concentrations. It seems to me that if the distribution of results were predictable, then I should be able to extrapolate back to what the best point estimate for the zero would be. (and I could then compare this value to that predicted by the reversed logit equation and the known fraction of deaths at measured value of zero). I believe that it might be reasonable to assume a log-normal distribution of results, but I am not sure about this. I found a method attributed to A.C. Cohen of doing essentially this which uses a lookup table to calculate the mean and standard deviation of an assumed log-normal distribution based upon the non-censored data and the proportion of data points that are censored, but there must be a better way to do this in Stata. Any thoughts on (1) whether it is reasonable to assume the log-normal distribution (I've played with qlognorm and plognorm, but it's hard to know what is good enough), and if so (2) how to do it? Thanks. * * 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/ * * 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**:**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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