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# st: RE: Interval regression with skewed data

 From "Feiveson, Alan H. (JSC-SK311)" To "statalist@hsphsun2.harvard.edu" Subject st: RE: Interval regression with skewed data Date Mon, 9 Jan 2012 11:32:29 -0600

```Gillian - I don't know what -intcens- does, but it is not too hard to write a maximum likelihood program for interval censored data from any assumed parametric distribution where the CDF is in a convenient form to evaluate in Stata - for example the Weibull, lognormal, normal, Gamma, Beta. Then you could let the parameters of the model depend either linearly or log-linearly or logit-linearly on your covariates. The contribution to the likelihood for non-censored observations is just the density evaluated at those observations. For censored observation known to lie in the interval(a, b) ,the contribution to the likelihood would be F(b) - F(a), where F(.) is the CDF of the assumed distribution.

AL Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Gillian.Frost@hsl.gov.uk
Sent: Monday, January 09, 2012 9:57 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Interval regression with skewed data

Hello all,

I am struggling with an analysis and would like your insight.  I think
that I am looking at using interval regression but there are certain
aspects of the data that are worrying me.  First some background...

A number of water samples have been taken from around the UK, and a
microbiological examination of the water has been undertaken.  Whenever a
sample is sent to a lab, a whole suite of tests are done to count the
number of colony forming units of various organisms.  I therefore have a
number of outcomes, whose units are the number of colony forming units per
ml.  The aim of this part of the analysis is to compare the organism
levels found in different regions of the UK.

Some observations are left censored (0-6% depending on the outcome) - ie
<1 CFU/ml, or <10 CFU/ml - and some are right censored (0-59%) - ie. >3000
CFU/ml.  The censoring point varies,and so I thought that I would have to
use interval regression (Stata's -intreg-).

However, the data are not Normally distributed (which is an assumption of
interval regression), but are positively skewed with some outcomes having
a high number of zero counts (one has 75% zeros!).  In the book by J S
Long (Regression models for categorical and limited dependent variables,
2007), there was a discussion about how accelerated failure time (AFT)
models can be used to perform interval regression when the data are not
Normally distributed, but there was no example of how to do this.
Unfortunately I no longer have the book to provide you with the page
reference.

I have found a user written command -intcens-, which can perform
interval-censored survival analysis and fits a number of different
distributions, but I cannot find any documentation or examples of its use
(apart from the help file).

Does anyone have any examples of using AFT models to perform interval
regression or examples of using -intcens-?  Or do you think that there is
a better way I could be handling the data?

Any help would be hugely appreciated.

Many thanks,

Gillian

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