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# Re: st: RE: Interval regression with skewed data

 From Gillian.Frost@hsl.gov.uk To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Interval regression with skewed data Date Tue, 10 Jan 2012 08:40:03 +0000

```Hello Nick, Alan,

Thank you both for your replies.

Nick, I apologise for not being clear in my original posting.  My
outcome/dependent variable is the number of colony forming units per ml,
and my predictor/independent variable is the region (North West, North
East, South East England,...) within which the sample was taken.  I
gravitated towards interval regression because I have some observations
that are left censored and some that are right censored but the censoring
value is not always the same, and I started to think about survival
analysis because I had seen a suggestion where this could be used to
perform interval regression when the Normality assumption was violated.
Unfortunately, my outcome has some zero counts and so I cannot really use
the logarithmic transform.  I am more than happy to consider other methods
of analysis if you have any ideas?

Alan, I am afraid that what you suggest is probably outside of my
programming and statistical expertise, and would also take me longer than
the time I have to look at this problem.

Many thanks,

Gillian

From:   Nick Cox <n.j.cox@durham.ac.uk>
To:     "'statalist@hsphsun2.harvard.edu'"
<statalist@hsphsun2.harvard.edu>
Date:   09/01/2012 16:15
Subject:        st: RE: Interval regression with skewed data
Sent by:        owner-statalist@hsphsun2.harvard.edu

I'd be more worried about violating linearity of functional form than
normality of errors, but you say nothing about that. Nor do you say

I can't see from your discussion that it can be a choice between interval
regression and some kind of survival analysis. What you have doesn't sound
to me at all like a survival analysis problem.

However, assuming the first, you could transform before you use -intreg-.
Your limits just transform to limits on your transformed scale. From other
experiences with hydrological data I would reach for a logarithmic
transform as first port of call. You would need to back-transform
afterwards.

Nick
n.j.cox@durham.ac.uk

Gillian.Frost@hsl.gov.uk

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?

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