# Re: st: Interpretation of regressionmodel of ln-transformed variable

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: Interpretation of regressionmodel of ln-transformed variable Date Tue, 4 Nov 2008 22:18:19 +0000 (GMT)

```You claim that there is no right censoring. That is very unusual for
this type of data. To me that suggests that some pre-processing of the
data took place in which the censored cases were deleted, which would
be bad as you will than be left with a rather selective subsample.

Anyhow, in any of these models you are not looking for the difference
in days but the ratio of geometric mean length of stays (-regress-), or
ratios of arithmatic mean length of stays (-glm- or -poisson-), or the
ratio of the hazard of leaving hospital (-stcox-). This is best
explained using an example.

In example 1 below you can see that in the first example the geometric
mean "LOS" (actually in this example time till death) for someone of
average age and getting drug 1 is 6.63 months (cons), while this
geometric mean LOS increases by a factor 2.11 when the individual
receives drug 1 and by a factor 3.22 if the individual receives drug 3,
but the time decreased by a factor .946 (that is, it decreases by
100*(1-.946) = 5.4%) when the individual gets a year older

In example 2 below you can see that the arithmetic mean LOS for someone
of average age and getting drug 1 is 9.21 (-glm-) or 8.92 (-poisson-),
while the arithmetic mean LOS increases by a 1.67 (-glm-) or 1.69
(-poisson-) when the individual receives drug 2.

In example 3 I don't show the baseline hazard (the hazard for the
individual with mean age and receiving drug 1) as Cox regression is
specifically designed to leave the baseline hazard unspecified (which
is why it is sometimes called a semi-parametric technique). It does
show that the hazard now decreases by a factor .18 (that is the hazard
of someone with drug 2 is 82% less than the hazard for someone
receiving drug 1)

*------------------ begin example --------------------
// some data preparation
sysuse cancer, clear
gen ln_t = ln(studytime)
sum age
gen c_age = age-r(mean)
gen cons = 1

// example 1:
xi: reg ln_t i.drug c_age cons, eform("exp(b)") nocons

// example 2:
xi: glm studytime i.drug c_age cons, ///
xi: poisson studytime i.drug c_age cons, irr vce(robust) nocons

// example 3:
stset studytime, failure(died)
xi: stcox i.drug c_age
*-------------------- end example -----------------------

Hope this helps,
Maarten

> Thank you Maarten.
>
> I have read someone mentioning to use survival analysis to model
> hospital LOS but have not seen it in practice or found a reference
> reference (Basu A et al, Health Economics 2004) which describes the
> use of OLS on log transformed data, GLM models with a log-link and
> Cox
> regression on LOS data. Do you have another reference?
>
> I understand that this was a more problematic task than I first
> realised. I am not sure that using Cox regression wilkl solve my
> problem as I would like to simply express the difference in LOS in
> days after adjustment for confounders. I do not think that
> Cox-regression will help me there.
>
> I will read your other references on the interpretation of log
> transformed regression output.
>
> Greetings
>
>
> 2008/11/3 Maarten buis <maartenbuis@yahoo.co.uk>:
> > The way to model length of stay data is to use survival analysis
> and
> > not to use -regress-. Some online resources for learning about that
> > are:
> > http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/
> >
>
http://www.ats.ucla.edu/stat/stata/seminars/stata_survival/default.htm
> > http://home.fsw.vu.nl/m.buis/wp/survival.html
> >
> > regarding the interpretation of a -regress- model after
> transforming
> > the dependent variable see:
> > http://www.stata.com/statalist/archive/2008-11/msg00039.html
> > http://www.stata.com/statalist/archive/2008-10/msg01362.html
> > http://www.stata.com/statalist/archive/2008-10/msg01364.html
> >
> > Hope this helps,
> > Maarten
> >
> >
> >> I am analysisng the impact of laparoscopic surgery on hospital
> length
> >> of stay (LOS). The LOS is skewed and the median and 5-95 percentil
> >> range is exactly the same for laparoscopic and open surgery. The
> >> Mann-Whitney test is non significant.
> >>
> >> I want to model the LOS with some confounders (diagnosis at
> >> operation,
> >> sex, comorbidity, age). I have used linear regression on the
> >> ln-transformed LOS
> >>
> >> lnLOS         Coef.            Std. Err.       t      P>t
>     [95% Conf.
> >> Interval]
> >> lapscopic     .0023183        .0070385        0.33    0.742
> -.0114774       .0161141
> >> snip
> >> a number of covariates
> >> snip
> >> _cons .7079673        .0127527        55.52   0.000   .6829717
>    .7329628
> >>
> >> How can I revert the result of the linear regresion of
> ln-transformed
> >> LOS to difference between laparoscopic and open in days?
> Exp(0.002)
> >> gives 1.002 but this can not represent the difference between the
> >> laparoscopic and open surgical methods.
> >>
> >> Somewhere on the statalist I have read that poissonregression can
> be
> >> used in this situation. This is the result of a poissonregression:
> >>
> >> LOS           Coef.   Std. Err.       z       P>z             [95%
> Conf.      Interval]
> >> lapscopic             -.0225546       .0075029        -3.01
> 0.003   -.03726 -.0078492
> >> snip
> >> a number of covariates
> >> snip
> >> _cons .986855 .0131518        75.04   0.000   .9610779
> 1.012632
> >>
> >> How do I interepret this result? Is the laparoscopic LOS
> >> significantly
> >> shorter with 0.02 days?
> >>
> >> I would appreciate your help.
> >>
> >> Regards
> >> *
> >> *   For searches and help try:
> >> *   http://www.stata.com/help.cgi?search
> >> *   http://www.stata.com/support/statalist/faq
> >> *   http://www.ats.ucla.edu/stat/stata/
> >>
> >
> >
> > -----------------------------------------
> > Maarten L. Buis
> > Department of Social Research Methodology
> > Vrije Universiteit Amsterdam
> > Boelelaan 1081
> > 1081 HV Amsterdam
> > The Netherlands
> >
> > Buitenveldertselaan 3 (Metropolitan), room N515
> >
> > +31 20 5986715
> >
> > http://home.fsw.vu.nl/m.buis/
> > -----------------------------------------
> >
> >
> >
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/help.cgi?search
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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```