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


From   "roland andersson" <rolandersson@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpretation of regressionmodel of ln-transformed variable
Date   Wed, 5 Nov 2008 08:32:43 +0100

Maarten

All patients have a date when they entered the hospital and another
date of discharge. I think this is the normal for this type of data. I
have not heard about hospital length of stay where there are censored
data. It is also difficult to imaging that there should be censoring
for conditions that normally need 1 to 7 days of hospital visit.

Anyhow thank you for the examples which I have tried out. It certainly
helps me understand. I still need your help how to interpret and
express the result.

What I need is to express the difference in LOS in days between open
and laparoscopic surgery after adjustment for confounders. I am sorry
but it would be too complicated to express the length of stay as a
hazard or as an IRR.

Following your example I have made this model

xi:regress lnLOS  lapscopic i.appdgn age agesq cons, eform("exp(b)") nocons

and get this result
						
lnLOS       	exp(b)	Std. Err.	t	        P>t	         [95% Conf.	Interval]
lapscopic  	1.018056	.006946	2.62	        0.009	1.004532	1.031762
_Iappdgn2_1	1.850726	.0132997	85.66	0.000	1.824841	1.876978
_Iappdgn2_3	1.174283	.013955	13.52	0.000	1.147247	1.201956
age            	.9852508	.0005668	-25.83	0.000	.9841405	.9863623
agesq	        1.000275	7.26e-06	37.90	0.000	1.000261	1.000289
cons	                2.208685	.0208339	84.01	0.000	2.168225	2.2499

I now understand that the exp(b) is a multiplicator, ie that open
appendectomy has a geometric mean LOS of 2.21 days whereas
laparoscopic patients have 1.02*2.21=2.25 days or 0.04 days longer
geometric mean LOS. Is it correct to recalculate the CI of this
difference as 2.21-1.0045*2.21=0.01 and 2.21-1.032*2.21=0.07?

Greetings

Roland Andersson, MD PhD



2008/11/4 Maarten buis <maartenbuis@yahoo.co.uk>:
> 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, ///
>    family(gaussian) link(log) nocons eform
> 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
>
> --- roland andersson <rolandersson@gmail.com> wrote:
>
>> 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
>> describing the principle. After reading your comment I found this
>> 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
>>
>> Roland Andersson
>>
>> 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
>> >
>> > --- roland andersson <rolandersson@gmail.com> wrote:
>> >
>> >> 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
>> >> Roland Andersson
>> >> *
>> >> *   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
>> >
>> > visiting address:
>> > 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
>
> visiting address:
> Buitenveldertselaan 3 (Metropolitan), room N515
>
> +31 20 5986715
>
> http://home.fsw.vu.nl/m.buis/
> -----------------------------------------
>
>
>
> *
> *   For searches and help try:
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>
*
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