[R] defining lower part of distribution with covariate

[Berton Gunter]

Troels:

It would be best if you discussed this with a local statistician to make
sure that the data and analysis are properly addressing the scientific
issues. Perhaps that is why no one replied to your previous post. Also, this
is primarily a **statistical** issue, not really an ** R-issue **.

Having said that, I'll take a stab at it ...

Probably the most important thing to say is that there is probably not much
that these data can tell you as you only have 36 cases in all and only 3 are
<= 12. While this probably represented a **lot** of work for you, the simple
fact is that when trying to understand what influences dichotomous
probabilities, you generally need lots of data (hundreds of cases,
typically). Note: This remark may be subject to correction by wiser
statisticians.

Next, the nature of your response, GCS. It appears to be a subjective rating
score that is probably best modeled as an ordered categorical response,
which in R is called an ordered factor. Dichotomizing it to <=12/>12 loses
information. Treating it as a continuous response (quantreg/ancova) seems
inappropriate for your data.

Finally, the model. Considering GCS to be an ordered category, a reasonable
modeling strategy seems to be "proportional odds logistic regression," which
models the GCS response as a linear function of the anstimes and anstypes
(which encompasses your ancova ideas). The results from this model would
then allow you to calculate the <=12 probability if you chose to do so. This
model can be fit using the polr() function in the MASS package.

However, I again urge you to discuss this with a local statistically
knowledgeable resource -- and not to expect too much from such rather meager
data. 

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
 
"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box
 
 

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Troels 
> Ring (by way of Troels Ring <tring at gvdnet.dk>)
> Sent: Wednesday, January 12, 2005 9:11 AM
> To: R-help
> Subject: [R] defining lower part of distribution with covariate
> 
> I try again - perhaps it is analysis of covariance with treatment 
> (thio,ultiva) as two categories and antime as covariate. On 
> the basis of 
> such a model, is then the probability of GCS <= 12 larger 
> with thio treatment ?
> 
> 
> Dear friends, forgive me a simple question, possibly related 
> to quantreg 
> but I failed to get it done and hope for basic instruction.
> 
> I have two sets of observed Glasgow coma scores at admission 
> to ICU after 
> operation, and accompanying time of anesthesia (in hours).
> Thio is cheap and perhaps old fashioned, and ultiva expensive 
> and rapidly 
> terminated. The problem is to estimate the probability of GCS 
> 12 or lower 
> on the two treatments after taking time of anesthesia into 
> account (antime) 
> which is longer for thio. How would I do that in the best way ?
> 
> Best wishes
> Troels Ring, MD
> Aalborg, Denmark
> 
> 
> thio
>        GCS antime
>   [1,]  14    4.5
>   [2,]  15    7.5
>   [3,]  11    7.5
>   [4,]  15    4.5
>   [5,]  14    4.5
>   [6,]  15    3.5
>   [7,]  15    5.5
>   [8,]  14    5.5
>   [9,]  15    3.5
> [10,]  14    8.5
> [11,]  13    4.5
> [12,]  12    5.5
> [13,]  15    3.5
> [14,]  13    6.5
> [15,]   9    8.5
> [16,]  15    6.5
>  > ultiva
>        GCS antime
>   [1,]  15    4.5
>   [2,]  15    4.5
>   [3,]  15    2.5
>   [4,]  15    3.5
>   [5,]  15    3.5
>   [6,]  12    5.5
>   [7,]  15    4.5
>   [8,]  15    3.5
>   [9,]  15    8.5
> [10,]  13    4.5
> [11,]  14    3.5
> [12,]  14    4.5
> [13,]  15    4.5
> [14,]  14    2.5
> [15,]  15    4.5
> [16,]  15    3.5
> [17,]  15    3.5
> [18,]  14    4.5
> [19,]  14    4.5
> [20,]  15    4.5
> 
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