## Logistic Regression: Confidence interval of predicted value?

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# Logistic Regression: Confidence interval of predicted value?

I've been doing a logistic regression of two variables. Dose [1,5,10,15] and response [binomial list of how many died after being given a specific treatment dose]. In PROC LOGISTIC, you can ask for confidence intervals with the l= and u= statements in the output. This results in a logistic regression model of what percentage of individuals you can expect to to die after being given a specific doseage.  The output will give the confidence intervals for predicted mortality at doses 1,5,10,and 15. I'm using the events / trails syntax, so I'm using a statement like this:

proc logistic data =data plots=effect plots=ROC   ;

output out=mortalitymeasures p=LT  l=lower95 u=upper95;

run;

However, what if I'm interested in confidence intervals between the treatment doses? Specifically I'm interested in 50% mortality, which occurs between doses 5 and 10 at 6.5. I'm rusty on my logistic regression, but is it even statistically feasible to try to calculate a confidence interval for mortality at 6.5 since there were no observations at this dose, and hence no sample size to generate a confidence interval? Seems like an issue of interpolation. If it's actually appropriate look for confidence intervals for predictions between treatments, how would I go about this for something like PROC LOGISTIC or LIFEREG?

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‎03-03-2013 01:24 PM
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Posts: 152

## Re: Logistic Regression: Confidence interval of predicted value?

I added an observation with non-missing independent variables but with missing dependent variables in the events/trials syntax to the PROC LOGISTIC ingots data set.  PROC LOGISTIC estimated a predicted value and its 95% confidence interval for this observation without any problem.

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Posts: 20,725

## Re: Logistic Regression: Confidence interval of predicted value?

See the example in the user guide on how to score a dataset.

SAS/STAT(R) 9.2 User's Guide, Second Edition

Regular Contributor
Posts: 152

## Re: Logistic Regression: Confidence interval of predicted value?

Does including in the original logistic regression a "dummy" observation with a value of DOSE=6.5 but missing values for DEAD and TRTSIZE yield a predicted value and its 95% confidence interval for that DOSE?

Super User
Posts: 20,725

## Re: Logistic Regression: Confidence interval of predicted value?

Missing values are excluded from the fitting of the data and the model wouldn't be able fit because there are no dead or trtsize values. Typically, when you fit for a specific variable the others are set to the average value of the observed data.

Solution
‎03-03-2013 01:24 PM
Regular Contributor
Posts: 152

## Re: Logistic Regression: Confidence interval of predicted value?

I added an observation with non-missing independent variables but with missing dependent variables in the events/trials syntax to the PROC LOGISTIC ingots data set.  PROC LOGISTIC estimated a predicted value and its 95% confidence interval for this observation without any problem.

Super User
Posts: 20,725

## Re: Logistic Regression: Confidence interval of predicted value?

You are correct. I forgot that dead/trtsize were the dependent variables.

Message was edited by: Reeza

Regular Contributor
Posts: 152

## Re: Logistic Regression: Confidence interval of predicted value?

Dead and Trtsize are the DEPENDENT variables whose predicted value PROC LOGISTIC estimates.  If any of the independent variables were missing from an observation, PROC LOGISTIC could NOT estimate its predicted value.

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