Trend Test and Ordinal Logistic Regression

[Shankar Kumar]

Hi All,

The Cochran-Armitage test for trend [http://en.wikipedia.org/wiki/Cochran-Armitage_test_for_trend] is equivalent to the score test for testing that the slope = 0 in a linear logistic model: i.e. Null Hypothesis: slope=0. 

Suppose the predictors are ordinal and the predictors {x_1,x_2,,,x_i} describe distances between categories of X, a linear logistic model is given by:

logit(p_i)  = alpha + beta_i x_i 

I am performing ordinal logistic regression to model the effect of an ordered categorical variable with 3 levels on the outcome which has ~3 levels. I have a couple of questions:  Is there an equivalent trend test in this case (analogous to the linear logit model)?  If so, what is it?  Second, the estimated odds ratios from my logistic model for these indicator variables increase with the order of the variable. If there is a trend, I would like to test this formally. How would I do that?

thanks,

Shankar

[Frank Harrell]

If you don't have another variable to adjust for, i.e., you have one
x, and if you do not need to estimate but just to test for trend, then
a rank correlation coefficient would be in order - probably one of the
Kendall tau's.

Frank