'Significant' product-term interaction but no significant simple main effect contrast

#1
:wave:
I'm conducting a conditional logistic regression to assess the association between a continuous predictor and a dichotomous outcome, adjusted for several covariates. I include product interaction terms between an exposure and a covariate in each of several models. In a few of these I am detecting a statistically significant product interaction term (i.e., P<0.10). Yet when I implement contrasts to evaluate the effect of the exposure on the outcome at each level of the covariate I detect no significant effects. I'm employing proc logistic in SAS 9.3 with contrast statements. Has anyone else run into this scenario; any plausible explanation?
 
#2
Re: 'Significant' product-term interaction but no significant simple main effect cont

:tup: So, in answering my own question (after some consultation with colleagues), I'm thinking that evaluation of the logistic regression product-term p-value in isolation is not informative; as we know the hierarchical principle demands that product terms be interpreted in the context of their component variables. While indicative of a potential statistical interaction the product term itself evaluates only the variability of the exposure effect across levels of a covariate, but not whether the overall effects differ from the null. The latter is determined by evaluating the simple effects using contrasts, which incorporate the additional variability contributed by the product term component variables. 'Eye-balling' the simple effect contrasts generated using the regression equation that incorporated the product term is useful, but unless differences are huge at different levels of a potentially interacting variable statistical testing proves useful to evaluate the homogeneity of the simple effects and whether or not a statistical interaction truly exists. Further thoughts on this issue?
 

noetsi

Fortran must die
#3
Re: 'Significant' product-term interaction but no significant simple main effect cont

I am not sure this helps but there is an accepted rule that when you have interaction effects in your model you do not remove the main effects even if not signficant. You would not comment on the main effects other than to note they were not signficant and that they were left in the model because of this "rule" (who's name I unfortunately forget).

That is for logistic regression, linear regression and ANOVA. I am not sure what conditional logistic regression is as I have not heard that term used before, but I assume it would apply to it as well.
 

hlsmith

Omega Contributor
#4
Re: 'Significant' product-term interaction but no significant simple main effect cont

Can you provide your syntax (code), including the contrast statements. This way we can tell what you are referencing for contrasts. Do you also want to specify how the original terms used in the interaction are formatted (continous, categorical (number of groups).
 
#5
Re: 'Significant' product-term interaction but no significant simple main effect cont

Absolutely,:) (SAS v.9.3)

proc logistic data=1.1;
strata matching;
class c (ref='0') /param=ref;
model id(event='Case')=a b c d e e*d /expb cl influence;
contrast 'e=0, d 1 vs 0' e 0 d 1 e*d 0/estimate=exp;
contrast 'e=1, d 1 vs 0' e 1 d 1 e*d 1 /estimate=exp;
run;

a is an interval/ordinal variable with 4 levels
b is a dichotomous variable
c is a categorical variable with 3 levels
d is a continuous variable (exposure of interest)
e is a dichotomous variable (covariate of 'interaction' interest)

So e*d is statistically significant (P<0.05) in the model; but upon examination of the contrasts, the odds ratios are similar to one another (0.987 vs. 0.854) and neither is significantly different from the null (P>0.50).

Thoughts?
 

hlsmith

Omega Contributor
#6
Re: 'Significant' product-term interaction but no significant simple main effect cont

Why are the categorical variables not in your class statement? Or am I forgetting something about conditional reg?
 
#7
Re: 'Significant' product-term interaction but no significant simple main effect cont

It is, only c is categorical; a is 0,1,2,3 and b and e are 0,1