We often see P trend and P heterogeneity in epidemiological papers. What are they and how to interpret them? Also, how can we get them in logistic regression (i.e. binary outcome)?
I'm surprised you want these statistics without knowing what they are!
If you look at the context in which you have seen these statistics you will learn what they are in a more meaningful way that an abstract explanation.
A trend test tests the hypothesis of an ordered relationship across the categories of a predictor variable. For example, you might test for an ordered relationship between social class and dementia.
Tests for heterogeneity are many, and used in many different contexts, and without knowing the context I can't help you there.
Thank you for your input. I have understood what a p-trend is. However, to share the context - the predictor variable is "body size" coded as 1-9. We then categorized it into 3 groups (i.e. lean, medium and heavy). If I want to estimate the p-trend, should I put the predictor variable in continuous form? If yes, then which one is better - original 1 to 9 or 1-3 as categorized later.
the usual chi- square , when significant , expresses that two variables are related (chi square of heterogeneity) . The extended Mantel-Haenszel chi square for linear trend (example attached), in addition, when significant, expresses that there is a dose-response relationship reinforcing causality between the two variables.
When we want to test the existence of a dose-response relationship using a logistic model for quantitative variables , this variable could be included in the model as ordinal variable with three (or more) categories corresponding to different classes that may be coded, for example, as 0 , 1 and 2 or 1, 2 and 3 .
The reference category is the one for which an OR = 1 is associated. In all cases , the coefficients should be significantly different from 0 in the presence of a dose -response relationship. In other words , the OR must be significantly different from 1 ( 95% confidence interval does not contain the reference value 1).
Some additional clarification on the identification of a dose -response relationship by use of logistic regression
When we want to test the existence of a dose-response relationship using a logistic model for quantitative variables , this variable could be included in the model as ordinal variable with three (or more) categories corresponding to different classes that may be coded, for example, as 0 , 1 and 2 or 1, 2 and 3 . With this technique, we have a single adjusted odds ratio . To have two adjusted odds ratios (for a better test of this relationship) with a variable with three modalities (lean, medium and heavy ) , this variable must be converted into two dichotomous variables that can be coded as annexed .