Significant regression for the dichotomised predictor variable and not the continuous version of a predictor variable?

Question

I am interested in examining the association between cardiorespiratory fitness and PCA derived dietary pattern scores in 264 adolescents. My cardiorespiratory fitness predictor is vo2max, and my outcomes are a "Treat Foods" pattern and a "Fruit and Vegetable" pattern. Both vo2max and my pattern scores are continuous variables. I have also dichotomised vo2max based on an adequate health cutoff (the FITNESSGRAM Healthy Zones). The sample is relatively fit, so the categories are unbalanced with 88% categorised as having adequate cardiorespiratory fitness. I am using multivariate regression analysis in STATA 12IC, and my models appear to be linear.

What I have found: 1) There is an association between vo2max and the "Fruit and Vegetable" score, but not between the FITNESSGRAM variable and the "Fruit and Vegetable" score. My assumption is that this may be due to a loss of power with the dichotomising. 2) While there is no association between vo2max and the "Treat Foods" pattern, there is an association between the FITNESSGRAM variable and the "Treat Foods" pattern.

Can anybody suggest a statistical reason for this discrepancy, or a better way of handling the data, for the second result in particular?

Answer 1

Welcome to the site

The first thing is to not think of it as "an association" and "no association" when what you almost surely mean is statistically significant associations (you may know that, your title has the word "significant" but you don't have it in the body of your question). Perhaps both are close to 0.05?

The next is to plot the continuous version of the two variables with a scatter plot and add a loess line. If you are using R or SAS to do the analysis, I can show you how to do this. If you are using some other software, maybe someone else can. In R, I believe this is a start:

plot(vo2gram~fruit, data = mydata)
lines(loess(vo2gram~fruit, data = mydata)

(but that code is untested)

in SAS

proc sgplot data = mydata;
 scatter x = fruit y = vo2gram;
 loess x = fruit y = vo2gram;
run;

should be a start, at least.

The idea is that there is some nonlinearity in your data, that could account for your results.