Using contrast post logistic to assess linear trend - response to a reviewer

[Francesmary Modugno]

Hello

I am assessing the relationship between a binary outcome variable and a 4-category variable (cat_boy_ful) while controlling for potential co-variates/confounders using logistic:

logistic cancer i.cat_boy_ful refage i.race_c4 i.ocmos_c i.num_full_c

and then assessing if there is a linear trend using contrast

contrast p.cat_boy_ful, noeffects

The ORs from the logistic model are:

------------------------------------------------------------------------------
cancer | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cat_boy_ful |
1 | 1.158866 .1314434 1.30 0.194 .9278688 1.447372
2 | 1.485356 .2044201 2.87 0.004 1.134189 1.945253
3+ | 1.374283 .2647452 1.65 0.099 .9421038 2.00472

and the results of contrast are:
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
cat_boy_ful |
(linear) | 1 3.89 0.0487
(quadratic) | 1 1.27 0.2590
(cubic) | 1 1.49 0.2224
Joint | 3 8.73 0.0331
------------------------------------------------

indicating a significant linear trend at the cutoff of 0.05.

A reviewer of the paper questioned this because the OR for the 3+ category is less than that of the 2 category (1.37 vs 1.49).

Can someone help me understand and respond to this reviewer?

Thank you!

[Marcos Almeida]

It seems the odds ratios are decreasing on a par with the categories. With regards to contrasts, maybe - contrasts a.cat_boy - would provide comparisons between comparisons. In order to perform a trend test, - nptrend yvar, by(groupvar) - will present the Jocnkhere-Terpstra test. This notwithstanding, the evidence favors just one categoy, not a trend.

That being said, one extra points to consider: CIs for the last category are large (unbalanced groups?) and this can explain the higher p values.

In case the "real" variable was continuous , maybe it should be used directly in the regression, thus providing information about linear or quadratic terms, for example.

[Francesmary Modugno]

Thank you Marcos.