Here goes:
I'm comparing pregnancy rates (binomial variable - pregnant versus non-pregnant) amongst 6 ordinal regular interval levels of progesterone prior to ovulation (levels 1 to 6). Previous studies have told us that age (which I divided in to ordinal groups of 3 year intervals, <25;25-28;28-31, 31-34 and over 34), concentration of 2 other hormones (FSH and Estradiol, both which I divided in to ordinal equally intervalled groups), stage of the embryo (day 3 or day 5 of evolution) and the amount of embryos (1 or 2...which, although numeric, I considered as non-continuous and ordinal) affect pregnancy outcome also (so, they act as confounders).
When I did the evaluation of the confounders in 6 levels of progesterone, age (continuous variable evaluated using Kruskall-Wallis), levels of FSH (continuous variable evaluated using Kruskall-Wallis), levels of Estradiol (continuous variable evaluated using Kruskall-Wallis) and amount day 5 embryos (pearson Chi2 of a dicotomous Day 3 vs Day 5) were different amongst the 6 levels of progesterone. On the other hand, the amount of patients with 2 embryos was not (pearson chi2... only a minorty, about 18%, of pregnancies were with more then one baby...this is in an IVF clinic, so there are a lot of twins!).
This is what I get if I control for all variables:
progesteone | Odds Ratio chi2 P>chi2 [95% Conf. Interval]
-------------+-------------------------------------------------------------
level 1 | 2.985859 1.68 0.1949 0.525242 16.973782
level 2 | 2.300867 4.13 0.0420 1.006566 5.259458
level 3 | 2.779715 6.48 0.0109 1.222276 6.321657
level 4 | 2.506451 5.30 0.0213 1.115158 5.633550
level 5 | 4.046512 6.61 0.0102 1.275204 12.840501
level 6 | 1.000000 . . . .
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Score test for trend of odds: chi2(1) = 2.28
Pr>chi2 = 0.1311
Hence, the difference is significant except when comparing levels 6 and 1, but with a CI very close to the unit in group 2.
If I don't control for the amount of embryos, the comparison results are the same, but the odds-ratios and confidence intervals are better (my theory is that since twins are a "rare" event of 18%, the over-stratification "ruins" everything).
Progesterone | Odds Ratio chi2 P>chi2 [95% Conf. Interval]
-------------+-------------------------------------------------------------
level 1 | 4.139169 2.85 0.0916 0.689299 24.855299
level 2 | 2.753272 6.64 0.0100 1.232656 6.149733
level 3 | 2.688303 6.80 0.0091 1.239542 5.830358
level 4 | 2.948541 7.59 0.0059 1.315549 6.608568
level 5 | 4.279392 6.75 0.0094 1.294115 14.151133
level 6 | 1.000000 . . . .
My objective is to show that low progesterone (level 1) is as detrimental as high progesterone (level 6 - the reference group).
Now, the question is...since, in my sample, the amount of twins is "only" 18% and homogenous amongst groups, can I not control for it, even though I know it is a potential confounder?
Again, thanks a lot! Let me know if I wasn't clear.
), in which the first and last hormonal levels are equally detrimental to pregnancy achievement (p=0.20). The p-values of the intermediate values, comparing to the last interval vary from 0.001 and 0.04.