(I am a clinician, not a statistician!)
I have been asked to advise on a study which uses logistic regression. The aim is to identify ultrasound measurements which predict miscarriage. The outcome variable is pregnancy loss (miscarriage) after 12 weeks’ pregnancy. There were ~750 women who did not have a miscarriage and 55 women who did.
There are 5 explanatory variables, all of which are expected to increase with gestational age (number of weeks’ pregnancy). Ultrasounds were done at 6 to 11 weeks’ pregnancy. Most measurements do not have published reference ranges.
As an example, one of the variables is the “trophoblast thickness” (TT). We want to ‘standardise’ this variable for gestational age. We considered:
z-score for a given gestational age: we could do this, but are not sure how to estimate the standard deviation (which clearly changes with gestational age).
centile for a given gestational age (we didn’t attempt this)
multiple of the median (MoM) for a given gestational age. We used quantile regression in the women who did not have a miscarriage to estimate the median for a given gestational age. We plotted MoMs against gestational age but the mean MoM varied by gestational age – we abandoned this approach.
We used quantile regression for the 50th, 25th and 75th centiles in the 750 women who did not have a miscarriage and used the formula:
new variable = (TT - GA[50th])/(GA[75th]-GA[25th])
...trying to give a value analagous to a z-score using number of “interquartile ranges” as the denominator, where TT = raw measurement of trophoblast thickness, GA[50th], GA[75th] and GA[25th] are estimated centiles for gestational age using quantile regression formulas
Plotting this value against gestational age gave an even scatter of values centred about zero.
My questions are:
(a) what is the best approach to standardise an explanatory variable (like TT) with a strong correlation with a second variable (like gestational age) given the second variable has no association with the outcome?
(b) is it valid to simply add gestational age at time of ultrasound as a covariate?