This question is a follow up to one of my previous questions asked on this site. The goal was to create a composite score for biomarkers related to a binary outcome and then use that in a regression to see if the composite score can significantly predict the outcome. I had 30+ biomarkers and I ended up selecting 4 of them which were bivariately ($p<0.10$) related to the outcome. I made a composite of these 4 biomarkers using ridge regression following the helpful answer by EdM. That way I could account for the natural correlation present among these markers and get adjusted $\beta$'s (adjusting for other biomarkers and covariates like age, sex, etc.). I had 109 complete observations. The coefficients look as follows:
> ridge.mod.bestlam <- glmnet(x, y, alpha = 0, lambda = 0.2387845, standardize = TRUE, intercept=TRUE) > coef(ridge.mod.bestlam) 10 x 1 sparse Matrix of class "dgCMatrix" s0 (Intercept) -0.0252900970 Age 0.0003756038 female 0.0603410625 Premorbid_depression -0.0338846415 antidep12 0.0556264177 nGCS_Bestin24 0.0135018439 log_med_IL_10 0.0530590200 log_med_ITAC 0.0478298328 log_med_sIL_6R -0.0881823906 log_med_RANTES 0.0568835030
I multiplied the last 4 coefficients with the respective (scaled) marker values and obtained the composite score that I'd call
ILS.ridge here. I used it as an input in a final logistic regression model. The odds ratio was 423.3499, extremely high. I must be doing something wrong but cannot figure it out. I checked the VIF and it was well below 1.5 for all variables. I also provide with the final regression results here.
glm(formula = nPTDCategory_m12 ~ Age + factor(female) + factor(nGCS_Bestin24) + factor(Premorbid_depression) + factor(antidep12) + ILS.ridge, family = "binomial", data = data2) Deviance Residuals: Min 1Q Median 3Q Max -1.0708 -0.6266 -0.4577 -0.2850 2.6085 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 4.5892763 2.6980108 1.701 0.08895 . Age -0.0008613 0.0170169 -0.051 0.95963 factor(female)1 0.4465424 0.6081925 0.734 0.46282 factor(nGCS_Bestin24)1 -0.0261555 0.6160321 -0.042 0.96613 factor(Premorbid_depression)1 -0.7174396 0.8567616 -0.837 0.40238 factor(antidep12)1 0.7393719 0.6429819 1.150 0.25018 ILS.ridge 6.0481991 2.3258686 2.600 0.00931 ** > exp(6.0481991)  423.3499
I'd like to know your thoughts about this problem. Can anyone tell if I'm doing something wrong?