How to explain ROC curve results that contradict the results of other statistical tests I have carried out a ROC curve analysis to determine how useful two acute phase proteins (APPs) and hair cortisol are at accurately discriminating tail bitten pigs from unbitten pigs. The ROC curve results indicate that the APPs are able to discriminate at chance level (AUC: 0.500) making them 'meaningless'. Hair cortisol was found to have moderately ability (AUC: ~ 0.750). 
However, I have also carried out mixed model procedures where I controlled for various variables e.g. weight, batch etc. These results indicated that one of the APPs was associated with tail lesions and is therefore a useful measure for indicating tail lesions. 
How do I discuss these conflicting findings?
Thank you
 A: The apparent conflict is just a matter of correctly interpreting the risk prediction and the logistic model, conditional and marginal analyses, as well as understanding the differences between predictiveness and statistical significance.
A risk factor can exhibit an association in a stratified model that is not apparent in crude analysis. This can be because of confounding or non-collapsibility of the logit link. For this reason you cannot compare risk factors in models that do and do not adjust for particular prognostic features, like weight, batch, and so on and so forth.
A mixed model is a conditional analysis, different from the predictive marginal model. In a cross sectional sample, where you observe one row of data per pig, the outcome (bitten/not bitten) does not vary within individual. You do not observe baseline covariates in a "non-bitten" status. Small changes in these values can be significant for an individual, but reflect a relatively small Z-score difference in the population baseline settings. The mixed/conditional model is sensitive to detecting these differences but a marginal model is not. This is the primary challenge of applying risk predictions in a non-cohort setting.
Lastly covariates may be predictive, but not statistically significant, or vice versa. While in most cases, large odds ratios for prevalent outcomes tend to be both statistically significant and predictive of the outcome, it is hard to visualize this in a multivariate setting. We use separate criteria to assess both conditions for that reason. 
As an example, if a 35 year old woman has both BRCA-1 and BRCA-2 mutations, her risk of incident breast cancer in the next 5 years is nearly 80%. Irrefutably, these markers are of high predictive value, but their prevalence in the population is very rare. In even decent sized sample, the precision of the odds ratio, despite being 10-fold, is typically not statistically significant because fewer than 10 women simultaneously exhibit such mutations.
