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Someone asked me about an analysis that showed certain factors were predictive of a health outcome when considered individually. When these factors were included in a multivariate model that included other factors, they were no longer statistically significant.
This is worth investigating further but perhaps you need to live with a bit of ambiguity in the data. Perhaps some of these variables are correlated strongly with other variables that are in the final model. You might find for example, that gestational age is a useful predictor of health outcomes in a univariate model, but it is not significant in a multivariate model that also includes birth weight. This is hardly surprising, since birth weight and gestational age are so tightly correlated.
There is also the possibility that the multivariate model is itself wrong. There is no approach to multivariate models that will guarantee that you end up with the "correct model" when you are done. Some approaches work better than others, but there will always be some unquantifiable degree of uncertainty about the final multivariate model that you choose.
This may not be as bad as it sounds though. George Box has a famous quote "All models are wrong, but some are useful."