Bivariate vs. multivariate analysis I have been reading a few papers lately that has done both bivariate and multivariate analysis on their data. What I have seen most of the times is that they usually do the bivariate analysis first, and if the p-value is below 0.05 they will do the multivariate as well. But what I have been reading that is, or at least CAN be an erroneous approach since there might not be much connection between variables if done alone, but sometimes when in combination with others, and reversely.
So what would be the correct approach ?
Let's say I want to make some kind of model that takes the important variables into account. What if the p-value is <0.05 for bivariate analysis, but above when multivariate is used. And what if it is above in bivariate and below in multivariate etc.
Basically, what would be the correct approach, or are there many different ? 
 A: There can be some valid rationales for what you call "bivariate" analysis.
For example, analysis of survival as a function of each individual predictor variable (a set of "bivariate" analyses in your terminology) gives clinicians assurance that the patient cohort being studied is reasonably representative. Clinicians might not be able to keep track in their heads the complex associations seen in multiple-predictor models, but for example in cancer studies they do know several single-predictor associations that should be expected in a representative patient cohort. There should be shorter survival for those with higher disease stage, smokers having some types of cancer should have shorter survival than non-smokers, certain disease characteristics (e.g, involvement of human papillomavirus) should be related to survival, etc. None of these single-predictor associations necessarily has causal or mechanistic significance, and may well be related to associations with other predictors, but they are descriptive characteristics expected of a type of patient cohort.
That said, your argument and that in @PaulHewson's answer are completely on point for analysis. Particularly in logistic regression and survival analysis, with their inherent omitted-variable biases, multiple-predictor models are needed. Use of an arbitrary p-value cutoff to choose those predictors can be misleading. See the link to model selection threads provided by  @whuber for extensive discussion.

Note that many prefer to reserve the term "multivariate" for situations with multiple outcome variables. I took your use of the term to represent a situation with multiple predictor variables.
A: I've never understood the rationale for bivariate analysis in this situation. I think you need a multivariate model to understand the data, you need a model.  If you have confounding between predictors and outcome you need to control for this in the model. Otherwise the bivariate analysis may be telling you more about confounded predictors than the outcome of interest.   Simpson's paradox explains this in a categorical case, Lord's paradox in a continuous case.
