I am aware that, in multiple regression cox model, we test (Wald) each variate to show if it has significant impact on survival. Also, we got the significance of overall model using Wald, LR and Score test. What does this overall model mean? The confusion is that We seperate our total dataset differently depending on which variate we are testing. How can we test our overall model when the grouping is not fixed?
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1$\begingroup$ multiple and multivariate are two totally different concepts in statistics.overall model is not common, and it maybe means the effect of all covariates in the model. For last question, maybe the example is needed. $\endgroup$– user158565Commented May 30, 2019 at 3:56
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$\begingroup$ Sorry, by multivariate I mean multiple regression cox model. The p-value calculated by Wald, LR and Score test is still the comparison between two regressions, right? However, depending on the different variate, we group our dataset differently. So what is excatly the "overall" model? $\endgroup$– unicornCommented May 30, 2019 at 5:12
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$\begingroup$ Where did you get the phrase of overall model? software output, book, or article? $\endgroup$– user158565Commented May 30, 2019 at 15:07
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A Wald test can be used to test whether any linear combination of estimated parameter values is significantly different from a specified null hypothesis. See the multiple parameters section of the Wikipedia page. This general form of the test uses estimates of the individual-coefficient variances and of the covariances among them to provide a single statistic for a given combination of coefficients. It's based on the formula for the variance of a sum of correlated variables.
The global Wald test of your Cox model is whether any of the coefficients in different from zero, using the statistic calculated from the formula shown at the beginning of this answer. That answer goes on to illustrate the situation for one specific coefficient. So these are both Wald tests, but applied to different combinations of coefficients.
