Which statistical test to compare mortality risk scores?


I am an ICU doctor and I am doing a study comparing the validity of three different mortality risk scores (lets call them test1, test2 and test3). They calculate a predicted mortality risk percentage based on various clinical parameters.
I have applied all three on the same population, which I know whether they have survived or not (outcome).

My question is this: is there a statistical test to check the significance between test1 vs outcome, test2 vs outcome, test3 vs outcome and the agreement between test1 and test3, test2 and test3 (independent of outcome)?

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to test how precise your three test methods predict the outcome, you can run a logistic regression model for each test, with the test-score as the predictor, and the OUTCOME as the categorical outcome variable. Size and significance related to the predictors give the information you want. To compare the three methods among themselves, you can compare the three models via AIC-value: The lowest Value gives you the prefered model. However, in order to develop a good survival prediction method, I would actually investigate also models which more that one of your test methods, i.e. the models

outcome ~ test1
outcome ~ test2
outcome ~ test3
outcome ~ test1 + test2
outcome ~ test1 + test3
outcome ~ test2 + test3
outcome ~ test1 + test2 + test3

probably the combination of different tests gives you the best prediction.

You can compare the test scores of the different methods independent of the outcome via correlation. Pearsons correlatin if data are normally distributed, Speamann's or Kendalls correlation else