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I'm reading a paper about survival analysis. After doing the univariate analysis, the paper only put covariates which have significant results in the univariate analysis into the multivairate regression. My questions are:

  1. Is it the right way to include only significant covariates in the multivariate regression?

2.If not, for survival analysis, what are the best variable selection methods for cox model and aft models? And is there any recommended packages in R?

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The method you are describing is known as bivariate screening. It is a very common method, but not a good one. For details, see Frank Harrell's book Regression Modelling Strategies but, briefly, all the output will be off: Standard errors will be too low, p values too low, parameter estimates biased away from 1.00, etc. Worst of all, using an automatic method prevents the analyst from thinking.

The best method is to use substantive knowledge. If you must use an automated method, LASSO is more reasonable than bivariate screening (or forwards or backwards or stepwise).

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