Criteria for confounders in survival function

This paper discusses the criteria for detecting confounders in the survival function under the condition that an exposure is binary, and the response and covariates are both continuous. To assess the amount of confounding bias by Martinussen and Vansteelandt (Lifetime Data Anal 19:279- 296, 2013), we need to detect whether the covariates are confounders. By the partition, we obtain the necessary and sufficient conditions for the uniformly irrelevant factor when the covariate is one-dimensional. Then the sufficient conditions for the conditional uniformly irrelevant factor vector are also obtained when the covariate is multidimensional. Further we propose the criteria for detecting a single confounder and multiple confounders in survival function.