Survival and competing risks outcomes are frequently the main interest of a clinical trial. Rather than comparing the entire survival or cumulative incidence curves of treatment groups, it is often preferable to compare these probabilities at a fixed time point of strong clinical importance. Adjustment for covariates in the analysis can improve the efficiency of these comparisons, but none of the currently available group sequential tests for fixed point analysis provide this adjustment. We propose group sequential tests of treatment effect on survival and cumulative incidence at a fixed time point that adjust for covariates. Their test statistics are shown to have an asymptotic distribution with independent increments, permitting use of common methods for specifying stopping boundaries. These tests are demonstrated through a redesign of BMT CTN 0402, a clinical trial that evaluated a prophylaxis for the occurrence of graft versus host disease following bone marrow transplantation. Moreover, an extensive simulation study demonstrates that these tests maintain the type I error rate and power at the targeted levels in a variety of of settings where influential covariates are at play.