Censoring balancing functions for weighted log-rank tests

Censoring is a common feature of survival data. Weighted log-rank tests are widely used to compare survival curves representing different treatments under study, but their performance is often negatively affected by censoring. In this work, censoring balancing functions (CBFs) are proposed to mitigate this problem. These functions are classified into two types: censoring penalty functions (monotone decreasing) and censoring compensation functions (monotone increasing). The choice between the two types depends on the hazard patterns exhibited by the treatments being compared. Both types of functions are capable of improving the power of weighted log-rank tests, although already powerful or optimal tests gain only minimal increases in power. By employing these functions, differences in survival distributions that might otherwise remain undetected due to censoring can be revealed. The impact of CBFs depends on the nature of a test, the magnitude of penalties or compensations imposed, and the hazard scenario under consideration. The results in our simulation settings are supported by the analysis of two real datasets in each of the three scenarios, to ensure that findings are not merely attributable to chance.