The limit of detection (LOD) is commonly encountered in observational studies when one or more covariate values fall outside the measuring ranges. Although the complete-case (CC) approach is widely employed in the presence of missing values, it could result in biased estimations or even become inapplicable in small sample studies. On the other hand, approaches such as the missing indicator (MDI) approach are attractive alternatives as they preserve sample sizes. This paper compares the effectiveness of different alternatives to the CC approach under different LOD settings with a survival outcome. These alternatives include substitution methods, multiple imputation (MI) methods, MDI approaches, and MDI-embedded MI approaches. We found that the MDI approach outperformed its competitors regarding bias and mean squared error in small sample sizes through extensive simulation.