# What is the minimum number of events needed for Kaplan-Meier estimation in survival analysis

I have a cohort of 1185 breast cancer patients - 40 patients are <40 years old, and 8 patients developed local recurrence (2 of which are <40). I want to see if there is any association between age <40 years and the risk of local recurrence. Are these numbers too small to do such analysis? When I try to run KM analysis in SPSS, I don`t get any data for Median Survival Time (only see data for Mean Survival Time, CI 95%) but Log Rank, Breslow and Tarone-Ware all yield p<0.05. However, I am not sure if these results are significant due to the small number of events?

The problem is that you don't know, because you never observed that moment. Thus, SPSS cannot report a median lifetime.

Regarding the minimum number of events: It depends. A small number of events results in a low power (higher probability for type-II-error). However, the power of the test depends also on the effect that should be revealed. If your age variable has a very strong effect on your survival rate, the power might still be high (low probability for type-II-error).

However, estimates will not be very precise. SPSS allows you to save the predicted survival rates and the standard error of those via the "save button". Now, take the standard error times 1.96 for computing the .95 confidence interval/band. After that you can plot the survival rate for each age-group and the group-specific confidence band. By doing that, you get both: the best estimation of the survival rate and the uncertainty caused by the low number of events.

Typically, small number of events should not increase type-I-error. Thus, the tests cannot become significant because the amount of events is small. However, small sample sizes can increase type-I-error in some special cases. For example, you tested several cut-offs, e.g., age<30, then age<35, and so on. In that case the chance for finding a sign. cut-off-point by accident increases generally but especially fast if the number of events is small.