Approximation for the variance of Kaplan-Meier
estimator.

The variance estimate is given by

$$V\left(S\left(t\right)\right)={S}^{2}\left(t\right){\displaystyle \sum _{{t}_{i}<T}\frac{{d}_{i}}{{r}_{i}\left({r}_{i}-{d}_{i}\right)}},$$

where *r*_{i} is
the number at risk at time *t*_{i},
and *d*_{i} is
the number of failures at time *t*_{i}.

## References

[1] Cox, D. R., and D. Oakes. *Analysis
of Survival Data*. London: Chapman & Hall, 1984.

[2] Lawless, J. F. *Statistical Models and Methods
for Lifetime Data*. 2nd ed., Hoboken, NJ: John Wiley &
Sons, Inc., 2003.