SAP HANA Predictive Analysis Library (PAL)

The Kaplan-Meier estimator can be regarded as a point estimate of the survival function S(t) at any time
t. We can construct 95% confidence intervals around each of these estimates. To compute the confidence
intervals, Greenwood’s Formula gives an asymptotic estimate of the variance of for large groups:
So the Greenwood’s confidence interval is:
Where Z α/2 is the α/2–th quantile of the normal distribution.
However the endpoints of Greenwood’s confidence interval can be negative or greater than one. Here we use
another confidence interval based on the large sample normal distribution of log(-log( )) with:
So we get:
Transform endpoints (ci_lower, ci_upper) back to obtain confidence interval:
(exp(-exp(ci_lower)), exp(-exp(ci_upper)))
Equality comparison of two or more Kaplan-Meier survival functions can be done using a statistical hypothesis
test called the log rank test by weighting all time points the same. It is used to test the null hypothesis where
there is no difference between the population survival functions.
For i=1, 2, ... , g and j=1, 2, … , k, where g is number of groups and k is number of distinct failure
times.
n ij = number at risk in i th group at j th ordered failure time
o ij = observed number of failures in i th group at j th ordered failure time
e ij = expected number of failures in i th group at j th ordered failure time =
SAP HANA Predictive Analysis Library (PAL)
PAL Functions P U B L I C 519