On the analysis of life tables for dependent observations

Applying methods assuming independence when observations are positively correlated means that confidence intervals become too short and significance levels of statistical tests are less extreme. This paper discusses elements of life-table analysis based on the standard product-limit estimator and a modified Greenwood formula for its variance to be used for dependent observations. An application from oral surgery is given. Erroneously assuming independence in the analysis of a life table could have serious consequences. It is demonstrated in a simulation study that the confidence levels can be much too low. The proposed modification of the Greenwood formula for the variance of the estimated survival function most often results in confidence levels not too much below the required level. Using the upper bound for the variance will give conservative confidence intervals but also larger standard errors. Averaging individual group survival curves should only be considered for situations with large groups.