The Nelson-Aalen estimator is a non-parametric estimator of the cumulative hazard function. The following R Markdown illustrates 3 ways for obtaining this estimator for a sample containing right-censored observations.
The following R code shows an (probably suboptimal) implementation of the log partial likelihood function as well as three real-data examples illustrating the calculation of the MPLE (using the command optim()). A comparison with the results obtained using the survival R package is also presented.
The R command spLT from the routinesSPLT.R source file performs the following steps:
-
It calculates all the change points from the date of diagnosis (birthdays and new years) and merges them with the time points of interest.
-
It extracts the hazard rates at these points from the life table.
-
It calculates the integrals of the step function defined in the previous steps up to each time point of interest. These integrals represent the cumulative hazard function.
-
It calculates the survival probabilities using the usual relationship between the cumulative hazard function and the survival function
$S(t) = \exp[-H(t)]$ .
The following R code presents a step-by-step illustrative example on the calculation of the survival probabilities of a set of individuals based on life tables from England for the years 2010-2015.:
SurvLT: Calculating survival probabilities from a Life Table
See also: SimLT