# kapmeier: Implements product-limit (Kaplan-Meier) method In epitools: Epidemiology Tools

## Description

Implements product-limit (Kaplan-Meier) method for time-to-event data with censoring.

## Usage

 `1` ```kapmeier(time, status) ```

## Arguments

 `time` numeric vector with individual observation times `status` integer vector indicating status at the end of the observation time: 1 = event, 0 = censored

## Details

This function implements the product-limit method for estimating survival probability for time-to-event data with censoring:

 ```1 2``` ``` S(t) = product[(nj - dj) / nj] for all tj <= t, ```

where `tj` are event times (i.e., times at which one or more events occur), `nj` are the number at risk at time `tj` (by convention, subjects censored at time `tj` are considered at-risk and included in `nj`), and `dj` are the number of events at time `tj`.

A primary purpose of this function was to demonstrate the use of available R functions to implement a simple statistical method. For example, `kapmeier` uses `sort`, `order`, `duplicated`, `tapply`, `unique`, `cumprod`, `cbind`, and `dimnames`. Studying this function carefully helps one understand and appreciate the utility of R functions to implement simple methods.

For serious survival analysis load the `survival` package. The `survfit` function in this package implements the product-limit method and much more. See examples.

## Value

Returns an individual-level data frame

## Author(s)

Tomas Aragon, [email protected], http://www.phdata.science

## References

Selvin S. Statistical Analysis of Epidemiologic Data (Monographs in Epidemiology and Biostatistics, V. 35). Oxford University Press; 3rd edition (May 1, 2004)

See also `survfit`
 ```1 2 3 4``` ```##Product-limit method using 'kapmeier' function tt <- c(1,17,20,9,24,16,2,13,10,3) ss <- c(1,1,1,1,0,0,0,1,0,1) round(kapmeier(tt, ss), 3) ```