# kphaz.fit: kphaz.fit In muhaz: Hazard Function Estimation in Survival Analysis

## Description

Calculates Kaplan-Meier type hazard estimates.

## Usage

 `1` ```kphaz.fit(time,status,strata,q=1,method="nelson") ```

## Arguments

 `time` A vector of time values; all values must be greater than or equal to zero. Missing values (NAs) are not allowed. `status` A vector of status values. The values are 0 for censored or 1 for uncensored (dead). Missing values (NAs) are not allowed. Must have the same length as time. `strata` An optional vector that will be used to divide the subjects into disjoint groups. Each group generates a hazard curve. If missing, all subjects are assumed to be in the same strata. Missing values (NAs) are allowed. `q` Number of failure times combined for estimatingthe hazard at their midpoint. Default is 1. `method` Type of hazard estimation made. Must be one of "nelson" or "product-limit". The default is "nelson".

## Details

Let

t[1] < t[2] < \cdots < t[m]

denote the m "distinct" death times.

1. Estimate the cumulative hazard, H[t[j]], and the variance of the cumulative hazard, Var(H[t[j]]), at each of the m distinct death times according to the method selected.

a. For the "nelson" method:

H[t[j]] = sum(t[i] <= t[j]) status[i]/(n-i+1)

Var(H[t[j]]) = ∑(t[i] <= t[j]) status[i]/((n-i+1)^2)

b. For the "product-limit" metod:

H[t[j]] = sum(t[i] <= t[j]) -log(1 - status[i]/(n-i+1))

Var(H[t[j]]) = sum(t[i] <= t[j]) status[i]/((n-i+1)*(n-i))

2. For k=1,...,(m-q), define the hazard estimate and variance at time[k] = (t[q+j]+t[j])/2 to be

haz[time[k]] = (H[t[q+j]]-H[t[j]])/(t[q+j]-t[j])

var[time[k]] = (Var(H[t[q+j]])-Var(H[t[j]]))/ (t[q+j]-t[j])^2

Note that if the final time is a death time rather than a censoring time, the "product-limit" estimate will be Inf for the final hazard and variance estimates.

## Value

A list representing the results of the hazard estimation, with the following components:

 `time` A vector containing the times at which hazard estimations were made. `haz` A vector containing the hazard estimate at each time. `var` A vector containing variance estimates for each hazard estimate. `strata` A vector which divides the hazard estimate into disjoint groups. This vector is returned only if 'strata' is defined when 'kphaz.fit' is called.

## References

Jarjoura, David (1988). Smoothing Hazard Rates with Cubic Splines. Commun. Statist. -Simula. 17(2), 377-392.

`kphaz.plot`
 ```1 2 3``` ```time <- 1:10 status <- rep(1,10) kphaz.fit(time,status) ```