kphaz.fit
Calculates Kaplan-Meier type hazard estimates.
kphaz.fit(time,status,strata,q=1,method="nelson")
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". |
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.
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. |
Jarjoura, David (1988). Smoothing Hazard Rates with Cubic Splines. Commun. Statist. -Simula. 17(2), 377-392.
time <- 1:10 status <- rep(1,10) kphaz.fit(time,status)
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