# sf: *s*urvival (or hazard) *f*unction based on e and n. In survMisc: Miscellaneous Functions for Survival Data

## Description

survival (or hazard) function based on e and n.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```sf(x, ...) ## Default S3 method: sf(x, ..., what = c("S", "H"), SCV = FALSE, times = NULL) ## S3 method for class 'ten' sf(x, ..., what = c("S", "H"), SCV = FALSE, times = NULL, reCalc = FALSE) ## S3 method for class 'stratTen' sf(x, ..., what = c("S", "H"), SCV = FALSE, times = NULL, reCalc = FALSE) ## S3 method for class 'numeric' sf(x, ..., n = NULL, what = c("all", "S", "Sv", "H", "Hv"), SCV = FALSE, times = NULL) ```

## Arguments

 `x` One of the following: defaultA numeric vector of events status (assumed sorted by time). numericVectors of events and numbers at risk (assumed sorted by time). A `ten` object. A `stratTen` object. `...` Additional arguments (not implemented). `what` See return, below. `SCV` Include the Squared Coefficient of Variation, which is calcluated using the mean mean(x) and the variance var(x): SCV[x] = var(x) / mean(x)^2 This measure of dispersion is also referred to as the 'standardized variance' or the 'noise'. `times` Times for which to calculate the function. If `times=NULL` (the default), times are used for which at least one event occurred in at least one covariate group. `reCalc` Recalcuate the values? If `reCalc=FALSE` (the default) and the `ten` object already has the calculated values stored as an `attribute`, the value of the `attribute` is returned directly. `n` Number at risk.

## Value

A data.table which is stored as an attribute of the `ten` object.
If `what="s"`, the survival is returned, based on the Kaplan-Meier or product-limit estimator. This is 1 at t=0 and thereafter is given by:

S[t] = prod (1 - e[t]) / n[t]

If `what="sv"`, the survival variance is returned.
Greenwoods estimtor of the variance of the Kaplan-Meier (product-limit) estimator is:

Var(S[t]) = S[t]^2 sum e[t] / (n[t] * (n[t] - e[t]))

If `what="h"`, the hazard is returned, based on the the Nelson-Aalen estimator. This has a value of H=0 at t=0 and thereafter is given by:

H[t] = sum(e[t] / n[t])

If `what="hv"`, the hazard variance is returned.
The variance of the Nelson-Aalen estimator is given by:

Var(H[t]) = sum(e / n^2)

If `what="all"` (the default), all of the above are returned in a `data.table`, along with:
Survival, based on the Nelson-Aalen hazard estimator H, which is:

S[t] = exp(H[t])

Hazard, based on the Kaplan-Meier survival estimator S, which is:

H[t] = -log(S[t])

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```data("kidney", package="KMsurv") k1 <- ten(Surv(time=time, event=delta) ~ type, data=kidney) sf(k1) sf(k1, times=1:10, reCalc=TRUE) k2 <- ten(with(kidney, Surv(time=time, event=delta))) sf(k2) ## K&M. Table 4.1A, pg 93. ## 6MP patients data("drug6mp", package="KMsurv") d1 <- with(drug6mp, Surv(time=t2, event=relapse)) (d1 <- ten(d1)) sf(x=d1\$e, n=d1\$n, what="S") data("pbc", package="survival") t1 <- ten(Surv(time, status==2) ~ log(bili) + age + strata(edema), data=pbc) sf(t1) ## K&M. Table 4.2, pg 94. data("bmt", package="KMsurv") b1 <- bmt[bmt\$group==1, ] # ALL patients t2 <- ten(Surv(time=b1\$t2, event=b1\$d3)) with(t2, sf(x=e, n=n, what="Hv")) ## K&M. Table 4.3, pg 97. sf(x=t2\$e, n=t2\$n, what="all") ```

survMisc documentation built on May 2, 2019, 3:16 a.m.