R: *s*urvival (or hazard) *f*unction based on e and n.

sf {survMisc} | R Documentation

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

### Description

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

### Usage

    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: default A numeric vector of events status (assumed sorted by time). numeric Vectors of events and numbers at risk (assumed sorted by time). A `ten` object. A `stratTen` object.
`...` | Additional arguments (not implemented).
`n` | Number at risk.
`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.

### 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

    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")

[Package survMisc version 0.5.4 Index]