COV {survMisc}

covariance matrix for survival data

Description

covariance matrix for survival data

Usage

COV(x, ...)

## S3 method for class 'ten'
COV(x, ..., reCalc = FALSE)

## S3 method for class 'stratTen'
COV(x, ..., reCalc = FALSE)

## S3 method for class 'numeric'
COV(x, ..., n, ncg)

Arguments

x

A numeric vector of number of events, e_t. These are assumed to be ordered by discrete times.
A method is available for objects of class ten.

...

Additional arguments (not implemented).

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.

–Arguments for the numeric method:

n

number at risk (total).

ncg

number at risk, per covariate group.
If there are 2 groups, this can be given as a vector with the number at risk for group 1.
If there are \geq 2 groups, it is a matrix with one column for each group.

Details

Gives variance-covariance matrix for comparing survival data for two or more groups.
Inputs are vectors corresponding to observations at a set of discrete time points for right censored data, except for n1, the no. at risk by predictor.
This should be specified as a vector for one group, otherwise as a matrix with each column corresponding to a group.

Value

An array.
The first two dimensions = the number of covariate groups K, k = 1, 2, \ldots K. This is the square matrix below.
The third dimension is the number of observations (discrete time points).

To calculate this, we use x (= e_t below) and n_1, the number at risk in covariate group 1.
Where there are 2 groups, the resulting sparse square matrix (i.e. the non-diagonal elements are 0) at time t has diagonal elements:

cov_t = - \frac{n_{0t} n_{1t} e_t (n_t - e_t)}{n_t^2(n_t-1)}

For \geq 2 groups, the resulting square matrix has diagonal elements given by:

cov_{kkt} = \frac{n_{kt}(n_t - n_{kt}) e_t(n_t - e_t)}{ n_t^2(n_t - 1)}

The off diagonal elements are:

cov_{klt} = \frac{-n_{kt} n_{lt} e_t (n_t-e_t) }{ n_t^2(n_t-1)}

Note

Where the is just one subject at risk n=1 at the final timepoint, the equations above may produce NaN due to division by zero. This is converted to 0 for simplicity.

See Also

Called by comp

The name of the function is capitalized to distinguish it from:
?stats::cov

Examples

## Two covariate groups
## K&M. Example 7.2, pg 210, table 7.2 (last column).
## Not run: 
data("kidney", package="KMsurv")
k1 <- with(kidney,
           ten(Surv(time=time, event=delta) ~ type))
COV(k1)[COV(k1) > 0]

## End(Not run)
## Four covariate groups
## K&M. Example 7.6, pg 217.
## Not run: 
data("larynx", package="KMsurv")
l1 <- ten(Surv(time, delta) ~ stage, data=larynx)
rowSums(COV(l1), dims=2)

## End(Not run)
## example of numeric method
## Three covariate groups
## K&M. Example 7.4, pg 212.
## Not run: 
data("bmt", package="KMsurv")
b1 <- asWide(ten(Surv(time=t2, event=d3) ~ group, data=bmt))
rowSums(b1[, COV(x=e, n=n, ncg=matrix(data=c(n_1, n_2, n_3), ncol=3))], dims=2)

## End(Not run)