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.
Usage
covMatSurv(t, n, e, n1)
Arguments
t
time
n
no. at risk
e
no. events
n1
no. at risk (by predictor).
If 2 groups,
should be given as a vector n1 with no. at risk for n1.
If more than 2 groups, a matrix with a column for
each group.
Value
An array. First two dimensions = no. groups.
Third
dimension is no. observations (time points).
Where there are two groups, the resulting sparse square
matrix at time $i$ has diagonal elements: $$v_i =
- \frac{n0_i n1_i e_i (n_i-e_i)}{n_i^2(n_i-1)}$$ where
$n1$ is the no. at risk in group 1.
For more
than two groups, the resulting square matrix has diagonal
elements: $$v_{kki} =
\frac{n_{ki}(n_i-n_{ki})e_i(n_i-e_i)}{n_i^2(n_i-1)}$$ and off diagonal elements: $$v_{kli} = \frac{ -n_{ki}n_{li}
e_i(n_i-e_i)}{n_i^2(n_i-1)}$$