6.2 Algortihm

\(k\)-survival curves algorithm

1. With \(\{(\widetilde{T}_{ij}, \Delta_{ij})\), \(i=1, \ldots, n_j\)}, \(j = 1, \ldots, J\), and using the Kaplan-Meier estimator obtain \(\hat S_j\).

2. Initialize with \(K = 1\) and test \(H_0(K)\):

• Obtain the ``best" partition \(G_1, \ldots, G_K\) by means of the \(k\)-means or \(k\)-medians algorithm.

• For \(k = 1, \ldots, K\), estimate \(M_k\) and retrieve the test statistic \(D\).

• Generate \(B\) bootstrap samples and calculate \(D^{\ast b}\), for \(b = 1, \ldots, B\).

• \(D > D^{\ast (1-\alpha)}\)
  • reject \(H_0(K)\)
  • \(K = K + 1\)

  • go back to the beginning of current section

    else

  • accept \(H_0(K)\) end

3. The number \(K\) of groups of survival curves is determined.