survConcordance           package:survival           R Documentation

_C_o_m_p_u_t_e _a _c_o_n_c_o_r_d_a_n_c_e _m_e_a_s_u_r_e.

_D_e_s_c_r_i_p_t_i_o_n:

     This function computes the concordance between a right-censored
     survival time and a single continuous covariate

_U_s_a_g_e:

     survConcordance(formula, data, weights, subset, na.action)

_A_r_g_u_m_e_n_t_s:

 formula: a formula with a survival time on the left and a single
          covariate on the right. 

    data: a data frame 

weights,subset,na.action: as for 'coxph'

_D_e_t_a_i_l_s:

     Concordance is defined as Pr(agreement) for any two randomly
     chosen observations, where in this case agreement means that the
     observation with the shorter survival time of the two  also has
     the larger risk score. The predictor (or risk score) will often be
     the result of a Cox model or other regression.

     For continuous covariates concordance is equivalent to Kendall's
     tau, and for logistic regression is is equivalent to the area
     under the ROC curve.  A value of 1 signifies perfect agreement,
     .6-.7  a common result for survival data, .5 an agreement that is
     no better than chance, and .3-.4 the performace of some stock
     market analysts.

     The computation involves all n(n-1)/2 pairs of data points in the
     sample. For survival data, however, some of the pairs are
     incomparable.   For instance a pair of times (5+, 8), the first
     being a censored value. We do not know whether the first survival
     time is greater than or less than the second. Among observations
     that are comparable, pairs may also be tied on survival time (but
     only if both are uncensored) or on the predictor. The final
     concondance is (agree + tied/2)/(agree + disagree + tied).

     There is, unfortunately, one aspect of the formula above that is
     unclear. Should the count of ties include observations that are
     tied on survival time y, tied on the predictor x, or both? In 2 by
     2 tables, Kendall's tau-b is equal to (agree - disagree)/ n, where
     n is the geometric mean of (agree + disagree + tied.x) and (agree
     + disagree + tied.y).  The Goodman-Kruskal Gamma statistic is
     (agree-disagree)/(agree + disagree), ignoring ties.  It ranges
     from -1 to  +1 similar to a correlation coefficient. 

     In this program we count those observations which were tied on x,
     but not tied on y (survival time), as `ties'.  All of the
     components are returned in the result, however, so people can
     compute other combinations if interested. (If two observations
     have the same survival and the same x, they are counted in the
     tied.time category).

_V_a_l_u_e:

     an object containing the concordance, followed by the number of
     pairs that agree, disagree, are tied, and are not comparable.

_S_e_e _A_l_s_o:

     summary.coxph

_E_x_a_m_p_l_e_s:

     survConcordance(Surv(time, status) ~age, data=lung)
     ## Not run: 
       n= 228 
     Concordance= 0.5501899 , Gamma= 0.1034234 
      agree disagree tied.x tied.time incomparable 
      10717     8708    589        28         5836
     ## End(Not run)

     options(na.action=na.exclude)
     fit <- coxph(Surv(time, status) ~ ph.ecog + age + sex, lung)
     survConcordance(Surv(time, status) ~predict(fit), lung)
     ## Not run: 
       n=227 (1 observations deleted due to missing values)
     Concordance= 0.6371102 , Gamma= 0.2759638 
      agree disagree tied.x tied.time incomparable 
      12544     7118    125        28         5836
     ## End(Not run)