We consider the competing risks problem with two risks and when the
data are grouped or discrete. We firstly obtain nonparametric maximum
likelihood estimates of the sub-survival functions corresponding to
the two risks under the restriction that they are uniformly ordered
and then use them to derive the likelihood ratio statistic for testing
the null hypothesis of equality of the two sub-survival functions
against ordered alternatives. The asymptotic null distribution of the
test statistic is seen to be of the chi-bar square ($\bar{\chi}^2$)
type. A simulation study has been performed to compare the power of
the new test with an existing one.