The Kaplan-Meier estimator then always gives a valid redistribution of the upper limits, though the result may not be applicable in wider contexts. The Gehan test assumes that the censoring patterns of the two samples are the same, but does not require that they be random. The logrank test results appear to be correct even when the censoring patterns differ somewhat. There is little known about the limitations of the other two-sample tests given here or the bivariate generalized Kendall's tau rank statistic. The two bivariate correlation coefficients, generalized Kendall's tau and Cox regression, are both known to be inaccurate when many tied values are present in the data.
Ties are particularly common when the data is binned.
Caution should be used in these cases. Astronomical luminosity functions, in contrast, are frequently modelled by power law distributions. It is not clear whether a Cox regression is significantly affected by this difference. First, only schmittbin works when censoring is present in both variables. Second, emmethod requires that the residuals about the fitted line follow a Gaussian distribution.