Asymptotic distribution of score statistics for spatial cluster detection with censored data

Cook, Gold, and Li (2007, Biometrics 63, 540-549) extended the Kulldorff (1997, Communications in Statistics 26, 1481-1496) scan statistic for spatial cluster detection to survival-type observations. Their approach was based on the score statistic and they proposed a permutation distribution for the maximum of score tests. The score statistic makes it possible to apply the scan statistic idea to models including explanatory variables. However, we show that the permutation distribution requires strong assumptions of independence between potential cluster and both censoring and explanatory variables. In contrast, we present an approach using the asymptotic distribution of the maximum of score statistics in a manner not requiring these assumptions.