A Spatial Scan Statistic for Survival Data

Abstract

Spatial scan statistics with Bernoulli and Poisson models are commonly used for geographical disease surveillance and cluster detection. These models, suitable for count data, were not designed for continuous outcome data. We propose a spatial scan statistic based on an exponential model to be used for uncensored or censored continuous survival data. The power and sensitivity of the developed model are investigated through intensive simulations. The method performs well for different survival distribution functions including the exponential, gamma and log normal distributions. How to adjust the analysis for covariates is described in detail. The method is illustrated using survival data for men diagnosed with prostate cancer in Connecticut from 1984 to 1995.

Multivariate scan statistics for disease surveillance

“…Other probability models have also been used for scan statistics. A Bernoulli model is used for 0/1 case-control type data [2], an ordinal model for ordinal data [20], an exponential model for survival data [21] and a space-time permutation model for looking at space-time interaction clusters when only case data is available [9]. The latter also uses the Poisson distribution but it is an approximate rather than an exact log likelihood ratio.…”

Measuring the spatial accuracy of the spatial scan statistic

“…Rather than considering distance, these studies consider the amount of overlap between true and detected clusters, and the amount of overlap between the detected clusters and those parts of the study region outside the true clusters. Examples of this approach can be found in Huang et al (2007) (2007) and Jung et al (2010). In an individual data set level, these can be expressed as = a/(a + b) and = a/(a+c), respectively.…”

“…An excellent example is the a, b, c, d notation used by Jacquez (2009), where areal units into one of four types (illustrated in Figure 1 A different, and slightly more succinct, subdivision method is used in papers introducing new versions of the SSS: Huang et al (2007), Jung et al (2007) and Jung et al (2010). This is shown below, the relationship to the notation above given in brackets:…”

“…The obvious choice is to take the arithmetic mean for each measure across all data sets in the batch. This is the approach taken by Huang et al (2007), Jung et al (2007), Jung et al (2010), Neill (2009), Olson et al (2006) and Que et al (2008).…”

“…It may be a more extensive set of points, e.g. home addresses as used by Huang et al (2007), or a set of area centroids, e.g. the county centroids used by Jacquez (2009).…”