SaTScan 9.0用户指南：空间分析统计软件操作详解

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SaTScan是一款专用于空间扫描统计的软件工具，其用户指南详细介绍了该软件的各个版本，本文档是针对v9.0版本的。由Martin Kulldorff编写，发布日期为2010年7月，可供用户参考和学习。该手册的主要内容包括： 1. **介绍**：首先，手册为读者提供了对SaTScan软件的概述，解释了其在空间数据分析中的应用价值和优势，以及为何对于公共卫生、地理学和流行病学等领域研究者来说至关重要。 2. **软件安装与测试运行**：指南指导用户如何下载和安装SaTScan软件，确保正确配置环境并进行初次运行，以便熟悉软件界面和基本操作流程。 3. **样本数据集**：文档提供了一些示例数据集，帮助用户了解如何导入和处理实际的数据，以便进行空间和时间扫描分析。 4. **统计方法论**：涵盖了软件支持的多种统计模型，如伯努利模型、离散泊松模型、空间-时间随机游走模型、多项式模型、有序模型、指数模型、正态模型和连续泊松模型，这些模型用于识别疾病或事件的空间和时间聚集模式。 5. **模型比较与评估**：讨论了如何通过似然比检验（Likelihood Ratio Test）来比较不同模型的优劣，以及如何处理次级聚类，即除了主要聚集区域外的额外发现。 6. **调整因素**：指南说明了如何在分析中考虑和调整可能影响结果的协变量，包括空间和时间上的调整，以及如何处理缺失数据。 7. **多变量扫描与多数据集分析**：对于涉及多个数据源的情况，介绍了如何使用SaTScan进行多变量扫描，以揭示更全面的空间-时间关联。 8. **与其他方法的对比**：这部分探讨了SaTScan在空间和空间-时间聚类检测方面的优势，以及它与其他流行的空间流行病学分析方法之间的区别。 9. **输入数据要求**：详细列出了进行空间扫描所需的各种数据类型，如病例、对照、人口、坐标、网格、非欧几里得邻接关系等，并介绍了如何使用SaTScan Import Wizard导入数据。 10. **SaTScan ASCII文件格式**：最后，指南覆盖了如何创建和使用SaTScan的ASCII文件格式，以支持不同的数据输入和导出需求。 SaTScan用户指南是一份详尽的操作手册，无论你是初次接触此软件还是希望深入理解其高级功能，都能从中找到关键信息和实用步骤。通过掌握这些内容，用户将能有效地利用SaTScan进行空间扫描统计分析，提升公共卫生决策的科学依据。

SaTScan User Guide v9.0 16

weighted normal scan statistic will produce the same results as the standard normal version. If all the

weights are multiplied by the same constant, the results will not change.

Related Topics: Analysis Tab, Likelihood Ratio Test, Methodological Papers, Probability Model

Comparison.

Continuous Poisson Model

All the models described above are based on data observed at discrete locations that are considered to be

non-random, as defined by a regular or irregular lattice of location points. That is, the locations of the

observations are considered to be fixed, and we evaluate the spatial randomness of the observation

conditioning on the lattice. Hence, those are all versions of what are called discrete scan statistics

174

. In a

continuous scan statistics, observations may be located anywhere within a study area, such as a square or

rectangle. The stochastic aspect of the data consists of these random spatial locations, and we are

interested to see if there are any clusters that are unlikely to occur if the observations where

independently and randomly distributed across the study area. Under the null hypothesis, the

observations follow a homogeneous spatial Poisson process with constant intensity throughout the study

area, with no observations falling outside the study area.

Example: The data may consist of the location of bird nests in a square kilometer area of a forest. The

interest may be to see whether the bird nests are randomly distributed spatially, or in other words,

whether there are clusters of bird nests or whether they are located independently of each other.

In SaTScan, the study area can be any collection of convex polygons, which are convex regions bounded

by any number straight lines. Triangles, squares, rectangles, rhombuses, pentagons and hexagons are all

examples of convex polygons. In the simplest case, there is only one polygon, but the study area can also

be the union of multiple convex polygons. If the study area is not convex, divide it into multiple convex

polygons and define each one separately. The study area does not need to be contiguous, and may for

example consist of five different islands.

The analysis is conditioned on the total number of observations in the data set. Hence, the scan statistic

simply evaluates the spatial distribution of the observation, but not the number of observations.

The likelihood function used as the test statistic is the same as for the Poisson model for the discrete scan

statistic, where the expected number of cases is equal to the total number of observed observations, times

the size of the scanning window, divided by the size of the total study area. As such, it is a special case of

the variable window size scan statistic described by Kulldorff (1997)

. When the scanning window

extends outside the study area, the expected count is still based on the full size of the circle, ignoring the

fact that some parts of the circle have zero expected counts. This is to avoid strange non-circular clusters

at the border of the study area. Since the analysis is based on Monte Carlo randomizations, the p-values

are automatically adjusted for these boundary effects. The reported expected counts are based on the full

circle though, so the Obs/Exp ratios provided should be viewed as a lower bound on the true value

whenever the circle extends outside the spatial study region.

The continuous Poisson model can only be used for purely spatial data. It uses a circular scanning

window of continuously varying radius up to a maximum specified by the user. Only circles centered on

one of the observations are considered, as specified in the coordinates file. If the optional grid file is

SaTScan User Guide v9.0 17

provided, the circles are instead centered on the coordinates specified in that file. The continuous Poisson

model has not been implemented to be used with an elliptic window.

Related Topics: Analysis Tab, Likelihood Ratio Test, Methodological Papers, Poisson Model,

Probability Model Comparison.

Probability Model Comparison

In SaTScan, there are seven different probability models for discrete scan statistics. For count data, there

are three different probability models: discrete Poisson, Bernoulli and space-time permutation. The

ordinal and multinomial models are designed for categorical data with and without an inherent ordering

from for example low to high. There are two models for continuous data: normal and exponential. The

latter is primarily designed for survival type data. For continuous scan statistics there is only the

homogeneous Poisson model.

The discrete Poisson model is usually the fastest to run. The ordinal model is typically the slowest.

With the discrete Poisson and space-time permutations models, an unlimited number of covariates can be

adjusted for, by including them in the case and population files. With the normal model, it is also

possible to adjust for covariates by including them in the case file, but only for purely spatial analyses.

With the Bernoulli, ordinal, exponential and normal models, covariates can be adjusted for by using

multiple data sets, which limits the number of covariate categories that can be defined, or through a pre-

processing regression analysis done before running SaTScan.

All discrete probability models can be used for either individual locations or aggregated data.

With the discrete Poisson model, population data is only needed at selected time points and the numbers

are interpolated in between. A population time must be specified even for purely spatial analyses.

Regardless of model used, the time of a case or control need only be specified for purely temporal and

space-time analyses.

The space-time permutation model automatically adjusts for purely spatial and purely temporal clusters.

For the discrete Poisson model, purely temporal and purely spatial clusters can be adjusted for in a

number of different ways. For the Bernoulli, ordinal, exponential and normal models, spatial and

temporal adjustments can be done using multiple data sets, but it is limited by the number of different

data sets allowed, and it is also much more computer intensive.

Purely temporal and space-time analyses cannot be performed using the homogeneous Poisson model.

Spatial variation in temporal trend analyses can only be performed using the discrete Poisson model.

Few Cases Compared to Controls

In a purely spatial analysis where there are few cases compared to controls, say less than 10 percent, the

discrete Poisson model is a very good approximation to the Bernoulli model. The former can then be

used also for 0/1 Bernoulli type data, and may be preferable as it has more options for various types of

adjustments, including the ability to adjust for covariates specified in the case and population files. As an

approximation for Bernoulli type data, the discrete Poisson model produces slightly conservative p-

values.

SaTScan User Guide v9.0 18

Bernoulli versus Ordinal Model

The Bernoulli model is mathematically a special case of the ordinal model, when there are only two

categories. The Bernoulli model runs faster, making it the preferred model to use when there are only two

categories.

Normal versus Exponential Model

Both the normal and exponential models are meant for continuous data. The exponential model is

primarily designed for survival time data but can be used for any data where all observations are positive.

It is especially suitable for data with a heavy right tail. The normal model can be used for continuous data

that takes both positive and negative values. While still formally valid, results from the normal model are

sensitive to extreme outliers.

Normal versus Ordinal Model

The normal model can be used for categorical data when there are very many categories. As such, it is

sometimes a computationally faster alternative to the ordinal model. There is an important difference

though. With the ordinal model, only the order of the observed values matters. For example, the results

are the same for ordered values ‘1 – 2 – 3 – 4’ and ‘1 – 10 – 100 – 1000’. With the normal model, the

results will be different, as they depend on the relative distance between the values used to define the

categories.

Discrete versus Homogeneous Poisson Model

Instead of using the homogeneous Poisson model, the data can be approximated by the discrete Poisson

model by dividing the study area into many small pieces. For each piece, a single coordinates point is

specified, the size of the piece is used to define the population at that location and the number of

observations within that small piece of area is the number of cases in that location. As the number of

pieces increases towards infinity, and hence, as their size decreases towards zero, the discrete Poisson

model will be asymptotically equivalent to the homogeneous Poisson model.

Temporal Data

For temporal and space-time data, there is an additional difference among the probability models, in the

way that the temporal data is handled. With the Poisson model, population data may be specified at one

or several time points, such as census years. The population is then assumed to exist between such time

points as well, estimated through linear interpolation between census years. With the Bernoulli, space-

time permutation, ordinal, exponential and normal models, a time needs to be specified for each case and

for the Bernoulli model, for each control as well.

Related Topics: Bernoulli Model, Poisson Model, Space-Time Permutation Model, Likelihood Ratio

Test, Methodological Papers.

Likelihood Ratio Test

For each location and size of the scanning window, the alternative hypothesis is that there is an elevated

risk within the window as compared to outside. Under the Poisson assumption, the likelihood function

for a specific window is proportional to

SaTScan User Guide v9.0 19

()

][][

cEC

cCc −













−













where C is the total number of cases, c is the observed number of cases within the window and E[c] is the

covariate adjusted expected number of cases within the window under the null-hypothesis. Note that

since the analysis is conditioned on the total number of cases observed, C-E[c] is the expected number of

cases outside the window. I() is an indicator function. When SaTScan is set to scan only for clusters with

high rates, I() is equal to 1 when the window has more cases than expected under the null-hypothesis, and

0 otherwise. The opposite is true when SaTScan is set to scan only for clusters with low rates. When the

program scans for clusters with either high or low rates, then I()=1 for all windows.

The space-time permutation model uses the same function as the Poisson model. Due to the conditioning

on the marginals, the observed number of cases is only approximately Poisson distributed. Hence, it is no

longer a formal likelihood ratio test, but it serves the same purpose as the test statistic.

For the Bernoulli model the likelihood function is

1,2

()

)()(

cCnN

cCnNcCcnc −−−−−













−

−−−













−













−













where c and C are defined as above, n is the total number of cases and controls within the window, while

N is the combined total number of cases and controls in the data set.

The likelihood function for the multinomial, ordinal, exponential, and normal models are more complex,

due to the more complex nature of the data. We refer to papers by Jung, Kulldorff and Richards

, Jung,

Kulldorff and Klassen

; Huang, Kulldorff and Gregorio

; Kulldorff et al

, and Huang et al.

for the

likelihood functions for these models. The likelihood function for the spatial variation in temporal trends

scan statistic is also more complex, as it involves the maximum likelihood estimation of several different

trend functions.

The likelihood function is maximized over all window locations and sizes, and the one with the

maximum likelihood constitutes the most likely cluster. This is the cluster that is least likely to have

occurred by chance. The likelihood ratio for this window constitutes the maximum likelihood ratio test

statistic. Its distribution under the null-hypothesis is obtained by repeating the same analytic exercise on

a large number of random replications of the data set generated under the null hypothesis. The p-value is

obtained through Monte Carlo hypothesis testing

, by comparing the rank of the maximum likelihood

from the real data set with the maximum likelihoods from the random data sets. If this rank is R, then p =

R / (1 + #simulation). In order for p to be a ‘nice looking’ number, the number of simulations is restricted

to 999 or some other number ending in 999 such as 1999, 9999 or 99999. That way it is always clear

whether to reject or not reject the null hypothesis for typical cut-off values such as 0.05, 0.01 and 0.001.

The SaTScan program scans for areas with high rates (clusters), for areas with low rates, or

simultaneously for areas with either high or low rates. The latter should be used rather than running two

separate tests for high and low rates respectively, in order to make correct statistical inference. The most

common analysis is to scan for areas with high rates, that is, for clusters.

SaTScan User Guide v9.0 20

Non-Compactness Penalty Function

When the elliptic window shape is used, there is an option to use a non-compactness (eccentricity)

penalty to favor more compact clusters

. The main reason for this is that the elliptic scan statistic will

under the null hypothesis typically generate an elliptic most likely cluster since there are more elliptic

than circular clusters evaluated, and it will often be a long and narrow ellipse, since there are more of

those. At the same time, the concept of clustering is based on a compactness criterion in the sense that

the cases in the cluster should be close to each other, so we are more interested in compact clusters.

When the non-compactness penalty is used, the pure likelihood ratio is no longer used as the test statistic.

Rather, the test statistic is defined as the log likelihood ratio multiplied with a non-compactness penalty

of the form [4s/(s+1)

]

, where s is the elliptic window shape defined as the ratio of the length of the

longest to the shortest axis of the ellipse. For the circle, s=1. The parameter a is a penalty tuning

parameter. With a=0, the penalty function is always 1 irrespectively of s, so that there is never a penalty.

When a goes to infinity, the penalty function goes to 0 for all s>1, so that only circular clusters are

considered. Other than this, there is no clear intuitive meaning of the penalty tuning parameter a. In

SaTScan, it is possible to use either a strong penalty (a=1) or a medium size penalty (a=1/2).

Related Topics: Batch Mode, Bernoulli Model, Covariate Adjustments, Elliptic Scanning Window,

Exponential Model, Monte Carlo Replications, Ordinal Model, Poisson Model, Secondary Clusters,

Space-Time Permutation Model, Standard Results File.

Secondary Clusters

For purely spatial and space-time analyses, SaTScan also identifies secondary clusters in the data set in

addition to the most likely cluster, and orders them according to their likelihood ratio test statistic. There

will almost always be a secondary cluster that is almost identical with the most likely cluster and that

have almost as high likelihood value, since expanding or reducing the cluster size only marginally will

not change the likelihood very much. Most clusters of this type provide little additional information, but

their existence means that while it is possible to pinpoint the general location of a cluster, its exact

boundaries must remain uncertain.

There may also be secondary clusters that do not overlap with the most likely cluster, and they may be a

great interest. The user can decide to what extent overlapping clusters are reported in the results files.

The default is that geographically overlapping clusters are not reported.

For purely temporal analyses, only the most likely cluster is reported.

Related Topics: Adjusting for More Likely Clusters, Likelihood Ratio Test, Clusters Reported Tab,

Criteria for Reporting Secondary Clusters, Standard Results File.

Adjusting for More Likely Clusters

When there are multiple clusters in the data set, the secondary clusters are evaluated as if there were no

other clusters in the data set. That is, they are statistically significant if and only if they are able to cause

a rejection of the null hypothesis on their own strength, whether or not the other clusters are true clusters

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SaTScan 9.0用户指南：空间分析统计软件操作详解

地理信息系统空间分析之第一篇熟悉软件

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