SaTScan TM 用户指南：版本9.3

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"SaTScanTM User Guide for version 9.3是Martin Kulldorff编写的用户指南，适用于2014年3月发布的SaTScanTM 9.3版本。该软件主要用于空间、时间和空间-时间扫描统计，提供多种统计模型，包括Bernoulli模型、离散泊松模型、空间-时间置换模型、多分类模型、有序模型、指数模型、正态模型以及连续泊松模型。此外，还包括概率模型比较、似然比测试、次要聚类检测、调整更可能的聚类、协变量调整、空间和时间调整、处理缺失数据、多变量扫描与多个数据集的配合，以及与其他方法的比较，如扫描统计、空间和空间-时间聚类等。" SaTScanTM是一款强大的地理统计分析软件，用于检测空间、时间和空间-时间的异常或聚集现象。在版本9.3中，用户可以下载并安装该软件进行测试运行。软件内置的帮助系统为用户提供指导，还有多个样例数据集可供学习和实践。在统计方法学方面，SaTScanTM支持多种模型，适应不同的研究需求。Bernoulli模型适用于二项分布的数据，离散泊松模型处理计数数据，空间-时间置换模型则考虑了事件发生的时间顺序。多分类模型和有序模型适用于类别数据，而指数模型和正态模型分别适用于非负连续数据和连续数据。连续泊松模型则用于处理连续的计数数据。除了基本的扫描统计，软件还提供了概率模型比较和似然比测试，用于评估不同模型的适用性。次要聚类功能可以帮助识别除了最大聚类之外的其他显著聚类。在实际应用中，用户可能需要调整聚类检测以考虑更可能的聚类，或者通过协变量调整来控制潜在的影响因素。对于数据处理，SaTScanTM可以处理缺失数据，并支持空间和时间调整，以适应各种复杂情况。在输入数据方面，软件需要的文件包括病例文件、对照文件、人口文件、坐标文件、网格文件、非欧几里得邻接文件、元位置文件、最大圆大小文件、调整文件以及备选假设文件等，确保了对不同类型数据的有效处理。 SaTScanTM 9.3用户指南详尽地介绍了如何使用该软件进行空间和时空数据分析，包括各种统计模型的应用、数据的准备和处理，以及与其他流行方法的对比，是进行疾病监测、公共卫生研究以及地理数据分析的有力工具。

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.

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.

SaTScan User Guide v9.2 13

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

()

][][

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

SaTScan User Guide v9.2 14

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.

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

SaTScan User Guide v9.2 15

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. 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.

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

may be of great interest. These are always reported. The p-values for such clusters should be interpreted

in terms of the ability of the secondary cluster to reject the null hypothesis on its own strength, whether or

not the more likely clusters are true clusters or not. Hence, these p-values are not adjusted for the fact that

there may be other clusters in the data. If such adjustments are desired, the iterative scan statistic should

be used.

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

Related Topics: Adjusting for More Likely Clusters, Likelihood Ratio Test, Spatial Output 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 or

not. That is often the desired type of inference. Sometime though, it is also of interest to evaluate

secondary clusters after adjusting for other clusters in the data.

As an advanced option, SaTScan is able to adjust the inference of secondary clusters for more likely

clusters in the data

. This is done in an iterative manner. In the first iteration SaTScan runs the standard

analysis but only reports the most likely cluster. That cluster is then removed from the data set, including

all cases and controls (Bernoulli model) in the cluster while the population (Poisson model) is set to zero

for the locations and the time period defining the cluster. In a second iteration, a completely new analysis

is conducted using the remaining data. This procedure is then repeated until there are no more clusters

with a p-value less than a user specified maxima or until a user specified maximum number of iterations

have been completed, whichever comes first.

For purely spatial analyses it has been shown that the resulting p-values for secondary clusters are quite

accurate and at most marginally biased.

Note that the circle of a secondary cluster may overlap with the circle of a previously detected more likely

cluster, and it may even completely encircle it so that the latter is a subset of the former. This does not

SaTScan User Guide v9.2 16

mean that the more likely cluster is detected twice. Rather, the more likely cluster is treated as a ‘lake’

with no population and no cases, and the new secondary cluster consist of the areas around that ‘lake’.

This may for example happen if a city has a very high elevated risk, while the surrounding suburbs have a

modest elevated risk. The same phenomena may occur when doing purely temporal or space-time

analyses.

This feature is not available for the continuous Poisson model.

Related Topics: Spatial Output Tab, Criteria for Reporting Secondary Clusters, Iterative Scan,

Likelihood Ratio Test, Secondary Clusters, Standard Results File.

Covariate Adjustments

A covariate should be adjusted for when all three of the following are true:

• The covariate is related to the disease in question.

• The covariate is not randomly distributed geographically.

• You want to find clusters that cannot be explained by that covariate.

Here are three examples:

• If you are studying cancer mortality in the United States, you should adjust for age since (i)

older people are more likely to die from cancer (ii) some areas such as Florida have a higher

percent older people, and (iii) you are presumably interested in finding areas where the risk of

cancer is high as opposed to areas with an older population.

• If you are interested in the geographical distribution of birth defects, you do not need to

adjust for gender. While birth defects are not equally likely in boys and girls, the

geographical distribution of the two genders is geographically random at time of birth.

• If you are studying the geography of lung cancer incidence, you should adjust for smoking if

you are interested in finding clusters due to non-smoking related risk factors, but you should

not adjust for smoking if you are interested in finding clusters reflecting areas with especially

urgent needs to launch an anti-smoking campaign.

When the disease rate varies, for example, with age, and the age distribution varies in different areas, then

there is geographical clustering of the disease simply due to the age covariate. When adjusting for

categorical covariates, the SaTScan program will search for clusters above and beyond that which is

expected due to these covariates. When more than one covariate is specified, each one is adjusted for as

well as all the interaction terms between them.

Related Topics: Covariate Adjustment Using the Input Files, Covariate Adjustment using Statistical

Regression Software, Covariate Adjustment Using Multiple Data Sets, Methodological Papers.

Covariate Adjustment Using the Input Files

With the Poisson and space-time permutation models, it is possible to adjust for multiple categorical

covariates by specifying the covariates in the input files. To do so, simply enter the covariates as extra

columns in the case file (both models) and the population file (Poisson model). There is no need to enter

any information on any of the window tabs.

For the Poisson model, the expected number of cases in each area under the null-hypothesis is calculated

using indirect standardization. Without covariate adjustment the expected number of cases in a location is

(spatial analysis):

E[c] = p*C/P

SaTScan User Guide v9.2 17

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