"SaTScan使用指南v10.1：下载、安装和软件介绍"

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SaTScan使用指南本文将对SaTScan软件进行详细的介绍和使用指南。SaTScan是一款用于空间和时间聚类检测的强大工具，可以帮助用户在地理和时间维度上发现异常集群。本指南是基于SaTScan的10.1版本，并提供了完整的下载和安装说明。首先介绍SaTScan软件本身。SaTScan是由Martin Kulldorff开发的一款免费的软件，旨在帮助研究人员发现各种异常集群，例如人群中的疾病暴发或交通事故的发生。该软件结合了统计方法和空间分析，可以帮助用户识别在特定时间和空间上具有统计显著性的异常聚类。因此，SaTScan在疾病监测、环境研究和公共安全等领域具有广泛的应用。 SaTScan的安装非常简单，用户只需从官方网站http://www.satscan.org/下载软件，并按照网站上提供的说明进行安装。本指南将提供更详细的下载和安装说明，以帮助新用户快速上手。安装完成后，用户可以打开SaTScan软件并开始使用。使用SaTScan的第一步是导入所需数据。SaTScan支持多种数据格式，包括空间数据和时间序列数据。用户可以根据自己的需求选择合适的数据导入方式。一旦数据导入完成，用户可以通过SaTScan的直观用户界面进行数据预览和处理。 SaTScan的核心功能是聚类检测。用户可以通过选择不同的聚类检测方法和设定参数来发现异常聚类。SaTScan提供了多种不同的聚类检测方法，包括空间扫描统计方法、时间窗口扫描统计方法和空间-时间联合扫描统计方法。用户可以根据自己的研究目的选择合适的方法。此外，用户还可以通过调整参数来控制聚类的敏感度和准确性。在聚类检测完成后，SaTScan会生成详细的报告和可视化结果。用户可以通过报告了解到每个异常聚类的统计显著性和空间范围。此外，SaTScan还提供了各种可视化工具，如热力图、密度图和聚类图，以帮助用户更直观地理解聚类结果。用户可以根据自己的需求导出报告和可视化结果，以便进一步分析和展示。 SaTScan还提供了许多其他功能和选项，如空间平滑、数据过滤和区域群组。用户可以利用这些功能进一步优化聚类结果，并进行更深入的分析。SaTScan还支持批处理模式，可以自动化执行多个聚类检测任务，提高工作效率。综上所述，SaTScan是一款功能强大且易于使用的空间和时间聚类检测工具。通过本指南，用户可以了解SaTScan的基本功能和使用方法，帮助用户快速上手。希望本指南能对SaTScan的新用户提供全面的帮助，并为进一步的研究和分析提供基础。更多详细信息和教程，请参考SaTScan的官方网站和用户手册。（总字数：1296）

SaTScan User Guide v10.1 12

Exponential Model

The exponential model

is designed for survival time data, although it could be used for other continuous

type data as well. Each observation is a case, and each case has one continuous variable attribute as well as

a 0/1 censoring designation. For survival data, the continuous variable is the time between diagnosis and

death or depending on the application, between two other types of events. If some of the data is censored,

due to loss of follow-up, the continuous variable is then instead the time between diagnosis and time of

censoring. The 0/1 censoring variable is used to distinguish between censored and non-censored

observations.

Example: For the exponential model, the data may consist of everyone diagnosed with prostate cancer

during a ten-year period, with information about either the length of time from diagnosis until death or from

diagnosis until a time of censoring after which survival is unknown.

When using the temporal or space-time exponential model for survival times, it is important to realize that

there are two very different time variables involved. The first is the time the case was diagnosed, and that

is the time that the temporal and space-time scanning window is scanning over. The second is the survival

time, that is, time between diagnosis and death or for censored data the time between diagnosis and

censoring. This is an attribute of each case, and there is no scanning done over this variable. Rather, we are

interested in whether the scanning window includes exceptionally many cases with a small or large value

of this attribute.

It is important to note, that while the exponential model uses a likelihood function based on the exponential

distribution, the true survival time distribution must not be exponential and the statistical inference (p-

value) is valid for other survival time distributions as well. The reason for this is that the randomization is

not done by generating observations from the exponential distribution, but rather, by permuting the space-

time locations and the survival time/censoring attributes of the observations.

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

Papers.

Normal Model

The normal model

is designed for continuous data. For each individual or for each observation, called a

case, there is a single continuous attribute that may be either negative or positive. The model can also be

used for ordinal data when there are many categories. That is, different cases are allowed to have the same

attribute value.

Example: For the normal model, the data may consist of the birth weight and residential census tract for all

newborns, with an interest in finding clusters with lower birth weight. One individual is then a ‘case’.

Alternatively, the data may consist of the average birth weight in each census tract. It is then the census

tract that is the ‘case’, and it is important to use the weighted normal model, since each average will have

a different variance due to a different number of births in each tract.

It is important to note that while the normal model uses a likelihood function based on the normal

distribution, the true distribution of the continuous attribute must not be normal. The statistical inference

(p-value) is valid for any continuous distribution. The reason for this is that the randomization is not done

by generating simulated data from the normal distribution, but rather, by permuting the space-time locations

and the continuous attribute (e.g. birth weight) of the observations. While still being formally valid, the

results can be greatly influenced by extreme outliers, so it may be wise to truncate such observations before

doing the analysis.

SaTScan User Guide v10.1 13

In the standard normal model

, it is assumed that each observation is measured with the same variance.

That may not always be the case. For example, if an observation is based on a larger sample in one location

and a smaller sample in another, then the variance of the uncertainty in the estimates will be larger for the

smaller sample. If the reliability of the estimates differs, one should instead use the weighted normal scan

statistic

that takes these unequal variances into account. The weighted version is obtained in SaTScan by

simply specifying a weight for each observation as an extra column in the input file. This weight may for

example be proportional to the sample size used for each estimate or it may be the inverse of the variance

of the observation.

If all values are multiplied with or added to the same constant, the statistical inference will not change,

meaning that the same clusters with the same log likelihoods and p-values will be found. Only the estimated

means and variances will differ. If the weight is the same for all observations, then the 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)1. 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

SaTScan User Guide v10.1 14

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 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 v10.1 15

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.

SaTScan User Guide v10.1 16

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

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.

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