1、A Tree-Based Scan Statistic for Database Disease Surveillance,Martin Kulldorff University of ConnecticutJoint work with: Zixing Fang, Stephen Walsh,Database Disease Surveillance,In what occupations are there an excess risk of dying from a particular disease?Are there pharmaceutical drugs that causes
2、 certain adverse effects?,Nested Variables,inhalation therapists therapists health occupations professional occupationsecotrin asprin nonsteoridal anti-inflammatory drugs analgesic drugs,Occupational Multiple Cause of Death Database,National Center for Health Statistics Based on Death Certificates O
3、ccupational Classification System Selected States,Occupational Multiple Cause of Death Database,Time period: 1985-1992 Age groups: 25 years Total deaths: 2,114,832 Silicosis deaths: 405,Occupational Classification System,A hierarchical structure of occupations created by the United States Bureau of
4、the Census.Number of occupational groups at each level:Level: 1 2 3 4 5 6 76 13 86 345 476 502 503,Farmers,Cowboys,Hunters,Teachers,Clerks,Root,Node,Branches,Leaf,A Small Three-Level Tree Variable,Occupational Classification System,Managerial and Professional Specialty OccupationsProfessional Specia
5、lty Occupations Mathematical and Computer ScientistsComputer Systems Analysts and Scientists (064)Operations and Systems Researchers and Analysts (065)Actuaries (066)Statisticians (067)Mathematical Scientists, n.e.c. (068)Natural ScientistsMedical Scientists (083), etc.Health Diagnosing OccupationsP
6、hysicians (084), etc.Health Assessment and Treatment OccupationsTherapists (098-105), etc.,Silicosis,A rare disease of the lung Chronic shortness of breath Caused by dust containing crystalline silica (quartz) particles No known cure,Silicosis,Described by Agricola in 1556:In the Carpathian mines, w
7、omen are found who have married seven husbands, all of whom this terrible consumption has carried awayAgricola G. (1556). De Re Metallica. Basel: Froben and Episopius.,Proportional Mortality (PM),N = Total number of deaths (2,114,832) C = Total number of silicosis deaths (405) n = Number of farmers
8、(266,715) c = Farmers dying from silicosis (12)All: C/N = 405/2,114,832 = 0.000192 Farmers: c/n = 12/266,715 = 0.000045,Proportional Mortality Ratio (PMR),N = Total number of deaths (2,114,832) C = Total number of silicosis deaths (405) n = Number of farmers (266,715) c = Farmers dying from silicosi
9、s (12)Farmers: PMR= c/n / (C-c)/(N-n) = 0.23,Standardized Proportional Mortality Ratio (SPMR),The same thing as proportional mortality ratio but adjusted for covariates. Adjusted for age and gender, for silicosis among farmers we have:SPMR = 0.29,Analysis Options,Evaluate each of the 503 occupationa
10、l groups, using a Bonferroni type adjustment for multiple testing. Use a higher group level, such as level 3 with 86 occupational groups.,Substantive Problem: We do not know whether the disease relationships effect a smaller or larger group.,Analysis Options,Take the 503 occupations as a base, and e
11、valuate all 2503 - 2 = 2.6 10151 combinations.,Problems: Computational, Statistical, Substantive,Ideal Analytical Solution,Use the Hierarchical Tree Evaluate Cuts on that Tree,Farmers,Cowboys,Hunters,Teachers,Clerks,A Small Three-Level Tree Variable,Cut,Problem,How do we deal with the multiple testi
12、ng?,Proposed Solution,Tree-Based Scan Statistic,One-Dimensional Scan Statistic Studied by Naus (JASA, 1965),Other Scan Statistics,Spatial scan statistics using circles or squares. Space-time scan statistics using cylinders. Variable size window, using maximum likelihood rather than counts.Applied fo
13、r geographical and temporal disease surveillance, and in many other fields.,Tree-Based Scan Statistic,H0: The probability of dying from silicosis is the same for all occupations.HA: There is at least one group of occupations (cut) for which the probability is higher.,Tree-Based Scan Statistic,1. Sca
14、n the tree by considering all possible cuts onany branch. 2. For each cut, calculate the likelihood. 3. Denote the cut with the maximum likelihood as the most likely cut (cluster). 4. Generate 9999 Monte Carlo replications under H0. 5. Compare the most likely cut from the real data set with the most
15、 likely cuts from the random data sets. 6. If the rank of the most likely cut from the real data set is R, then the p-value for that cut is R/(9999+1).,Result Most Likely Cut,Occupations: Mining machine operatorsObserved: 56, Expected: 5.5SPMR = 11.8, p=0.0001,Result: Second Most Likely Cut,Occupati
16、ons: Molding and casting machine operators, Metal plating machine operators, Heat treating equipment operators, Misc. metal and plastic machine operatorsObserved: 22, Expected: 1.2SPMR = 20.5, p=0.0001,Result Ninth Most Likely Cut,Occupation: Heavy equipment mechanicsObserved: 5, Expected: 1.0SPMR =
17、 4.8, p=0.72,Extension to Complex Cuts,Consider a node with 4 branches: A, B, C, D.Simple cuts: A, B, C, DCombinatorial cuts: A, B, C, D AB, AC, AD, BC, BD, CD ABC, ABD, ACD, BCDOrdinal cuts: A, B, C, D AB, BC, CD, ABC, BCD,Result Most Likely Cut,Occupations: Mining machine operators, Mining occupat
18、ions n.e.cObserved: 59, Expected: 6.0SPMR = 11.5, p=0.0001,Extension to Multiple Trees,There may not be one unique suitable tree. It is trivial to extend the method to multiple trees, by simply scanning over all trees.,Result Most Likely Cut,Occupations: Mining machine operators, Mining engineers, M
19、ining occupations n.e.cObserved: 60, Expected: 6.0SPMR = 11.6, p=0.0001,Evaluated Combinations,Simple cuts: 1,000 Mixed cuts: 1,000,000 Two trees: 1,000,000,Comparison with Computer Assisted Regression Trees (CART),Similarity: The letters T, R, E and E.Both are Data Mining Methods,Difference,CART: T
20、here are multiple continuous or categorical variables, and a regression tree is constructed by making a hierarchical set of splits in the multi- dimensional space of the independent variables. Tree-Based Scan Statistic: There may be only one independent variable (e.g. occupation). Rather than using
21、this as a continuous or categorical variable, it is defined as a tree structured variable. That is, we are not trying to estimate the tree, but use the tree as a new and different type of variable.,Conclusions,The tree-based scan statistic is a useful data mining tool when we want to do know if a de
22、tected clusters is due to chance or not, adjusting for the multiple testing of all possible cluster locations considered. Requires a variable that are suitably expressed in a tree structure, although the method may be extended to other structures as well.,Conclusions,There are many other potential application areas, such as pharmacovigilance where one is interested in detecting unsuspected adverse drug effects. Extensions can be made to tree-structured dependent variables, and to multiple tree-structured independent variables.,
