2013 Industrial MathStat Modeling Workshop for Graduate Students

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2013 Industrial Math/Stat Modeling Workshop for Graduate Students 발표자 : 장기훈

2013 Industrial Math/Stat Modeling Workshop for Graduate Students 발표자 : 장기훈

SAMSI Statistical and Applied Mathematical Sciences Institute NSF, Duke, NCSU, UNC, NISS SAMSI's mission

SAMSI Statistical and Applied Mathematical Sciences Institute NSF, Duke, NCSU, UNC, NISS SAMSI's mission is to forge a synthesis of the statistical and the applied mathematical sciences to confront the very hardest and most important data, model-driven scientific challenges

SAMSI 2013 Industrial Math/Stat Modeling Workshop for Graduate Students July 15 -23, 2013 Objective

SAMSI 2013 Industrial Math/Stat Modeling Workshop for Graduate Students July 15 -23, 2013 Objective was to expose graduate students in mathematics, engineering, and statistics to challenging and exciting real-world problems arising in industrial and government laboratory research

SCHEDULE 8 -9 am : Breakfast 9 am ~ 5 am : Working sessions

SCHEDULE 8 -9 am : Breakfast 9 am ~ 5 am : Working sessions Make the report Presentation of results

PROJECTS Numerical Modeling and Simulation of Fluid Flow with Application to Current Environmental Challenges

PROJECTS Numerical Modeling and Simulation of Fluid Flow with Application to Current Environmental Challenges Burden of Sexual Transmitted Diseases in the US: Trend Analysis of Incidence Rates Photoresponsive Polymer Beam Design for Solar Concentrator Self-steering Heliostats Microbes and Molecules: A Microscopic Analysis of Asthma Network Analytics and Visualization in Healthcare Urban Route Planning from Aerial Imagery

Burden of Chlamydia in the US: Trend Analysis of Incidence Rates Ridouan Bani, Anna

Burden of Chlamydia in the US: Trend Analysis of Incidence Rates Ridouan Bani, Anna D. Broido, Andrew F. Brouwer, Shih-Han Chang, Kihoon Jang, Qianqian Ma, Jiani Yin Faculty Mentors: Howard Chang, Emory Problem Presenter: Simone Gray, CDC

Outline Chlamydia and reporting delays Graphical trends Modeling National and State level incidence rates

Outline Chlamydia and reporting delays Graphical trends Modeling National and State level incidence rates Modeling incidence rates by population demographics Hierarchical modeling

Chlamydia Most commonly reported bacterial STI in the US. Caused by bacterium Chlamydia trachomatis.

Chlamydia Most commonly reported bacterial STI in the US. Caused by bacterium Chlamydia trachomatis. Though it is often asymptomatic, especially in men, Chlamydia can lead to other serious illnesses in both men and women. Reporting delays (administrative) mean current incidence data is unavailable.

National Incidence Rates: By Race African Americans had about 9 times higher incidence than

National Incidence Rates: By Race African Americans had about 9 times higher incidence than Whites and Asians

Objectives Use available data 2000 -2011 to project chlamydia incidence rates with quantified uncertainty

Objectives Use available data 2000 -2011 to project chlamydia incidence rates with quantified uncertainty for 2012 -2013 for: The United States Each state Each demographic group Sex Race (American Indian, Asian, Black, Hispanic, White) Create a hierarchical model to incorporate spatial effects on variations in incidence rates

Poisson Regression Assume incident cases follow a Poisson distribution Natural for positive counts Log-transformed

Poisson Regression Assume incident cases follow a Poisson distribution Natural for positive counts Log-transformed rates are not normally distributed Y= incident cases, λ = rate, N = population, xi = year, spatial, and demographic variables

Model Assessment Average absolute relative deviation (AARD) Akaike information criterion (AIC)

Model Assessment Average absolute relative deviation (AARD) Akaike information criterion (AIC)

National and State Model Variables 1 Year 2 Year + State AIC AARD-National AARD-State

National and State Model Variables 1 Year 2 Year + State AIC AARD-National AARD-State 634406 1. 2% 30. 5% 98631 1. 2% 7. 3% AARD calculated over 2000 -2011 incident cases Population projected linearly Model 1: National level projections

Demographic Model Variables AIC AARD 3 Year + Sex + Race 118525 13. 1%

Demographic Model Variables AIC AARD 3 Year + Sex + Race 118525 13. 1% 4 Year + Sex × Race 53191 7. 4% 5 Year × Race + Sex 102259 12. 3% 6 Year × Race + Sex × Race 36831 6. 6% 7 Year × Sex × Race 8987 3. 3% AARD calculated over 2000 -2011 incident cases Note the importance of the Sex-Race interaction over the Year-Race interaction.

Conclusions Incidence follows strong temporal trends that vary spatially and demographically. Poisson regression allows

Conclusions Incidence follows strong temporal trends that vary spatially and demographically. Poisson regression allows reasonable projection for recent and current incidence. Increased complexity does not necessarily improve predictions for aggregate data. Current approach for uncertainty quantification gives conservative estimates.

Future Work Improve confidence in projections by training data on 2000 -2009 data and

Future Work Improve confidence in projections by training data on 2000 -2009 data and testing on 2010 -2011 for all models Include specific race-state interactions (particularly for American Indian populations in certain states) Include spatial correlation terms that decrease with distance. Investigate ways to relax the Poisson assumption and account for over-dispersion Project incidence beyond 2013

PROGRAM

PROGRAM

WORKING Compile the data Analysis the data by using R Make simple statistic data

WORKING Compile the data Analysis the data by using R Make simple statistic data Double check the data

THANK YOU

THANK YOU