Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Part 09 Application of Multi-level Models to Spatial Epidemiology Term 4, 2005 BIO656--Multilevel Models 1 DATA STRUCTURE & GOALS • We have geographically indexed dependent variable and covariates – Outcome, exposures, demographics, ... • Want to study the relation between spatiotemporal variation in the dependent variable and covariates Term 4, 2005 BIO656--Multilevel Models 2 Term 4, 2005 BIO656--Multilevel Models 3 Term 4, 2005 BIO656--Multilevel Models 4 Term 4, 2005 BIO656--Multilevel Models 5 CRUDE, COUNTY-SPECIFIC RELATIVE RISKS Rates appear to cluster, with a noticeable grouping of counties with SMR> 200 in the North Term 4, 2005 BIO656--Multilevel Models 6 Term 4, 2005 BIO656--Multilevel Models 7 Term 4, 2005 BIO656--Multilevel Models 8 Term 4, 2005 BIO656--Multilevel Models 9 Term 4, 2005 BIO656--Multilevel Models 10 Term 4, 2005 BIO656--Multilevel Models 11 Term 4, 2005 BIO656--Multilevel Models 12 Term 4, 2005 BIO656--Multilevel Models 13 Term 4, 2005 BIO656--Multilevel Models 14 Term 4, 2005 BIO656--Multilevel Models 15 Term 4, 2005 BIO656--Multilevel Models 16 Term 4, 2005 BIO656--Multilevel Models 17 Term 4, 2005 BIO656--Multilevel Models 18 SHRINKAGE When the population in a region is large • The statistical uncertainty is relatively small • High credibility (weight) is given to the direct (MLE) estimate • The smoothed rate is close to observed rate When the population in a region is small • The statistical uncertainty is relatively large • Little credibility (weight) is given to the direct (MLE) estimate • The smoothed rate is shrunken toward a local (computed by other nearby regions) or a global target Term 4, 2005 BIO656--Multilevel Models 19 THE CAR MODEL Local Smoothing Crude SMR Term 4, 2005 Smoothed SMR BIO656--Multilevel Models 20 Posterior distribution of Relative Risk for maximum exposure (Maximum AFF) Global smoothing (posterior mean = 3.25) Term 4, 2005 Local smoothing (posterior mean = 2.18) BIO656--Multilevel Models 21 Posterior distribution of Relative Risk for average exposure Global smoothing (posterior mean = 1.08) Term 4, 2005 Local smoothing (posterior mean=1.09) BIO656--Multilevel Models 22 Best Histogram Term 4, 2005 BIO656--Multilevel Models 23 Term 4, 2005 BIO656--Multilevel Models 24 Comparison of Ranks Term 4, 2005 BIO656--Multilevel Models 25 Percentiles and Moments Term 4, 2005 BIO656--Multilevel Models 26 Highest estimated relative risk regions Term 4, 2005 BIO656--Multilevel Models 27 Lowest estimated relative risk regions Term 4, 2005 BIO656--Multilevel Models 28 DISCUSSION • It is important to explore sensitivity of the results to modeling assumptions – Priors, data models, ..... • For spatially correlated data use of global smoothing may not be effective • In the lip cancer study, the sensitivity of results to choice of prior (global and local smoothing) suggest presence of spatially correlated latent factors Term 4, 2005 BIO656--Multilevel Models 29 Term 4, 2005 BIO656--Multilevel Models 30 Term 4, 2005 BIO656--Multilevel Models 31 Term 4, 2005 BIO656--Multilevel Models 32 Socio-economic and dietary factors of pellagra deaths in southern US Shum, Dominici & Marks • • • 1930 data from approximately 800 counties in 9 states in Southern US Outcome is county-specific observed and expected number of pellagra deaths Data set includes county-specific socio-economic characteristics and dietary factors • % acres in cotton • % farms under 20 acres • dairy cows per capita • Access to a mental hospital • % afro-american • % single women Term 4, 2005 BIO656--Multilevel Models 33 PELLAGRA • Disease caused by a deficient diet or failure of the body to absorb B complex vitamins or an amino acid • Prevalent in locations where people consume large quantities of corn • Characterized by scaly skin sores, diarrhea, mucosal changes and mental symptoms such as schizophrenialike dementia • May develop after gastrointestinal diseases or alcoholism Term 4, 2005 BIO656--Multilevel Models 34 THE SMR Term 4, 2005 BIO656--Multilevel Models 35 Computing Expected Deaths Term 4, 2005 BIO656--Multilevel Models 36 Crude SMR (Observed/Expected) of Pellagra Deaths in Southern USA in 1930 (Courtesy of Harry Marks) Term 4, 2005 BIO656--Multilevel Models 37 Analysis Questions & Framework Use a Conditional Autoregressive (CAR) Model • To assess which social, economic, behavioral or dietary factors best explain the spatial distribution of pellagra in southern US • Which of the above factors are most important in explaining the history of pellagra incidence in the US • To what extent have state laws affected pellagra incidence • To adjust and smooth estimated rates Term 4, 2005 BIO656--Multilevel Models 38 Crude and smoothed SMRs: Pellagra Deaths in Southern USA in 1930 Crude SMR Term 4, 2005 Smoothed SMR BIO656--Multilevel Models 39 Complex Spatial Relations and Data Structures Requiring a hierarchical model to sort things out Term 4, 2005 BIO656--Multilevel Models 40 Term 4, 2005 BIO656--Multilevel Models 41 Term 4, 2005 BIO656--Multilevel Models 42 Term 4, 2005 BIO656--Multilevel Models 43 Need a rosetta stone! Mugglin, A.S., and Carlin, B.P. (1998) Hierarchical Modeling in Geographic Information Systems, Population interpolation over incompatible zones J. Agricultural, Biolological and Environmental Statistics, 3: 111-130 Term 4, 2005 BIO656--Multilevel Models 44