Application of Multi-level Models to Spatial Epidemiology Part 09 Application of Multi-level Models to Spatial Epidemiology BIO656--Multilevel Models

BIO656--Multilevel Models DATA STRUCTURE & GOALS We have geographically indexed dependent variable and covariates Outcome, exposures, demographics, ... Want to study the relation between spatio-temporal variation in the dependent variable and covariates BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

CRUDE, COUNTY-SPECIFIC RELATIVE RISKS Rates appear to cluster, with a noticeable grouping of counties with SMR> 200 in the North BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models 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 BIO656--Multilevel Models

THE CAR MODEL Local Smoothing Crude SMR Smoothed SMR BIO656--Multilevel Models

BIO656--Multilevel Models Posterior distribution of Relative Risk for maximum exposure (Maximum AFF) Global smoothing (posterior mean = 3.25) Local smoothing (posterior mean = 2.18) BIO656--Multilevel Models

Posterior distribution of Relative Risk for average exposure Global smoothing (posterior mean = 1.08) Local smoothing (posterior mean=1.09) BIO656--Multilevel Models

BIO656--Multilevel Models Best Histogram BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models Comparison of Ranks BIO656--Multilevel Models

Percentiles and Moments BIO656--Multilevel Models

Highest estimated relative risk regions BIO656--Multilevel Models

Lowest estimated relative risk regions BIO656--Multilevel Models

BIO656--Multilevel Models 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 BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models 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 BIO656--Multilevel Models

BIO656--Multilevel Models 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 schizophrenia-like dementia May develop after gastrointestinal diseases or alcoholism BIO656--Multilevel Models

BIO656--Multilevel Models THE SMR BIO656--Multilevel Models

Computing Expected Deaths BIO656--Multilevel Models

BIO656--Multilevel Models Crude SMR (Observed/Expected) of Pellagra Deaths in Southern USA in 1930 (Courtesy of Harry Marks) BIO656--Multilevel Models

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  BIO656--Multilevel Models

Crude and smoothed SMRs: Pellagra Deaths in Southern USA in 1930 Crude SMR BIO656--Multilevel Models

Complex Spatial Relations and Data Structures Requiring a hierarchical model to sort things out BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models

BIO656--Multilevel Models 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 BIO656--Multilevel Models