• Introduction to Mortality Disparities in the US
• The role of residential segregation
• Research Questions
• Data
• Methods - The INLA approach to Bayesian analysis
• Results & visualizations
• Wrap up

• Black-White disparities in mortality rates persist
• Most research focuses on individual level factors
  • SES, Health behaviors
• More recent work is multilevel
  • Context of health, neighborhoood conditions
• Role of residential segregation on aggregate mortality rates still poorly understood

• Williams and Collins (2001) offer one of the first conceptual pieces to link segregation to poor health.
• Segregation spatially and socially patterns:
  • Poverty
  • Economic and educational opportunities
  • Social order or disorder
  • Access to resources
• Segregation could lead to better health outcomes (political representation, social support, cohesion)

• Does the effect of segregation produce the same disparity in black and white mortality rates over time?
• Do counties with persistently high segregation show the same mortality disadvantage for both black and white mortality rates?
• Does segregation have any protective advantage on county-level mortality rates?
  • For black mortality specifically

• NCHS Compressed Mortality File
  • County - level counts of deaths by year, age, sex, race/ethnicity and cause of death
  • 1980 to 2010

  • Age, sex and race (white & black) specific rates for all US counties

  • In total: 35748276 deaths in the data
  • Standardized to 2000 Standard US population age structure
  • Rates stratified by race and sex for each county by year
  • n = 2 sexes * 2 races * 3106 counties * 31 years = 385144 observations

  • Analytic n = 315,808 nonzero rates

• You can basically get these data from the CDC Wonder website
• Supresses counts where the number of deaths is less than 10
• Rates are labeled as "unreliable" when the rate is calculated with a numerator of 20 or less
  • Big problem for small population counties
  • Still a problem for large population counties!
• Restricted use data allows access to ALL data

Bexar County, TX 1980 - 1982

##  cofips year     race_sex mortality
##   48029 1980 White Female       7.9
##   48029 1980 Black Female      10.0
##   48029 1980   White Male      13.5
##   48029 1980   Black Male      17.2
##   48029 1981 White Female       8.2
##   48029 1981 Black Female       9.8
##   48029 1981   White Male      12.9
##   48029 1981   Black Male      15.4
##   48029 1982 White Female       7.6
##   48029 1982 Black Female      10.1
##   48029 1982   White Male      12.9
##   48029 1982   Black Male      16.7

Bexar County, TX Temporal Trends 1980 - 2010

Spatial Distribution of White & Black Mortality in TX: 1980-2010 Average

• I specify a Bayesian Hierarchical model for the standardized mortality rate \[ \begin{align*} \ Y_{ij} & \sim N(\mu_{ij}, \sigma_y ^2) \\ \ \mu_{ij} & = \beta_{0} + x'\beta + v_j + u_j + \tau_t \\ \ v_j & \sim N(0, \sigma_v ^2) \\ \ u_j & \sim CAR(\bar u_j, \sigma_u ^2/n_j) \\ \ \tau_t & \sim N(0, \sigma_{\tau}^2) \\ \end{align*}\\ \]
• We assume vague conjugate gamma priors for all the \(\sigma\)'s
• We assume vague Normal priors for all the fixed effect \(\beta\)'s

• This type of model is commonly used in epidemiology and public health
• Various types of data likelihoods may be used
• Need to get at: \(p(\theta|y) \propto p(y|\theta)p(\theta)\)
• Traditionally, we would get \(p(\theta|y)\) by:
  • either figure out what the full conditionals for all our model parameters are (hard)
  • Use some form of MCMC to arrive at the posterior marginal distributions for our parameters (time consuming)

• Integrated Nested Laplace Approximation - Rue, Martino & Chopin (2009)
• One of several techniques that approximate the marginal and conditional posterior densities
  • Laplace, PQL, E-M, Variational Bayes
• Assumes all random effects in the model are latent, zero-mean Gaussian random field, \(x\) with some precision matrix
  • The precision matrix depends on a small set of hyperparameters
• Attempts to construct a joint Gaussian approximation for \(p(x | \theta, y)\)
  • where \(\theta\) is a small subset of hyper-parameters

• Apply these approximations to arrive at:

• \(\tilde{\pi}(x_i | y) = \int \tilde{\pi}(x_i |\theta, y)\tilde{\pi}(\theta| y) d\theta\)

• \(\tilde{\pi}(\theta_j | y) = \int \tilde{\pi}(\theta| y) d\theta_{-j}\)

• where each \(\tilde{\pi}(. |.)\) is an approximated conditional density of its parameters

• Approximations to \(\pi(x_i | y)\) are computed by approximating both \(\pi(\theta| y)\) and \(\pi(x_i| \theta, y)\) using numerical integration to integrate out the nuisance parameters.
  • This is possible if the dimension of \(\theta\) is small.
• Approximations to \(\tilde{\pi}(\theta|y)\) are based on the Laplace appoximation of the marginal posterior density for \(\pi(x,\theta|y)\)

• Their approach relies on numerical integration of the posterior of the latent field, as opposed to a pure Gaussian approximation of it

• We see that, while there is a persistence of the gap in black-white mortality:
  • The mortality rate appears to be converging
  • The convergence is faster in highly segregated areas
  • Suggests some evidence to support the Williams and Collins (2001) perspective
• INLA allows for rapid deployment of Bayesian statistical models with latent Gaussian random effects
  • Faster and generally as accurate as MCMC
  • Potentially an attractive solution for problems where large data/complex models may make MCMC less desireable

corey.sparks@utsa.edu

Coreysparks1

UTSA Demography