Bayesian Methods for
Monitoring Public Health
Surveillance Data
October 17, 2002
Owen Devine
Division of STD Prevention
National Center for HIV, STD and TB Prevention
Centers for Disease Control and Prevention
• Spatially referenced data
• Temporally referenced data
Focus on detection of aberrations in public
health surveillance data
Mapping Surveillance Data
Observed rates can
be “unstable” estimates
of the true underling risk
County
1998 Pop.
Num. Of
Events
Rate per
/100000
Rich
1793
1
56
Davis
229393
128
56
Rich
1793
2
112
Bayesian Smoothing
 i = Underlying true risk of disease in area i
Prior
yi
= Observed number of cases in area i
Likelihood

i | ~ h(i | )
yi |  i ~ l ( yi |  i )
= Parameters describing prior uncertainty about true risk
Hyper-prior
 ~ g ( )
Bayesian Smoothing
Updated (Posterior) distribution of i | yi
i | yi  l ( yi | i ) h(i | , ) g ()
Fully Bayesian :
ˆ i  E[ i | yi , ]
Empirical Bayes :
ˆ i  E[i | yi ,ˆ]
Bayesian Smoothing for Detecting Spatial Aberrations
Advantages:
•
•
•
Stabilization of observed risk measures in areas with small
populations
Evaluation of etiologic models  i  f (  X i )
Two stage model is intuitive for observed measures of health
disease burden
Disadvantages:
•
•
Analytic and computational resources may not be available to
utilize these methods in local health departments
Over-smoothing
Bayesian Smoothing for Detecting Spatial Aberrations
2001 P&S Syphilis Rates in North Carolina
Observed
Rate  2
2 < Rate  10
Rate > 10
Bayesian Smooth
Population Weighted Average
An Approach to Bayesian Aberration Detection in
Temporally Referenced Health Surveillance Data
4000
3500
Crashes
3000
2500
2000
0
10
20
30
40
50
60
Month
Prior :
E[t ]  f ( y1 , ..., yt 1 , X , )  ~ g ()
h(  t |  )
Likelihood :
l ( yt | t )
Model :
An Approach to Bayesian Aberration Detection in
Temporally Referenced Health Surveillance Data
4000
3500
Crashes
3000
2500
2000
0
10
20
30
40
50
60
Month
Posterior :
k ( t | y1 , ..., yt )  l ( yt | t ) h( t |  ) g ( )
An Approach to Bayesian Aberration Detection in
Temporally Referenced Health Surveillance Data
Advantages:
•
•
Successive updating fits nicely with temporal surveillance
Evaluation of etiologic models t  f ( y1 , ..., yt 1 , X , )
Disadvantages:
•
•
Analytic and computational resources may not be available to
utilize these methods in local health departments
Model for  t may differ between outcomes, locations, etc.
Bayesian Aberration Detection For Health Surveillance Data
Bayesian Approach
Pros
Cons
Stabilization
Lack of Portability
Etiologic Evaluation
Lack of Transparency
Intuitive Models
Bayesian Decision Making
Suppose some rule, r ( yt ) , leads to a decision, for example
r ( yt )  K
 Sound alarm
r ( yt )  K
 Do not sound alarm
Let l (r ( yt ) , t ) be the loss due to making an incorrect
decision, then choose r ( yt ) to minimize the posterior risk,
 ( r ( yt ) ) , where
 ( r ( yt ) )   l ( r ( yt ),  t ) k (  t | yt ) d  t