Temporal Changes in the Geographical Pattern of Infant Deaths, Des Moines, Iowa 198994

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Temporal Changes in the Geographical Pattern of
Infant Deaths, Des Moines, Iowa 89-94
Aniruddha Rudy Banerjee Department of
Geography, The University of Iowa
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purpose of this study

• To determine significant changes in infant
  mortality patterns through time

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Study Area
Des Moines urban area, Iowa
17miles E-W 11miles N-S
N
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first time period
Location of infant births deaths in Des Moines,
Iowa, 1989-92
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second time period
Location of infant births deaths in Des Moines,
Iowa, 1993-94
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Motivation

• Often, as geographers, we study whether the rate
  of occurrence of some event changes from one
  period to another
• These rates may be the relationship between
• infant deaths and infant births
• fire damage of homes in an urban area
• cancer deaths and the population at risk

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Motivation

• These changing relationships are usually mapped
  to identify patterns
• However
• When mapping these changing patterns, can we
  infer true rates from observed rates?
• Problem overlooked by geographers

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Goal

• Is there a method that determines change in true
  rate patterns from change in observed rates?

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Possible solutions

• One way to observe changing relationship between
  patterns of events is to map their location in
  space and time
• i.e. map the observed rates

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Calculating rates
Location of infant births deaths in Des Moines,
Iowa, 1989-92
0 deaths! 22 births or 0 imr
29 deaths 603 births or 31 imr
4 deaths, 247 births or 17 imr
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How to Map these rates?

• Rates being a continuous variable we may use a
  powerful cartographic technique
• Isopleth Mapping
• Isopleth mapping converts rates observed at
  sample locations to a continuous spatial
  distribution using spatial interpolation
  techniques
• Square grid (0.4 miles) vertices are used for
  sample locations

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Calculating rates from a spatial grid
Location of grid points (0.4miles apart)
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Selecting spatial filters
Spatial filters (0.8 miles, 1.2 miles and 1.6
miles)
Adjacent local estimates share information
because of overlaps
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isopleths time period 1
Infant death rates (0.8 miles) in Des Moines,
Iowa, 1989-92
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isopleths time period 2
Infant death rates (0.8miles) in Des Moines,
Iowa, 1993-94
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Any Regional Change?
Statistically, the region as a whole experienced
a significant decline in IMR (drop from 9.2 to
7.9) A general test was done using the following
z-test statistic
8.56
Z-critical is 1.96 at p lt 0.5
where, r1 rate in first period r2 rate in
second period l total number of live births
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detect any change within?
Infant death rates in Des Moines, Iowa, 1989-92
1993-94
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Map the Change
Difference in IMR (93-94) - (89-92)
increase() or decrease(-)
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Problems?

• Yes!
• When mapping changes in these patterns, can we
  determine real changes from observed changes?
• Unusually high or low rates in local areas may
  result from the small number problem

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small number problem
1989-92
1993-94
A large change in imr (from 250 to 0!) with 1
fewer death
0.4 mi
1 deaths,4 births, 250 imr!
0.8 mi
2 deaths,204 births, 9.8 imr!
0 deaths,4 births, 0 imr!
0 deaths,93 births, 0 imr!
A small change in imr (from 9.8 to 0!) with 1
fewer death
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small number problem
1989-92
1993-94
A small change in imr (from 9.5 to 7.5!) with 1
fewer death
4 deaths,419 births, 9.5 imr!
3 deaths,402 births, 7.5 imr!
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variability and the small number problem
Expected change between two time periods i.e. 9.2
- 7.9 1.3 imr
Small numbers
large numbers
1.3
1.3
Large variations
Small variations
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What do we do?
We would like to map real changes in rates
instead of observed changes in rates
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Past research

• Examples
• Choynowski 1959, Berry 1960s -- Probability maps
• Spatial point processes -- Cluster Statistics -
  1980s-90s
• Bayesian Adjustments Maps-- 1980s-90s
• Monte Carlo Simulation -- 1990s

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Past research

• Few studies done on temporal change of geographic
  pattern

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Present research

• To determine real changes in geographic pattern
• We follow a stochastic model that has the form
• ? imrt1 - imrt ?
• To model the error-distribution D(?) a Monte
  Carlo simulation is used
• the Monte Carlo simulation generates a null
  distribution from an expected hypothesis for any
  area without the use of parametric distributional
  assumptions

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Monte Carlo Simulation vs theoretical
distributions

• In a Monte Carlo simulation
• i.i.d assumptions are not required
• each filter at any grid point generates its own
  distribution by appropriate transformation of the
  expected or null hypothesis for non-i.i.d
  variables, the Jacobian (determinant vector) of
  the transformation is theoretically intractable

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simulations from chance the null hypothesis

• To Simulate rate changes a null hypothesis may be
  stated
• each birth, in a given time period, has the same
  chance of dying
• in other words what expected changes would occur
  if in each period each infant birth had the same
  risk of becoming a death?

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Null Hypothesis Simulation

• Time Period 2
• there were 73 deaths and 9241 births
• 73 deaths are selected randomly from the
  locations of the 9241 births
• made 500 maps

• Time Period 1
• there were 178 deaths and 19,348 births
• 178 deaths are selected randomly from the
  locations of the 19,348 births
• made 500 maps

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generating simulated differences

• We have
• Each time period has 500 simulated maps
• Now, simulation 1 for time period 1 may differ
  with all the 500 simulations in time period 2
• simulation 2 for time period 1 may differ with
  all the 500 simulations in time period 2
• . And so on for 500 times

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generating simulated differences

• We have for any area 500500 or 250,000 simulated
  (or expected) differences
• We have 1084 grid points with observed
  differences this makes 250,0001084 or
  approximately a quarter billion differences
• All these quarter billion calculations are done
  by a computer program written in an object
  oriented language (C) and uses 30 minutes on a
  100 MHz processor speed

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observed versus expectedapplying (constrained)
Monte Carlo simulations

• We compare the observed difference with the
  differences generated from the null
• In doing so, we measure how many times the
  simulated differences for any area (here, spatial
  filter) are lower than the observed difference
  in IMR

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example of simulated differences
Figure 1 Simulated differences of infant
mortality rates (period 1 period 2) and the
observed difference at one grid point.
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Significance of IMR differences in Des Moines,
Iowa 1989-94
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Significance of IMR differences in Des Moines,
Iowa 1989-94
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conclusions

• In this case, several small areas of Des Moines,
  Iowa were shown to have significant declines in
  infant mortality rates between 1989-92 1993-94.
  No areas showed significant increases in imr.
• We have developed and tested a model that
  successfully separates change in disease rates in
  small areas due to chance from changes that are
  NOT due to chance and therefore MUST be real
• By using spatially filtered data (as in this case
  study), this model can be implemented at any
  chosen geographical scale

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future work

• Redefining the null hypothesis
• by redefining the null hypothesis for every local
  area a more powerful map can be produced that
  estimates the risk of change in infant mortality
• to achieve this a bootstrapping method is
  applied to achieve unique local acceptable null
  hypotheses
• bootstrapping is an approach designed to
  iteratively reach an acceptable null estimate

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future work

• introduce independent variables to estimate
  causal relationship in studying change

f(xi )
? imrt1 - imrt ?

• Where f(xi ) are functions of independent
  variables (i 1, 2, 3 ) affecting infant
  mortality change, e.g.
• Health policy, welfare of neighborhood, education
  of mother etc.

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We shall not cease from exploration And the end
of all our exploring Will be to arrive where we
started And know the place for the first
time. (T. S. Eliot)
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References
Chowynowski M. 1959. Maps based upon
probabilities. Journal of American Statistical
Association, 54385-388. Grimson, R.C. and Oden,
N. 1996. Disease clusters in structured
environments. Statistics in Medicine,
15851-871. Langford I., 1994. Using empirical
Bayes estimates in the geographical analysis of
disease mapping. Area 26142-149. Nagarwalla, N.
1996. A Scan Statistic with a variable window.
Statistics in Medicine, 15845-850. Rushton G.
and Lolonis P., 1996. Exploratory spatial
analysis of birth defect rates in an urban
population. Statistics in Medicine, 15717-726.
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This paper was presented at the Annual Meetings
of The Association of American Geographers,
Boston, Massachusetts, March 1998
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Acknowledgements
Dr. Gerard Rushton, Professor, Department of
Geography, University of Iowa Diane S.
Krishnamurti, M.P.H., Birth Defects Registry,
University of Iowa
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for further information contact
Aniruddha Rudy Banerjee (email
aniruddha-banerjee_at_uiowa.edu) for information on
software to run the models used in this research.
The programs are written in the object oriented
C programming language and run on Windows95?
Windows NT? operating systems
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End