A New Paradigm for Birth Weight Distribution

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• A New Paradigm for Birth Weight Distribution
• Lorie Wayne Chesnut, M.P.H.
  MCH Epidemiology Conference
• 
  
  December 7, 2006 Atlanta, GA

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Collaborators

• Richard J. Charnigo, Ph.D.
• University of Kentucky, College of Public Health
• Tony LoBianco, Ph.D., M.P.H.
• University of Kentucky, Human Development
  Institute

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The Impact of Birth Weight

• Increased morbidity and mortality
• (low and even high birth weight)
• Complex medical problems and developmental delays
• Increasing evidence of long-term health impacts

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Challenging Questions Remain

• Why does birth weight vary across populations?
• Are ideal birth weight ranges common to all
  populations or do they vary across groups?
• What factors besides gestational age influence
  birth weight?
• Is there an unobservable confounder associated
  with higher mortality and morbidity in LBW and
  VLBW infants?
• Why does the pediatric paradox exist?

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A typical birth weight distribution is not normal

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Contaminated Normal Models and Birth Weight
Distribution

• Two-component model proposed by Wilcox and
  Russell (1983)
• Included primary distribution and residual at
  left tail
• Three-component model proposed by Umbach and
  Wilcox (1996)
• Included primary distribution and residual at
  both left and right tails

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Contaminated Normal Model

• Wilcox and Russell (1983)
  http//eb.niehs.nih.gov/bwt/

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Finite Mixture Models

• Reveal a limited number of normally distributed
  components, providing a good approximation to a
  non-normal distribution
• This is important because a Gaussian distribution
  hints at the workings of orderly biological
  processes (Wilcox, 1983)
• Thus, through judicious statistical modeling, we
  may visualize naturally occurring patterns.

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Finite Mixture Models

• Computationally intensive powerful computers
  make these calculations possible
• Used in many fields including genetics, biology,
  medicine, economics and engineering.
• --------------------------
• Finite Mixture Models are expressed by the
  probability density function
• ? jk 1 pj f(x µj , sj )
• f(x µj, sj ) is the probability density
  function for the normal distribution with mean µj
  and standard deviation sj that governs component
  j.
• pj is the fraction of observations originating
  from component j
• k is the number of components

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Illustrating a Mixture Model
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Finite Mixture Models

• Two-component mixture model for birth weight
  distribution proposed by Gage and Therriault
  (1998)
• Main distribution included most births
• Second distribution included compromised births
  from VLBW (left tail) to HBW (right tail)
• A better fit but with a conceptual difficulty
  should VLBW and HBW births be modeled as a part
  of the same component?

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A two-component fit is better
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Methods

• NCHS Public-Use Perinatal Mortality Data Files
• 2001 and 2002 (resident births)
• Birth weight trimmed to between 500 and 5500
  grams
• Gestational age trimmed to 22 weeks
• Random sample of 50,000 singleton live births
  and fetal deaths per population
• SPSS used for random sample selection

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Methods

• FLIC (Flexible Information Criterion) applied for
  each sample (Pilla and Charnigo, 2006)
• Improving upon AIC and BIC
• Restriction imposed that no component could have
  a standard deviation of lt100 grams
• Parameters estimated for between 2 and 7
  components
• FLIC ascertains the optimal number of components
  to fit the data
• Version 2.3.1 of the R statistical software
  package
• Maximum likelihood estimation completed using
  expectation maximization (EM)
• algorithm (preliminary estimates)
• Rs nonlinear minimization (nlm) procedure for
  final estimates
• Log likelihood computed for each normal
  mixture. FLIC is equivalent to the log
  likelihood minus a
• penalty that becomes greater as more
  components are added.

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Results General Pattern Established

• Component 1 - ELBW VLBW
• Component 2 - LBW including compromised births
  in normal and high birth weight ranges (largest
  standard deviation)
• Component 3 - Primarily normal birth weight
  births
• Component 4 - High-normal and HBW (4000 grams )

• Populations Preferring
• 4 Components
• White (General, Favorable, Optimal)
• American Indian
• Asian Indian
• Black (Optimal only)
• Chinese
• Mexican
• Puerto Rican
• Smoking Status (non, light to moderate, high)

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4-Component Model for Non-Smokers
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4-Component Model for Light-Moderate Smokers
(1-19 cigarettes/day)
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Results

• Some populations did not fit the general
• pattern
• Term Births
• Black Births (except for Black Optimal)
• Twins
• The most exciting phrase to hear in science, the
  one that heralds new discoveries, is not
  Eureka! (I found it!) but rather,
• Thats funny --Isaac Asimov

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3-Component Model for Term Births
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5-Component Model for Black General
Filters Non-Hispanic, U.S. resident live births
and fetal deaths
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4-Component Model for Black Favorable
Filters Previous filters plus maternal age gt 20
years with at least a high school education
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4-Component Model for Black Optimal
Filters Previous filters plus non-smoker, age lt
35 with a college degree, first-trimester
prenatal care and multiparous status
(specifically one or two previous births)
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Future Research

• Component membership must be linked to
  observable covariates
• Pattern anomalies between the black population
  and other groups must be investigated
• Birth weight patterns within various gestational
  age categories should be examined
• Birth weight-specific mortality curves must be
  developed

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A Traditional Mortality Curve
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Our Mortality Curves
Light to Moderate Smoking
Heavy Smoking
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Limitations

• Inherent issues with vital records data
• Component membership not observed directly, but
  rather inferred on the basis of birth weight and
  probabilistically assigned to a particular infant
• Assumption of normal components

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Question

• Do the current cut-points of ELBW, VLBW, LBW and
• HBW over-simplify the relationship between
  mortality and
• birth weight?
• The cut-points are
• Simple to understand and to calculate
• A convenient way to monitor birth weight
  distribution
• But they
• Miss compromised normal birth weight births
• Assume that all populations conform to the same
• birth weight standards

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The take-home message

• New methods are necessary for more accurate and
  sensitive research on birth weight and its
  interaction with gestational age
• New partners and new resources must come to the
  table. Other fields are using many
  cutting-edge methodologies that may be useful to
  perinatal epidemiology.
• Finite mixture models are just one example of
  such methodologies.

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Contact Information

• For general questions
• Lorie Wayne Chesnut, MPH
• University of Alabama at Birmingham
• School of Public Health
• cheslor_at_uab.edu
• For questions specific to the statistical
  methodology
• used in this presentation
• Richard J. Charnigo, Ph.D.
• University of Kentucky, College of Public Health
• 859.257.5678 x82072 richc_at_ms.uky.edu

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Thank you!
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Data Tables Selected Populations
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6-Component Model for Twins
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Example of Close-Up Views Smoking Status
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References

• Finite Mixture Models
• Charnigo R, Pilla R. Semiparametric Mixtures of
  Generalized Exponential Families. Scandinavian
  Journal of Statistics. 2006. To appear.
• Dempster AP, Laird NM, Rubin DB. Maximum
  likelihood from incomplete data via the EM
  algorithm J R Stat Soc. 1977391-22.
• Lindsay BG. Mixture Models Theory, Geometry and
  Applications. IMS NSF-CBMS Regional Conference
  Series, Hayward 1995.
• McLachlan G, Peel D. Finite Mixture Models.
  Wiley, New York 2000.
• Pilla R, Charnigo R. 2006. Consistent
  Estimation and Model Selection in Semiparametric
  Mixtures. Under review.
• Titterington D, Smith AFM, Makov U. Statistical
  Analysis of Finite Mixture Distributions. Wiley,
  New York1985.

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References

• Birth Weight and Birth Weight Distribution
• Gage T, Therriault G. Variability of
  Birth-Weight Distributions by Sex and Ethnicity
  Analysis Using Mixture Models. Hum Biol.
  199870517-534
• Gage T, Bauer M, Heffner N, Stratton H.
  Pediatric Paradox Heterogeneity in the Birth
  Cohort. Hum Biol. 200476327-342
• Umbach D, Wilcox AJ. A Technique for Measuring
  Epidemiologically Useful Features of Birthweight
  Distributions. Stat Med. 1996151333-1348.
• Wilcox AJ, Russell IT. Birthweight and Perinatal
  Mortality I. On the Frequency Distribution of
  Birthweight. Int J Epidemiol. 198312314-319.
• Wilcox AJ, Russell IT. Birthweight and
  Perinatal Mortality II. On Weight-Specific
  Mortality. Int J Epidemiol. 198312319-325.
• Wilcox AJ, Russell IT. Birthweight and Perinatal
  Mortality III. Towards a New Method of
  Analysis. Int J Epidemiol. 198615188-196
• Wilcox, AJ and Russell, IT. Why small black
  infants have lower mortality than small white
  infants the case for population-specific
  standards for birthweight. J Pediatr.
  19901167-10
• Wilcox AJ. On the importance-and the
  unimportance-of birthweight.
• Int J Epidemiol. 2001301233-241