# Presentation: 479168

## A New Paradigm for Birth Weight Distribution

Lorie Wayne Chesnut, M.P.H.                                MCH Epidemiology Conference
                                                                                                December 7, 2006 – Atlanta, GA

**Lorie Wayne Chesnut, M.P.H.****                                MCH Epidemiology Conference**
**                                                                                                ****December 7, 2006 – Atlanta, GA**

## 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

## 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

## 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?

## A typical birth weight distribution is not normal ...

**A typical birth weight distribution is not normal ...**

## 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

## Contaminated Normal Model

**Wilcox and Russell (1983)                                     ****http://eb.niehs.nih.gov/bwt/#**

## 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**.

## 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 , σj )
- f(x ; μj, σj ) is the probability density function for the normal distribution with mean μj and standard deviation σj that governs component j.
- pj is the fraction of observations originating from component j
- k is the number of components

## Illustrating a Mixture Model

**Illustrating a Mixture Model**

## 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?**

## A two-component fit is better ...

**A two-component fit is better ...**

## 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

## 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 <100 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)
- * R’s 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.

## 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)

## 4-Component Model for Non-Smokers

**4-Component Model for Non-Smokers**

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

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

## 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,
- “ That’s funny ...”    --Isaac Asimov

## 3-Component Model for Term Births

**3-Component Model for Term Births**

## 5-Component Model for Black General

- Filters:  Non-Hispanic, U.S. resident live births and fetal deaths

**5-Component Model for Black General**

## 4-Component Model for Black Favorable

- Filters:  Previous filters plus maternal age > 20 years with at least a high school education

**4-Component Model for Black Favorable**

## 4-Component Model for Black Optimal

- Filters:  Previous filters plus non-smoker, age < 35 with a college degree, first-trimester prenatal care and multiparous status (specifically one or two previous births)

**4-Component Model for Black Optimal**

## 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

## A Traditional Mortality Curve

## Our Mortality Curves ...

**Light to Moderate Smoking**

**Heavy Smoking**

**Our Mortality Curves ...**

## 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

## 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

## 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.

## Contact Information

- For general questions:
**Lorie Wayne Chesnut, MPH**
**University of Alabama at Birmingham**
**School of Public Health**
- _[cheslor@uab.edu](mailto:cheslor@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@ms.uky.edu**_

## Thank you!

## Data Tables – Selected Populations

## 6-Component Model for Twins

**6-Component Model for Twins**

## Example of Close-Up Views – Smoking Status

## 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.  *1977;**39**:1-22.
- 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 York;1985.

## 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. *1998;**70**:517-534
- Gage T, Bauer M, Heffner N, Stratton H.  Pediatric Paradox: Heterogeneity in the Birth Cohort.  *Hum Biol.*  2004;**76**:327-342
- Umbach D, Wilcox AJ.  A Technique for Measuring Epidemiologically Useful Features of Birthweight Distributions.  *Stat Med. *1996;**15**:1333-1348.
- Wilcox AJ, Russell IT.  Birthweight and Perinatal Mortality: I. On the Frequency Distribution of Birthweight.  *Int J Epidemiol. *1983;**12**:314-319.
- Wilcox AJ, Russell IT.   Birthweight and Perinatal Mortality: II. On Weight-Specific Mortality.  *Int J Epidemiol.  *1983;**12**:319-325.
- Wilcox AJ, Russell IT.  Birthweight and Perinatal Mortality: III.  Towards a New Method of Analysis.  *Int J Epidemiol.* 1986;15:188-196
- 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. *1990;**116**:7-10
- Wilcox AJ.  On the importance-and the unimportance-of birthweight.
*     **Int J Epidemiol.  *2001;**30**:1233-241