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Thinking outside the curve, part I: modeling birthweight distribution.

Charnigo R, Chesnut LW, Lobianco T, Kirby RS - BMC Pregnancy Childbirth (2010)

Bottom Line: We address a number of methodological issues, including how the number of components selected depends on the sample size, how the choice of model selection criterion influences the results, and how estimates of mixture model parameters based on multiple samples from the same population can be combined to produce confidence intervals.The framework developed in this paper avoids assuming the existence of an interval of birthweights over which there are no compromised pregnancies and does not constrain birthweights within compromised pregnancies to be normally distributed.Thus, the present framework can reveal heterogeneity in birthweight that is undetectable via a contaminated normal model or a 2-component normal mixture model.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Statistics and Biostatistics University of Kentucky Lexington, KY 40506-0027, USA. RJCharn2@aol.com

ABSTRACT

Background: Greater epidemiologic understanding of the relationships among fetal-infant mortality and its prognostic factors, including birthweight, could have vast public health implications. A key step toward that understanding is a realistic and tractable framework for analyzing birthweight distributions and fetal-infant mortality. The present paper is the first of a two-part series that introduces such a framework.

Methods: We propose describing a birthweight distribution via a normal mixture model in which the number of components is determined from the data using a model selection criterion rather than fixed a priori.

Results: We address a number of methodological issues, including how the number of components selected depends on the sample size, how the choice of model selection criterion influences the results, and how estimates of mixture model parameters based on multiple samples from the same population can be combined to produce confidence intervals. As an illustration, we find that a 4-component normal mixture model reasonably describes the birthweight distribution for a population of white singleton infants born to heavily smoking mothers. We also compare this 4-component normal mixture model to two competitors from the existing literature: a contaminated normal model and a 2-component normal mixture model. In a second illustration, we discover that a 6-component normal mixture model may be more appropriate than a 4-component normal mixture model for a general population of black singletons.

Conclusions: The framework developed in this paper avoids assuming the existence of an interval of birthweights over which there are no compromised pregnancies and does not constrain birthweights within compromised pregnancies to be normally distributed. Thus, the present framework can reveal heterogeneity in birthweight that is undetectable via a contaminated normal model or a 2-component normal mixture model.

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Mixture Models in Simulation Studies. (a) Probability densities for the normal mixture models used in our simulation studies are compared. (b) to (d) Close-up views of the probability densities are displayed.
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Figure 3: Mixture Models in Simulation Studies. (a) Probability densities for the normal mixture models used in our simulation studies are compared. (b) to (d) Close-up views of the probability densities are displayed.

Mentions: For our first simulation study we generated 25 nonoverlapping data sets of size 5000 from designs A through E in Table 3; see also Figure 3. Designs A through E represent the fitted 2- through 6-component models derived from the 25 samples of size 50,000 in Table 1. Values in the data sets less than 500 or greater than 5500 were discarded since the 2- through 6-component models were meant to mimic a birthweight distribution; new values were drawn as needed to complete the data sets. We assessed how often the FLIC, BIC, and AIC recovered the correct number of components. This was repeated for data sets of different sizes up to 100,000.


Thinking outside the curve, part I: modeling birthweight distribution.

Charnigo R, Chesnut LW, Lobianco T, Kirby RS - BMC Pregnancy Childbirth (2010)

Mixture Models in Simulation Studies. (a) Probability densities for the normal mixture models used in our simulation studies are compared. (b) to (d) Close-up views of the probability densities are displayed.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2927479&req=5

Figure 3: Mixture Models in Simulation Studies. (a) Probability densities for the normal mixture models used in our simulation studies are compared. (b) to (d) Close-up views of the probability densities are displayed.
Mentions: For our first simulation study we generated 25 nonoverlapping data sets of size 5000 from designs A through E in Table 3; see also Figure 3. Designs A through E represent the fitted 2- through 6-component models derived from the 25 samples of size 50,000 in Table 1. Values in the data sets less than 500 or greater than 5500 were discarded since the 2- through 6-component models were meant to mimic a birthweight distribution; new values were drawn as needed to complete the data sets. We assessed how often the FLIC, BIC, and AIC recovered the correct number of components. This was repeated for data sets of different sizes up to 100,000.

Bottom Line: We address a number of methodological issues, including how the number of components selected depends on the sample size, how the choice of model selection criterion influences the results, and how estimates of mixture model parameters based on multiple samples from the same population can be combined to produce confidence intervals.The framework developed in this paper avoids assuming the existence of an interval of birthweights over which there are no compromised pregnancies and does not constrain birthweights within compromised pregnancies to be normally distributed.Thus, the present framework can reveal heterogeneity in birthweight that is undetectable via a contaminated normal model or a 2-component normal mixture model.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Statistics and Biostatistics University of Kentucky Lexington, KY 40506-0027, USA. RJCharn2@aol.com

ABSTRACT

Background: Greater epidemiologic understanding of the relationships among fetal-infant mortality and its prognostic factors, including birthweight, could have vast public health implications. A key step toward that understanding is a realistic and tractable framework for analyzing birthweight distributions and fetal-infant mortality. The present paper is the first of a two-part series that introduces such a framework.

Methods: We propose describing a birthweight distribution via a normal mixture model in which the number of components is determined from the data using a model selection criterion rather than fixed a priori.

Results: We address a number of methodological issues, including how the number of components selected depends on the sample size, how the choice of model selection criterion influences the results, and how estimates of mixture model parameters based on multiple samples from the same population can be combined to produce confidence intervals. As an illustration, we find that a 4-component normal mixture model reasonably describes the birthweight distribution for a population of white singleton infants born to heavily smoking mothers. We also compare this 4-component normal mixture model to two competitors from the existing literature: a contaminated normal model and a 2-component normal mixture model. In a second illustration, we discover that a 6-component normal mixture model may be more appropriate than a 4-component normal mixture model for a general population of black singletons.

Conclusions: The framework developed in this paper avoids assuming the existence of an interval of birthweights over which there are no compromised pregnancies and does not constrain birthweights within compromised pregnancies to be normally distributed. Thus, the present framework can reveal heterogeneity in birthweight that is undetectable via a contaminated normal model or a 2-component normal mixture model.

Show MeSH