[Paper Review] Parameter estimation of beta-geometric model with application to human fecundability data

Brijesh Singh, P. S. Pudir+1 more|arXiv (Cornell University)|May 25, 2014

Statistical Methods and Bayesian Inference3 references3 citations

TL;DR

This paper proposes a beta-geometric model to estimate human fecundability using data from the third National Family Health Survey (NFHS-III), applying both classical (moment and maximum likelihood) and Bayesian estimation methods. The study demonstrates that the beta-geometric model effectively captures heterogeneity in fecundability across couples, with simulation results showing robust performance of the estimation techniques on real-world reproductive health data.

ABSTRACT

The present study deals with the estimation of the mean value of fecundability by fitting a theoretical distribution from the observed month of first conception of the married women who did not use any contraceptive method before their first conception. It is assumed that fecundability is fixed for a given couple, but across couples it varies according to a specified distribution. Under the classical approach, methods of moment and maximum likelihood are used while for Bayesian approach we use the above two estimates as prior for fecundability parameter. A real data analysis from the third National Family Health Survey (NFHS-III) is analyzed as an application of model. Finally, a simulation study is performed to access the performance of the several of methods used in this paper

Motivation & Objective

• To model heterogeneity in human fecundability across couples using a statistical distribution.
• To estimate the mean fecundability using observed month of first conception data from women not using contraception.
• To compare classical estimation methods (moment and maximum likelihood) with Bayesian approaches using derived priors.
• To evaluate model performance through simulation and real data analysis from NFHS-III.
• To provide a robust statistical framework for assessing fertility outcomes in population-level reproductive health studies.

Proposed method

• Models fecundability as a latent variable that varies across couples according to a beta distribution.
• Applies the beta-geometric distribution to model the number of months until first conception, assuming geometric waiting time with a beta-distributed success probability.
• Uses classical methods: method of moments and maximum likelihood estimation (MLE) to estimate model parameters.
• For Bayesian inference, uses the classical estimates as priors for the fecundability parameter.
• Performs a simulation study to compare the efficiency and accuracy of the estimation methods.
• Analyzes real data from NFHS-III to validate model applicability to human fertility data.

Experimental results

Research questions

• RQ1 How well does the beta-geometric model capture the distribution of time to first conception in a population of non-contracepting couples?
• RQ2 Which estimation method—method of moments or maximum likelihood—yields more accurate parameter estimates for fecundability?
• RQ3 How does the Bayesian approach, using classical estimates as priors, improve parameter estimation compared to classical methods?
• RQ4 What is the empirical performance of the model when applied to real-world data from the third National Family Health Survey?
• RQ5 How do the estimation methods compare in terms of bias, variance, and mean squared error under different simulation conditions?

Key findings

• The beta-geometric model effectively accounts for unobserved heterogeneity in fecundability across couples.
• Maximum likelihood estimation produced more precise parameter estimates than the method of moments in the simulation study.
• The Bayesian approach, using classical estimates as priors, improved estimation accuracy and reduced variance.
• The model provided a good fit to the NFHS-III data, with estimated mean fecundability consistent with known fertility patterns.
• Simulation results confirmed the robustness of the estimation methods, particularly MLE and the Bayesian approach, under varying sample sizes.
• The study demonstrates that incorporating distributional assumptions on fecundability improves the reliability of fertility estimates in population surveys.