Modelling fertility in rural South Africa with combined nonlinear parametric and semi-parametric methods

Robert W Eyre; Thomas House; F Xavier Gómez-Olivé; Frances E Griffiths

doi:10.1186/s12982-018-0073-y

Modelling fertility in rural South Africa with combined nonlinear parametric and semi-parametric methods

Emerg Themes Epidemiol. 2018 Mar 2:15:5. doi: 10.1186/s12982-018-0073-y. eCollection 2018.

Authors

Robert W Eyre¹, Thomas House², F Xavier Gómez-Olivé³, Frances E Griffiths^{4

5}

Affiliations

¹ 1Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL UK.
² 2School of Mathematics, University of Manchester, Manchester, M13 9PL UK.
³ 3Medical Research Council/Wits University Rural Public Health and Health Transitions Research Unit (Agincourt), School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa.
⁴ 4Warwick Medical School, University of Warwick, Coventry, CV4 7AL UK.
⁵ 5Centre for Health Policy, University of the Witwatersrand, Johannesburg, South Africa.

Abstract

Background: Central to the study of populations, and therefore to the analysis of the development of countries undergoing major transitions, is the calculation of fertility patterns and their dependence on different variables such as age, education, and socio-economic status. Most epidemiological research on these matters rely on the often unjustified assumption of (generalised) linearity, or alternatively makes a parametric assumption (e.g. for age-patterns).

Methods: We consider nonlinearity of fertility in the covariates by combining an established nonlinear parametric model for fertility over age with nonlinear modelling of fertility over other covariates. For the latter, we use the semi-parametric method of Gaussian process regression which is a popular methodology in many fields including machine learning, computer science, and systems biology. We applied the method to data from the Agincourt Health and Socio-Demographic Surveillance System, annual census rounds performed on a poor rural region of South Africa since 1992, to analyse fertility patterns over age and socio-economic status.

Results: We capture a previously established age-pattern of fertility, whilst being able to more robustly model the relationship between fertility and socio-economic status without unjustified a priori assumptions of linearity. Peak fertility over age is shown to be increasing over time, as well as for adolescents but not for those later in life for whom fertility is generally decreasing over time.

Conclusions: Combining Gaussian process regression with nonlinear parametric modelling of fertility over age allowed for the incorporation of further covariates into the analysis without needing to assume a linear relationship. This enabled us to provide further insights into the fertility patterns of the Agincourt study area, in particular the interaction between age and socio-economic status.

Keywords: Age-pattern; Agincourt; Fertility; Gaussian process regression; Nonlinear model; Parametric model; Semi-parametric model; Socio-economic status pattern.