Abstract
BackgroundCentral 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).MethodsWe 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.ResultsWe 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.ConclusionsCombining 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.
Highlights
Central to the study of populations, and 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
Though we did consider the inclusion of other covariates such as education, our analysis focused on fertility over age and socio-economic status (SES), both of which we measured at the midyear point for each year
We can see that the model has captured the standard skewed relationship, as we would expect from our choice of parametric model
Summary
Central to the study of populations, and 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). The measurement of fertility rates and their relationships to socioeconomic variables are essential to the analysis of the population dynamics of that society. A variety of nonlinear models for fertility over age have been developed, such as the Hadwiger, Gamma, and Beta functions [6, 17]. These models fail to incorporate further covariates in anything more than a linear fashion [2], and impose their own strong assumptions ( these are potentially much better justified than generalised linearity)
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