Original article
Adjustment for selection bias in cohort studies: An application of a probit model with selectivity to life course epidemiology

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Abstract

Sample attrition is potentially a source of bias in cohort studies. The outcome may not be observed in a considerable proportion of the subjects. This article proposes the application of a probit model with sample selection to handle the problem. Two equations are simultaneously estimated and their error terms allowed to correlate: one regressing an observed outcome on a set of baseline variables, another regressing the probability of the outcome being observed upon a set of (perhaps the same) baseline variables. The method was applied to a study of a birth cohort, half of whose members were interviewed again at age 26. Baseline variables were observed for all the subjects included. The focus was on the association between birth weight and mental health in adults. The probit model with sample selection revealed a stronger and more significant (P = 0.037) relation between birth weight and mental health than an ordinary probit regression model (P = 0.170). Interpretation and practical considerations are discussed.

Introduction

Insults in fetal life may affect mental health and developmental outcomes in later life. Barker hypothesized that fetal growth failure might undermine development of the fetus' nervous system and cause a long-term impact on sympathetic nervous activity [1]. Children who suffered growth stunting were found to have increased physiological response to psychological and physical stressors [2]. A large number of studies have demonstrated associations between birth weight and psychological and developmental outcomes in children. It is uncertain whether the associations will persist into adulthood. Lagerstrom et al. did not find any association between low birth weight and psychiatric disturbances at age 16–18 years [3].

Cohort studies often suffer a problem of losses to follow-up. Independent variables at baseline are measured in virtually all subjects, but the outcome is not observed in some of them. Sample attrition can cause a bias if it is related to both the independent variables and the outcome variable. In life course epidemiology, which is partly inspired by the fetal origin hypothesis proposed by Barker [1], sample attrition can be substantial because of very long follow-up period. Kramer and Joseph were skeptical about the fetal origin hypothesis and criticized that the cohort studies in support of the hypothesis often could only trace a small proportion of the original cohort members [4].

Econometricians developed a class of statistical models for the testing of a selection bias and estimating covariate effects in the face of it. To my knowledge this class of models has not been applied in clinical research, although it has been mentioned in a study of mastitis in cows [5] and has been used in the evaluation of social programs [6]. The primary objective of this article is to introduce and illustrate the use of a probit model with sample selection in epidemiological investigation, or probit selectivity model in short. It is hoped that this article will encourage clinical epidemiologists to consider the use of advanced statistics for handling selection bias. The secondary objective is to estimate the association between birth weight and mental health in adults in a birth cohort, half of whose members were followed up at the age of 26 years.

Section snippets

Methods

There are various types of data structures and various types of missing values in each data structure. The present article only concerns a data structure in which all independent variables are observed, and in which there is only one single outcome variable which may be observed or missing (i.e., not repeated measurement of outcomes). This is the common situation in studies of the Barker hypothesis, in which an adult outcome is regressed upon size at birth. The impact of sample attrition is

Application

Data from the 1970 British birth cohort study is used for the examination of an association between birth weight and mental health in adults. The study originally included almost all births in a week in 1970 in Britain (n = 17,196). Details of the 1970 British birth cohort study have been reported elsewhere 15, 16.

The present analysis focuses on the question of whether birth weight is related to mental health in adults, taking into account covariates. In line with Barker's hypothesis that birth

Discussion

Life course epidemiology and the fetal origin hypothesis have caused a paradigm shift in preventive medicine. Some researchers have suggested that fetal growth failure may also have a long-term impact on mental health. Advances in this research area have been limited by the lack of long-term follow-up data. The 1970 birth cohort study provides a valuable opportunity to investigate this hypothesis. However, sample attrition is substantial in this study, as in any other cohort study with a long

Acknowledgements

Thanks are due to the Social Statistics Research Unit, City University, and The Data Archive, for providing the 1970 Birth Cohort Study data. The author has benefited from the comments given by two reviewers.

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