Brief Report
A regression model with unexplained residuals was preferred in the analysis of the fetal origins of adult diseases hypothesis

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Abstract

Background and Objective

A continued controversy exists whether the assessment of the influence of low birth weight on adult blood pressure necessitates adjustment for adult weight in the analysis on the fetal origins of adult diseases hypothesis. Here we first explain the difficulty in understanding an adjusted multivariate regression model, and then propose another way of writing the regression model to make the interpretation of the separate influence of birth weight and changes in weight later in life more straightforward.

Study Design and Setting

We used a multivariate regression model containing birth weight (standard deviation score; SDS), and residual adult weight (SDS) to explore the effect on blood pressure (or any other outcome) separately. Residual adult weight was calculated as the difference between actual adult weight and the expected adult weight (SDS) given on a certain birth weight (SDS).

Results

The coefficients of birth weight and residual adult weight show directly the effect on the analyzed outcome variable.

Conclusions

We prefer to use this regression model with unexplained residuals when the adjusted variable is in the causal pathway in the analyses of data referring to the fetal origins of adult diseases hypothesis.

Introduction

In the literature on the fetal origins hypothesis, a continued controversy exists whether the assessment of the influence of low birth weight on adult blood pressure necessitates adjustment for adult weight [1], [2]. The controversy was fueled by the meta-analysis of Huxley et al. [3], who described little or no relation between birth weight and adult blood pressure if unadjusted for adult weight, and implied that such adjustment might even be misleading. The effect of adding adult weight as a variable in the regression of blood pressure on weight at birth is intricate: a review by Lucas et al. [4] suggested that such a regression model should in fact be interpreted as the influence of a change in weight between birth and adulthood—and no longer as the influence of birth weight. Nonetheless, the interpretation of data by this concept remains confusing.

Our objective here is first to explain the difficulty in understanding the adjusted regression for the general reader, and then to propose another way of writing the regression model to make the interpretation of the separate influence of birth weight and changes in weight later in life more straightforward. We will explain the model not only conceptually and algebraically, but also by an example on data from an ongoing study on the effect of birth weight on blood pressure. Validation of the model in future analysis is warranted.

Section snippets

The adjusted regression analysis

Originally the association between birth weight and adult blood pressure was analyzed mainly without adjustments for additional variables [5]. Later, it was shown that subjects born with low birth weight tended to gain more weight compared with subjects born with a normal birth weight. Weight gain alone was also associated with an increased risk for high blood pressure. Therefore, adult weight was seen as a potential confounder in the analysis, and adjustment for it became more common [6]. Some

Which analysis meets the researcher's concerns?

Whether later size (e.g., adult weight) is a confounder in the analysis of early size (e.g., birth weight) and adult diseases, such as hypertension, or is rather a factor in the causal pathway is an ongoing debate in the literature. Adjustment for adult weight might not be justified after all [1], [2], [3]. Whatever the causal explanation, birth weight is positively correlated with adult weight and adult weight is correlated with adult blood pressure; therefore, we do first of all expect that

Conclusion, and proposal

Algebraically, the combined model of Lucas et al. [4] and our combined model with the residuals increase in weight can be rewritten in terms of each other, except for the situation where an interaction term is entered (see Appendix A). In the proposal by Lucas et al. [4], however, one needs two separate models: first estimating the coefficient from the early model, and then looking at the coefficient for attained weight in the combined model (without paying attention to the coefficient of birth

Acknowledgments

We thank S. LeCessie (Dept. of Medical Statistics, LUMC, Leiden, The Netherlands) and M.J.J. Finken (Department of Clinical Epidemiology, LUMC, Leiden, The Netherlands) for their comments on the manuscript.

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