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The four models proposed for exploring the foetal origins of adult disease (FOAD) hypothesis use the product term between size at birth and current size to determine the relative importance of pre- and post-natal growth on disease in later life. This is a common approach for testing the interaction between an exposure (in this instance size at birth) and an effect modifier (in this instance current size)—incorporating the product term obtained by multiplying the exposure and effect modifier variables within a statistical regression model. This study examines the mathematical basis for this approach and uses computer simulations to demonstrate two potential statistical flaws that might generate misleading findings. The first of these is that the expected value of the partial regression coefficient for the product term (between exposure and effect modifier) will be zero when the outcome, exposure and effect modifier are all continuously distributed and follow a multivariate normal distribution. This is because testing the product interaction term amounts to testing for multivariate normality among the three variables, irrespective of the pair-wise correlations amongst them. The second flaw is that it is possible to generate a statistically significant interaction between exposure and effect modifier, even when none exists, simply by categorising either or both of these variables. These flaws pose a serious challenge to the four models approach proposed for exploring the FOAD hypothesis. The interaction between exposure and effect modifier variables should be interpreted with caution both here and elsewhere in epidemiological analyses.