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There is a growing literature that suggests environmental exposure during key developmental periods could have harmful impacts on growth and development of humans. Understanding and estimating the relationship between early-life exposure and human growth is vital to studying the adverse health impacts of environmental exposure. We compare two statistical tools, mixed-effects models with interaction terms and growth mixture models, used to measure the association between exposure and change over time within the context of non-linear growth and non-monotonic relationships between exposure and growth. We illustrate their strengths and weaknesses through a real data example and simulation study. The data example, which focuses on the relationship between phthalates and the body mass index growth of children, indicates that the conclusions from the two models can differ. The simulation study provides a broader understanding of the robustness of these models in detecting the relationships between any exposure and growth that could be observed. Data-driven growth mixture models are more robust to non-monotonic growth and stochastic relationships but at the expense of interpretability. We offer concrete modeling strategies to estimate complex relationships with growth patterns. [ABSTRACT FROM AUTHOR]