Introduction

It is useful in many applied settings to estimate the expected pattern of within-individual change in some continuously distributed variable over time. This may involve developing depictions of growth or maturation in development studies (for example, reference [1]), 'course' in a chronic disorder (for example, reference [2]), short-term patterns of change in response to a stimulus such as an oral glucose load (for example, reference [3]), or change in a clinical trial [4]. There are many possible approaches to estimating such patterns of change. However, many have serious limitations when longitudinal changes in data vary with individual characteristics; not all individuals are measured the same number of times, and not all individuals are measured at the same intervals. These are common occurrences in observational studies.

Hierarchical linear modelling (HLM) [5], an extension of the mixed model - also referred to as random coefficient regression modelling [6], multilevel linear modelling [7], nested modelling, or seemingly unrelated regression - is a very flexible approach to such situations [8-11]. Among other reviews, Sullivan et al. [12] recently presented a tutorial on HLM in the spirit of analysis of covariance (ANCOVA) with random coefficients. The purpose of the present paper is to illustrate how HLM can be extended to develop growth curves with an easily understandable and clinically important example, body mass index (BMI; kg/m2). In Section 2, we present a pedagogical exposition with hypothetical data and introduce available statistical software for conducting HLM. In Section 3, the clinical implication of derived BMI growth curves is discussed. In Section 4, procedures for selecting specific databases for developing BMI growth curves are presented. In Section 5, specific statistical approaches for conducting HLM are introduced. In Section 6, results are presented and the nuances of the growth curves discussed. In Section 7, methodological issues related to HLM and clinical application of developed curves are reviewed.

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