Abstract
Background: Many statistical methods are available to model longitudinal growth data and relate derived summary measures to later outcomes.Aim: To apply and compare commonly used methods to a realistic scenario including pre- and postnatal data, missing data, and confounders.Subjects and methods: Data were collected from 753 offspring in the Southampton Women’s Survey with measurements of bone mineral content (BMC) at age 6 years. Ultrasound measures included crown-rump length (11 weeks’ gestation) and femur length (19 and 34 weeks’ gestation); postnatally, infant length (birth, 6 and 12 months) and height (2 and 3 years) were measured. A residual growth model, two-stage multilevel linear spline model, joint multilevel linear spline model, SITAR and a growth mixture model were used to relate growth to 6-year BMC.Results: Results from the residual growth, two-stage and joint multilevel linear spline models were most comparable: an increase in length at all ages was positively associated with BMC, the strongest association being with later growth. Both SITAR and the growth mixture model demonstrated that length was positively associated with BMC.Conclusions: Similarities and differences in results from a variety of analytic strategies need to be understood in the context of each statistical methodology.
Highlights
There is increasing interest in modelling longitudinal data and determining relationships with a future outcome
Sayers et al (2017) compared six methods that relate a linear trajectory of change to a later outcome, using simulated data, concluding that two-stage approaches result in biased unconditional associations
The findings from residual growth modelling and both multilevel linear spline models are the most straightforward to compare and showed that all measures of growth were positively associated with bone mineral content (BMC)
Summary
There is increasing interest in modelling longitudinal data and determining relationships with a future outcome. For the SITAR method, age was defined as years from birth because this analysis provides a data-driven developmental age adjustment BMC was regressed on each of the standardised individual-level random effects from the multilevel model in turn, adjusting for sex, age at BMC measurement and individual-level random effects relating to earlier age intervals and length at 11 weeks. ÁÁ þ eij where the lengthij are measurements at ages tij, with i indexing the occasion and j the subject; h(.) is a function in transformed age defining the mean spline curve; aj, bj and cj are subject-specific random effects for size, timing and intensity, respectively, and the eij are normally distributed residuals. Differences in BMC in the ‘descending’ and ‘ascending’ classes compared with the ‘stable’ class are illustrated in Figure 7B; all pairwise comparisons were significant
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