A discussion of statistical methods to characterise early growth and its impact on bone mineral content later in childhood

Figures & data

Table 1. Descriptive statistics.

Characteristic	n	Value^a
11 week crown-rump length (cm)	503	5.3 (0.8)
19 week femur length (cm)	712	3.1 (0.2)
34 week femur length (cm)	746	6.5 (0.3)
Birth supine length (cm)	737	50.1 (1.9)
6 month supine length (cm)	746	67.5 (2.5)
12 month supine length (cm)	735	75.9 (2.7)
2 year height (cm)	705	86.8 (3.1)
3 year height (cm)	719	96.1 (3.5)
Males, n (%)	753	393 (52%)
6 year BMC (kg)	753	0.54 (0.07)
Age at BMC (years)	753	6.7 (6.5–6.8)

^a Percentage for categorical data, mean (SD) for continuous data except age at BMC, for which median (IQR) is presented.

Figure 1. Length of SWS participants by age.

Figure 2. Residual growth modelling: conditional change in length as predictors of 6 year whole body BMC (g).

Figure 3. Two stage multilevel linear spline: conditional change in length as predictors of 6 year whole body BMC (g).

Figure 4. Joint multilevel linear spline: conditional change in length as predictors of 6 year whole body BMC (g).

Figure 5. (A) Mean distance and velocity curves for length back-transformed from the square root scale. Age at peak velocity is marked. (B) SITAR-predicted length growth curves corresponding to BMC z-scores of −2, 0 and +2, respectively.

Figure 6. Growth mixture model.

Figure 7. (A) Growth mixture model: average estimated length LMS z-scores by class and (B) Growth Mixture Model: Differences in BMC (g) from ‘stable’ group.

Table 2. Guidelines for choice of statistical method to characterise growth.

Question	Data characteristics	Approach
How does growth relate to a later outcome?	Measures taken at same time for everyone. Little/no missing data. Fairly small number of measures. Outcome can be continuous or categorical.	Residual growth model Advantages: simple to implement and interpret. Disadvantages: does not describe pattern of growth; can only relate outcome to growth at ages measured; difficult to use where there are large amounts of missing data.
What is the pattern of growth, how does it vary between individuals, how does it relate to a later outcome?	Measures do not need to be at same times for everyone, nor does everyone need to have the same number of measures. Measures not too close together. Outcome can be continuous or categorical.	Two-stage multilevel linear spline model Advantages: fairly simple to interpret, pattern of growth modelled in an intuitive way. Can be moderately simple to implement. Disadvantages: Assumes periods of linear growth; biased associations with outcome unless all random effects included in model; autocorrelation may be a problem (if measures close together). If pattern of growth complex, model convergence may be problematic.
What is the pattern of growth, how does it vary between individuals, how does it relate to a later outcome?	As above, but with continuous (Normally distributed) outcome.	Joint multilevel linear spline model Advantages: Interpretable results for both pattern of growth and association with outcome. Unbiased (providing model correctly specified). Disadvantages: Can be complex to fit, and model convergence may be problematic.
How does growth vary with chronological and developmental age? How does this relate to a later outcome?	As for two-stage multilevel linear spline models.	SITAR Advantages: Biological interpretation to the association between growth and later outcome. Fewer parameters than linear spline model if pattern of growth is complex. Disadvantages: Biased associations with outcome unless all random effects included. Pattern of growth not easy to interpret. Random effects may be highly correlated. More complex to fit than linear models.
Are there sub-groups of the population with different growth patterns? Do these groups have different outcomes?	As above.	Growth Mixture Model Advantages: Spline model more flexible than linear spline model, may be more realistic pattern of growth. Identifies latent sub-groups (all above methods assume there are no sub-groups). Disadvantages: Fairly complex to fit. Many parameters, so some assumptions need to be made. Pattern of growth may not be easily interpretable (graphs will be needed). Association is with group membership—can’t identify associations with specific periods of growth.