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Sample size and sample composition for constructing growth reference centiles.

ABSTRACT: Growth reference centile charts are widely used in child health to assess weight, height and other age-varying measurements. The centiles are easy to construct from reference data, using the LMS method or GAMLSS (Generalised Additive Models for Location Scale and Shape). However, there is as yet no clear guidance on how to design such studies, and in particular how many reference data to collect, and this has led to study sizes varying widely. The paper aims to provide a theoretical framework for optimally designing growth reference studies based on cross-sectional data. Centiles for weight, height, body mass index and head circumference, in 6878 boys aged 0-21 years from the Fourth Dutch Growth Study, were fitted using GAMLSS. The effect on precision of varying the sample size and the distribution of measurement ages (sample composition) was explored by fitting a series of GAMLSS models to simulated data. Sample composition was defined as uniform on the age^λ scale, where λ was chosen to give constant precision across the age range. Precision was measured on the z-score scale, and was the same for all four measurements, with a standard error of 0.041 z-score units for the median and 0.066 for the 2nd and 98th centiles. Compared to a naïve calculation, the process of smoothing the centiles increased the notional sample size two- to threefold by 'borrowing strength'. The sample composition for estimating the median curve was optimal for λ=0.4, reflecting considerable over-sampling of infants compared to children. However, for the 2nd and 98th centiles, λ=0.75 was optimal, with less infant over-sampling. The conclusion is that both sample size and sample composition need to be optimised. The paper provides practical advice on design, and concludes that optimally designed studies need 7000-25,000 subjects per sex.

SUBMITTER: Cole TJ

PROVIDER: S-EPMC8008444 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BACKGROUND: Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (lambda) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of lambda-Jensen's Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of lambda due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of lambda. METHODOLOGY/PRINCIPAL FINDINGS: Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating lambda for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of lambda with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography. CONCLUSIONS/SIGNIFICANCE: We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities.

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Sample size and sample composition for constructing growth reference centiles.

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