R/builtin_references.R
builtin_references.RdA data frame containing the age-dependent distribution of the D-score for children aged 0-5 years. The distribution is modelled after the LMS distribution (Cole & Green, 1992) or BCT model (Stasinopoulos & Rigby, 2022) and is equal for both boys and girls. The LMS/BCT values can be used to graph reference charts and to calculate age-conditional Z-scores, also known as the Development-for-Age Z-score (DAZ).
builtin_referencesA data.frame with the following variables:
| Name | Label |
population | Name of the reference population |
key | D-score key, e.g., "dutch", "gcdg" or "gsed" |
distribution | Distribution family: "LMS" or "BCT" |
age | Decimal age in years |
mu | M-curve, median D-score, P50 |
sigma | S-curve, spread expressed as coefficient of variation |
nu | L-curve, the lambda coefficient of the LMS/BCT model for skewness |
tau | Kurtosis parameter in the BCT model |
P3 | P3 percentile |
P10 | P10 percentile |
P25 | P25 percentile |
P50 | P50 percentile |
P75 | P75 percentile |
P90 | P90 percentile |
P97 | P97 percentile |
SDM2 | -2SD centile |
SDM1 | -1SD centile |
SD0 | 0SD centile, median |
SDP1 | +1SD centile |
SDP2 | +2SD centile |
Here are more details on the reference population:
The "dutch" references were calculated from the SMOCC data, and cover
age range 0-2.5 years (van Buuren, 2014).
The "gcdg" references were calculated from the 15 cohorts of the
GCDG-study, and cover age range 0-5 years (Weber, 2019).
The "phase1" references were calculated from the GSED Phase 1 validation
data (GSED-BGD, GSED-PAK, GSED-TZA) cover age range 2w-3.5 years. The
age range 3.5-5 yrs is linearly extrapolated and is only indicative.
The "preliminary_standards" were calculated from the GSED Phase 1 validation
data (GSED-BGD, GSED-PAK, GSED-TZA) using a subset of children with
covariate indicating healthy development.
The "who_descriptive" references were calculated from the GSED Phase 1 & 2
validation data (GSED-BGD, GSED-BRA, GSED_CHN, GSED-CIV, GSED-NLD, GSED-PAK,
GSED-TZA) cover age range 2w-3.5 years. The age range 3.5-5 yrs is linearly
extrapolated and is only indicative. The source code for the relevant
calculations can be found in https://github.com/D-score/gsedscripts/blob/main/inst/scripts/phase2/models/purify.R
and https://github.com/D-score/gsedscripts/blob/main/inst/scripts/phase2/models/fit_core_model.R.
Cole TJ, Green PJ (1992). Smoothing reference centile curves: The LMS method and penalized likelihood. Statistics in Medicine, 11(10), 1305-1319.
Van Buuren S (2014). Growth charts of human development. Stat Methods Med Res, 23(4), 346-368. https://stefvanbuuren.name/publication/van-buuren-2014-gc/
Weber AM, Rubio-Codina M, Walker SP, van Buuren S, Eekhout I, Grantham-McGregor S, Caridad Araujo M, Chang SM, Fernald LCH, Hamadani JD, Hanlon A, Karam SM, Lozoff B, Ratsifandrihamanana L, Richter L, Black MM (2019). The D-score: a metric for interpreting the early development of infants and toddlers across global settings. BMJ Global Health, BMJ Global Health 4: e001724. https://gh.bmj.com/content/bmjgh/4/6/e001724.full.pdf
van Buuren S, Eekhout I, McCray G, Lancaster GA, Waldman MR, McCoy DC, Gladstone M, Cavallera, V, Dua T, Black MM, GSED Team (2025). Enhancing comparability in early child development assessment with the D-score. International Journal of Behavioral Development, 49(4), 348-364, https://doi.org/10.1177/01650254241294033
Stasinopoulos M, Rigby R (2022). gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape, R package version 6.0-3, https://CRAN.R-project.org/package=gamlss.dist
# get an overview of available references per key
table(builtin_references$population, builtin_references$key)
#>
#> 293_0 dutch gcdg gsed1912 gsed2212 gsed2406 gsed2510
#> dutch 0 144 0 0 185 185 185
#> gcdg 0 0 121 121 0 0 0
#> phase1 186 0 0 0 186 186 0
#> preliminary_standards 0 0 0 0 0 186 186
#> who_descriptive 0 0 0 0 0 0 188