Scoring GSED

D-score and DAZ

Suppose you have administered GSED SF, GSED LF (World Health Organization (WHO) 2023; McCray et al. 2023) or GSED HF to one or more children. The next step is calculating each child’s developmental score (D-score) and age-adjusted equivalent (DAZ). This step is known as scoring. The present section provides recipes for calculating the D-score and DAZ. We may pick one of the following two methods:

  1. Online calculator. The online app D-score calculator is a convenient option for users not familiar with R. The app contains online documentation and instructions and will not be further discussed here.
  2. R package dscore. The R package dscore at https://CRAN.R-project.org/package=dscore is a flexible option with all the tools needed to calculate the D-score. It is an excellent choice for users familiar with R and users who like to incorporate D-score calculations into a workflow.

Preliminaries

Install the dscore package

The dscore package contains tools to

The required input consists of item level responses on milestones collected using instruments for measuring child development, including the GSED LF, GSED SF and GSED HF.

There are two versions of the dscore package. For daily use, we recommend the curated and published version on CRAN. In R, install the dscore package as

install.packages("dscore")

In some cases, you might need a more recent version that includes extensions and bug fixes not yet available on CRAN. You can install the development version from GitHub by:

install.packages("remotes")
remotes::install_github("d-score/dscore")

The development version requires a local C++ compiler for building the package from source.

GSED 9-position item names

The dscore() function accepts item names that follow the GSED 9-position schema. A name with a length of nine characters identifies every milestone. The following table shows the construction of names.

Position Description Example
1-3 instrument by3
4-5 developmental domain cg
6 administration mode d
7-9 item number 018

Thus, item by3cgd018 refers to the 18th item in the cognitive scale of the Bayley-III. The label of the item can be obtained by

library(dscore)
get_labels("by3cgd018")
##           by3cgd018 
## "Inspects own hand"

The dscore package maintains a list of items names.

Response data format

Rows: One measurement, i.e., one test administration for a child at a given age, occupies a row in the data set. Thus, if a child is measured three times at different ages, there will be three rows for that child in the dataset.

Columns: There should be at least two columns in the data set:

The dataset may contain additional columns, e.g., the child number or health information. These are ignored by the D-score calculation.

The most important steps is preparing the data for the D-score calculations are:

GSED Instruments

The table below lists the five available GSED instruments:

Instrument Year Code Domains Mode Range Status
GSED SF 2023 gs1 cg|lg|li|mo|se c 001-139 Active
GSED LF 2023 gl1 gm|lg|fm d 001-049|052|054 Active
GSED HH 2023 gh1 cg|lg|li|mo|se c 001-055 Active
GSED SF 2020 gpa any c 001-139 Retired
GSED LF 2020 gto gm|lg|fm d 001-049|052|054 Retired

Select the section corresponding to your instrument for further instructions.

::: {.panel-tabset group = “GSED”}

GSED SF

The GSED Short Form (GSED SF) is a caregiver-reported instrument containing 139 items. It has instrument code gs1.

Check

Obtain the full list of item name for as

instrument <- "gs1"
items <- get_itemnames(instrument = instrument, order = "indm")
length(items)
## [1] 139
head(items)
## [1] "gs1sec001" "gs1moc002" "gs1sec003" "gs1lgc004" "gs1moc005" "gs1cgc006"

The order argument is needed to sort items according to sequence number 1 to 139. Check that you have the correct version by comparing the labels of the first few items as:

labels <- get_labels(items)
head(cbind(items, substr(labels, 1, 50)))
##           items                                                           
## gs1sec001 "gs1sec001" "SF001 Does your child smile?"                      
## gs1moc002 "gs1moc002" "SF002 When lying on his/her back, does your child "
## gs1sec003 "gs1sec003" "SF003 Does your child look at your face when you s"
## gs1lgc004 "gs1lgc004" "SF004 Does your child cry when he/she is hungry, w"
## gs1moc005 "gs1moc005" "SF005 Does your child grasp your finger if you tou"
## gs1cgc006 "gs1cgc006" "SF006 Does your child look at and focus on objects"

Renaming example

Suppose that you stored your data with items names sf001 to sf139. For example,

sf <- dscore::sample_sf
head(sf[, c(1:2, 101:105)])
##   subjid agedays sf099 sf100 sf101 sf102 sf103
## 1      1     811     1     1     1     1     1
## 2      2     898     1     1     1     1     1
## 3      3     203    NA    NA    NA    NA    NA
## 4      4     966    NA    NA    NA     1    NA
## 5      8     770     1     1     1     0     1
## 6      9     306    NA    NA    NA    NA    NA

Make sure that the items are in the correct order. Rename the columns with gsed 9-position item names.

colnames(sf)[3:141] <- items
head(sf[, c(1:2, 101:105)])
##   subjid agedays gs1lgc099 gs1lgc100 gs1moc101 gs1sec102 gs1lic103
## 1      1     811         1         1         1         1         1
## 2      2     898         1         1         1         1         1
## 3      3     203        NA        NA        NA        NA        NA
## 4      4     966        NA        NA        NA         1        NA
## 5      8     770         1         1         1         0         1
## 6      9     306        NA        NA        NA        NA        NA

The data in sf are now ready for the dscore() function.

Calculate D-score

Once the data are in proper shape, calculation of the D-score is straightforward. The sf dataset has properly named columns that identify each item.

results <- dscore(sf, xname = "agedays", xunit = "days")
head(results)
##        a  n      p     d      sem    daz
## 1 2.2204 29 0.7586 67.67 1.658818 -0.043
## 2 2.4586 39 0.6923 69.05 1.411819 -0.352
## 3 0.5558 48 0.6667 38.97 1.649425  1.058
## 4 2.6448 36 0.7500 74.47 1.471799  0.624
## 5 2.1081 50 0.5000 66.45 1.244876 -0.033
## 6 0.8378 48 0.7083 42.18 1.699459 -0.839

The table below provides the interpretation of the output:

Name Interpretation
a Decimal age in years
n Number of items used to calculate the D-score
p Proportion of passed milestones
d D-score (posterior mean)
sem Standard error of measurement (posterior standard deviation)
daz D-score corrected for age

The number of rows of result is equal to the number of rows of sf. We save the result for later processing.

sf2 <- data.frame(sf, results)

It is possible to calculate D-score for item subsets by setting the items argument. We do not advertise this option for practical application, but suppose we are interested in the D-score based on items from gs1 and gl1 for domains mo or gm (motor) only. The “motor” D-score can be calculated as follows:

items_motor <- get_itemnames(
  instrument = c("gs1", "gl1"),
  domain = c("mo", "gm")
)
results <- dscore(sf, items = items_motor, xname = "agedays", xunit = "days")
head(results)
##        a  n      p     d      sem    daz
## 1 2.2204  6 0.8333 67.40 3.391252 -0.116
## 2 2.4586  8 0.7500 69.16 3.049288 -0.324
## 3 0.5558 30 0.7333 39.89 1.946849  1.347
## 4 2.6448  5 0.8000 75.78 3.154717  0.981
## 5 2.1081 10 0.7000 69.52 2.808620  0.814
## 6 0.8378 31 0.7419 42.35 1.983714 -0.790

GSED LF

The GSED Long Form (GSED LF) instrument is a directly-observed instrument containing 155 items with instrument code gl1.

Check

Obtain the full list of item name for as

instrument <- "gl1"
items <- get_itemnames(instrument = instrument)
length(items)
## [1] 155
head(items)
## [1] "gl1fmd001" "gl1fmd002" "gl1fmd003" "gl1fmd004" "gl1fmd005" "gl1fmd006"

Reorder item names so that they corresponds to streams A, B and C, respectively.

items <- items[c(55:155, 1:54)]
head(items)
## [1] "gl1gmd001" "gl1gmd002" "gl1gmd003" "gl1gmd004" "gl1gmd005" "gl1gmd006"

Check that you have the correct version by comparing the labels of the first few items as:

labels <- get_labels(items)
head(cbind(items, substr(labels, 1, 50)))
##           items                                                           
## gl1gmd001 "gl1gmd001" "A1  Moves body in reaction to caregiver"           
## gl1gmd002 "gl1gmd002" "A2  Moves body, kicking legs and moving arms equal"
## gl1gmd003 "gl1gmd003" "A3  Pulls to sit - no head lag"                    
## gl1gmd004 "gl1gmd004" "A4  Lifts head in prone 45 degrees (2X)"           
## gl1gmd005 "gl1gmd005" "A5  Lifts head, shoulders, chest when prone (2X)"  
## gl1gmd006 "gl1gmd006" "A6  Puts hands together in front of face"

Renaming example

Suppose that you stored your data with items names lf001 to lf155. For example,

lf <- dscore::sample_lf
head(lf[, c(1:2, 60:64)])
##   subjid agedays lf058 lf059 lf060 lf061 lf062
## 1      1     811    NA    NA    NA    NA    NA
## 2      2     898    NA    NA    NA    NA    NA
## 3      3     203     0     0     0    NA    NA
## 4      4     966    NA    NA    NA    NA    NA
## 5      8     770     0     0     0     0     0
## 6      9     306     1     1     0     1     0

Make sure that the items are in the correct order. Rename the columns with gsed 9-position item names.

colnames(lf)[3:157] <- items
head(lf[, c(1:2, 60:64)])
##   subjid agedays gl1lgd009 gl1lgd010 gl1lgd011 gl1lgd012 gl1lgd013
## 1      1     811        NA        NA        NA        NA        NA
## 2      2     898        NA        NA        NA        NA        NA
## 3      3     203         0         0         0        NA        NA
## 4      4     966        NA        NA        NA        NA        NA
## 5      8     770         0         0         0         0         0
## 6      9     306         1         1         0         1         0

The data in lf are now ready for the dscore() function.

Calculate D-score

Once the data are in proper shape, calculation of the D-score is straightforward. The lf dataset has properly named columns that identify each item.

results <- dscore(lf, xname = "agedays", xunit = "days")
head(results)
##        a  n      p     d      sem    daz
## 1 2.2204 42 0.5476 66.91 1.328849 -0.246
## 2 2.4586 49 0.6122 70.69 1.239337  0.082
## 3 0.5558 31 0.5484 34.27 1.661074 -0.397
## 4 2.6448 52 0.5000 70.11 1.165718 -0.529
## 5 2.1081 53 0.1509 40.67 1.820166 -4.554
## 6 0.8378 31 0.5806 44.85 1.554783 -0.038

The table below provides the interpretation of the output:

Name Interpretation
a Decimal age in years
n Number of items used to calculate the D-score
p Proportion of passed milestones
d D-score (posterior mean)
sem Standard error of measurement (posterior standard deviation)
daz D-score corrected for age

The number of rows of result is equal to the number of rows of lf. We save the result for later processing.

lf2 <- data.frame(lf, results)

It is possible to calculate D-score for item subsets by setting the items argument. We do not advertise this option for practical application, but suppose we are interested in the D-score based on items from gs1 and gl1 for domains mo or gm (motor) only. The “motor” D-score can be calculated as follows:

items_motor <- get_itemnames(
  instrument = c("gs1", "gl1"),
  domain = c("mo", "gm")
)
results <- dscore(lf, items = items_motor, xname = "agedays", xunit = "days")
head(results)
##        a  n      p     d      sem    daz
## 1 2.2204 12 0.5833 64.88 2.844278 -0.772
## 2 2.4586 17 0.6471 70.62 2.244729  0.063
## 3 0.5558 19 0.6842 36.27 2.010557  0.213
## 4 2.6448 12 0.4167 65.46 2.707788 -1.626
## 5 2.1081 12 0.5000 60.25 2.784830 -1.589
## 6 0.8378 14 0.7143 45.20 2.350039  0.070

GSED HF

The GSED Houshold Form (GSED HF) instrument contains a subset of 55 items from the GSED SF designed to be used for population surveys. It has instrument code gh1.

Check

Obtain the full list of item name for as

instrument <- "gh1"
items <- get_itemnames(instrument = instrument, order = "indm")
length(items)
## [1] 55
head(items)
## [1] "gh1sec001" "gh1sec002" "gh1lgc003" "gh1cgc004" "gh1moc005" "gh1sec006"

The order argument is needed to sort items according to sequence number 1 to 55. Check that you have the correct version by comparing the labels of the first few items as:

labels <- get_labels(items)
head(cbind(items, substr(labels, 1, 50)))
##           items                                                           
## gh1sec001 "gh1sec001" "Does your child smile?"                            
## gh1sec002 "gh1sec002" "Does your child look at your face when you speak t"
## gh1lgc003 "gh1lgc003" "Does your child cry when he/she is hungry, wet, ti"
## gh1cgc004 "gh1cgc004" "Does your child look at and focus on objects in fr"
## gh1moc005 "gh1moc005" "Does your child bring his/her hand to his/her mout"
## gh1sec006 "gh1sec006" "Does your child smile when you smile or talk with "

Renaming example

Suppose that you stored your data with items names hf001 to hf055. For example,

hf <- dscore::sample_hf
head(hf[, c(1:2, 30:35)])
##   subjid agedays hf028 hf029 hf030 hf031 hf032 hf033
## 1      1     811    NA    NA    NA    NA    NA    NA
## 2      2     898    NA    NA    NA    NA    NA    NA
## 3      3     203     1     1     0     1     0     0
## 4      4     966    NA    NA    NA    NA    NA    NA
## 5      8     770    NA    NA    NA    NA    NA    NA
## 6      9     306     1     1     1     1     1     1

Make sure that the items are in the correct order. Rename the columns with gsed 9-position item names.

colnames(hf)[3:57] <- items
head(hf[, c(1:2, 30:35)])
##   subjid agedays gh1cgc028 gh1moc029 gh1lic030 gh1moc031 gh1moc032 gh1moc033
## 1      1     811        NA        NA        NA        NA        NA        NA
## 2      2     898        NA        NA        NA        NA        NA        NA
## 3      3     203         1         1         0         1         0         0
## 4      4     966        NA        NA        NA        NA        NA        NA
## 5      8     770        NA        NA        NA        NA        NA        NA
## 6      9     306         1         1         1         1         1         1

The data in hf are now ready for the dscore() function.

Calculate D-score

Once the data are in proper shape, calculation of the D-score is straightforward. The hf dataset has properly named columns that identify each item.

results <- dscore(hf, xname = "agedays", xunit = "days", key = "gsed2406")
head(results)
##        a  n      p     d      sem    daz
## 1 2.2204  8 0.7500 66.46 3.099626 -0.365
## 2 2.4586  8 1.0000 73.55 3.959115  0.862
## 3 0.5558 29 0.6207 37.36 2.190590  0.552
## 4 2.6448  3 1.0000 74.12 4.231796  0.528
## 5 2.1081  7 1.0000 70.72 3.841959  1.149
## 6 0.8378 30 0.7000 42.55 2.182150 -0.731

The key = "gsed2406" argument is needed here because GSED HH is not yet supported by the default key "gsed2510".

The table below provides the interpretation of the output:

Name Interpretation
a Decimal age in years
n Number of items used to calculate the D-score
p Proportion of passed milestones
d D-score (posterior mean)
sem Standard error of measurement (posterior standard deviation)
daz D-score corrected for age

The number of rows of results is equal to the number of rows of hf. We save the result for later processing.

hf2 <- data.frame(hf, results)

It is possible to calculate D-score for item subsets by setting the items argument. We do not advertise this option for practical application, but suppose we are interested in the D-score based on items from gs1, gl1 and gh1 for domains mo or gm (motor) only. The “motor” D-score can be calculated as follows:

items_motor <- get_itemnames(
  instrument = c("gs1", "gl1", "gh1"),
  domain = c("mo", "gm")
)
results <- dscore(
  hf,
  items = items_motor,
  xname = "agedays",
  xunit = "days",
  key = "gsed2406"
)
head(results)
##        a  n      p     d      sem    daz
## 1 2.2204  1 1.0000 69.63 4.504147  0.491
## 2 2.4586  1 1.0000 71.52 4.583980  0.306
## 3 0.5558 18 0.5000 36.65 2.506216  0.331
## 4 2.6448  1 1.0000 72.86 4.642396  0.189
## 5 2.1081  1 1.0000 68.67 4.467450  0.577
## 6 0.8378 18 0.6111 42.29 2.508751 -0.807

:::

Other GSED instruments`

The GSED SF and GSED LF 2020 instruments are included only for backward compatibility.

Phase 1 references and DAZ

We used the GSED Phase I data to calculate age-conditional reference scores for the D-score. The references are based on about 12,000 administration of the GSED SF and GSED LF from Bangladesh, Pakistan and Tanzania. Extract the references as

library(dplyr, warn.conflicts = FALSE, quietly = TRUE)
ref <- builtin_references |>
  filter(population == "phase1") |>
  select(population, age, mu, sigma, nu, tau, SDM2, SD0, SDP2)
head(ref)
##   population    age    mu  sigma     nu    tau     SDM2      SD0     SDP2
## 1     phase1 0.0383 13.68 0.2456 1.1731 15.422 6.042690 13.68707 20.71620
## 2     phase1 0.0575 14.36 0.2324 1.2062 15.540 6.699401 14.36568 21.30880
## 3     phase1 0.0767 15.02 0.2206 1.2375 15.652 7.354450 15.02457 21.88555
## 4     phase1 0.0958 15.68 0.2100 1.2670 15.758 8.014796 15.68368 22.47481
## 5     phase1 0.1150 16.35 0.2005 1.2951 15.860 8.680976 16.35299 23.09062
## 6     phase1 0.1342 17.03 0.1917 1.3218 15.957 9.363085 17.03241 23.72268

The columns mu, sigma, nu and tau are the age-varying parameters of a Box-Cox \(t\) (BCT) distribution.

The script below creates a figure with -2SD, 0SD and +2SD centiles plus 20 D-scores (10 LF and 10 SF) for the lf2 and sf2 data.

library(ggplot2)
library(patchwork)

r <- builtin_references |>
  filter(population == "phase1" & age <= 3.5) |>
  mutate(m = age * 12)

lf2$ins <- "lf"
lf2$m <- lf2$a * 12
sf2$ins <- "sf"
sf2$m <- sf2$a * 12
data <- bind_rows(lf2, sf2)
g1 <- ggplot(data, aes(x = m, y = d, group = ins, color = ins)) +
  theme_light() +
  annotate(
    "polygon",
    x = c(r$age, rev(r$age)),
    y = c(r$SDM2, rev(r$SDP2)),
    alpha = 0.06,
    fill = "#C5EDDE"
  ) +
  annotate("line", x = r$m, y = r$SDM2, lwd = 0.5, color = "#C5EDDE") +
  annotate("line", x = r$m, y = r$SDP2, lwd = 0.5, color = "#C5EDDE") +
  annotate("line", x = r$m, y = r$SD0, lwd = 1, color = "#C5EDDE") +
  scale_x_continuous(
    "Age (in months)",
    limits = c(0, 42),
    breaks = seq(0, 42, 12)
  ) +
  scale_y_continuous(
    expression(paste(italic(D), "-score", sep = "")),
    breaks = seq(0, 80, 20),
    limits = c(0, 90)
  ) +
  geom_point(size = 2) +
  theme(legend.position = "none")
g2 <- ggplot(data, aes(x = m, y = daz, group = ins, color = ins)) +
  theme_light() +
  scale_x_continuous(
    "Age (in months)",
    limits = c(0, 42),
    breaks = seq(0, 42, 12)
  ) +
  scale_y_continuous(
    "DAZ",
    breaks = seq(-4, 4, 2),
    limits = c(-5, 5)
  ) +
  geom_point(size = 2) +
  theme(legend.position = "none")
g1 + g2

References

McCray, G, D McCoy, P Kariger, M Janus, MM Black, SM Chang, F Tofail, et al. 2023. “The Creation of the Global Scales for Early Development (GSED) for Children Aged 0-3 Years: Combining Subject Matter Expert Judgements with Big Data.” BMJ Glob Health 8 (1).
World Health Organization (WHO). 2023. “Global Scales for Early Development (GSED) V1.0: Technical Report.” Geneva: World Health Organization. https://www.who.int/publications/i/item/WHO-MSD-GSED-package-v1.0-2023.1.