Getting started

Overview

The D-score is a one-number summary measure of early child development. The D-score has a fixed unit. In principle, we may use the D-score to answer questions on the individual, group and population level, but be aware that no instruments have yet been validated for individual application. For more background, see the introductory booklet D-score: Turning milestones into measurement.

This vignette shows how to estimate the D-score and the D-score age-adjusted Z-score (DAZ) from child data on developmental milestones. The vignette covers some typical actions needed when estimating the D-score and DAZ:

1. Identify whether the dscore package covers your measurement instrument;
2. Map your variable names to the GSED 9-position schema;
3. Calculate D-score and DAZ;
4. Summarise your results.

Is your measurement instrument covered?

The dscore package covers a subset of all possible assessment instruments. Moreover, it may have a restricted age range for a given instrument. Your first task is to evaluate whether the current dscore package can convert your measurements into D-scores.

A 2017 Worldbank report (Fernald et al. 2017) identified 147 instruments for assessing the development of children aged 0-8 years. Well-known examples include the Bayley Scales for Infant and Toddler Development and the Ages & Stages Questionnaires. The D-score is defined by and calculated from, subsets of milestones from such instruments.

Assessment instruments connect to the D-score through a measurement model, the Rasch model. We use the term key to refer to a particular set of parameters (difficulty estimates) of a fitted Rasch model. The key defines how 0/1 milestone scores are translated into a D-score, as thus can be seen as part of the scoring system.

The dscore package contains a generic algorithm that takes:

1. the 0/1 scores on a set of milestones for a given child;
2. the age(s) of the child at which the test is administered;
3. a specification of the key;

and then calculates the D-score and its Standard Error of Measurement (SEM) for the child at each age.

The dscore package currently supports the following keys (in historic order):

Different keys lead to (slightly) different D-scores. We may only compare D-scores that are calculated under the same key. Our advice to set the key is:

• For new data, use the generic key = "gsed". This choice will automatically fetch the latest GSED key, which is key = "gsed2510";
• Key gsed2406 has a wider coverage, Use that if your instrument is not covered by gsed2510.
• Use older keys dutch, gcdg or gsed1912 to regenerate old results. These are unlikely to be useful for new data;
• Superseded keys are: gsed2212, gsed2206, gsed2208, lf2206, sf2006, 294_0 and 293_0. Use for research purposes only.

The table given below displays the number of items per instrument for various keys. If the entry is blank, the key does not cover the instrument.

You can’t compute a D-score if your instrument isn’t supported. If it does measure child development, we can often extend the key to include it. This requires a one-time effort—mapping your items to the milestone schema and estimating difficulty parameters. Once added, the key is reusable, and you’ll be able to compute valid D-scores for that instrument. The table shows two such extensions: one for Mullen and one for ECDI.

The designs of the original cohorts determine the age coverage for each instrument. The figure above indicates the age range currently supported by the "gsed2406" key. Some instruments contain many items for the first two years (e.g., by1, dmc), whereas others cover primarily upper ages (e.g., tep, ecd).

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.

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"

You may decompose item names into components as follows:

decompose_itemnames(c("by3cgd018", "denfmd014"))

##   instrument domain mode number
## 1        by3     cg    d    018
## 2        den     fm    d    014

This function returns a data.frame with four character vectors for further processing.

The dscore package recognises 3843 item names. The expression get_itemnames() returns a (long) vector of all known item names. Let us study the table of instruments by domain:

items <- get_itemnames()
din <- decompose_itemnames(items) |>
  dplyr::filter(!instrument %in% c("gsd", "gpa", "gto", "rap"))
knitr::kable(with(din, table(instrument, domain)), format = "html") |>
  kableExtra::column_spec(1, monospace = TRUE)

We obtain the first three item names and labels from the mdt domain gm as

items <- head(get_itemnames(instrument = "mdt", domain = "gm"), 3)
get_labels(items)

##                                          mdtgmd001 
##                             "Lifts chin off floor" 
##                                          mdtgmd002 
## "Prone (on tummy), can lift head up to 90 degrees" 
##                                          mdtgmd003 
##             "Holds head upright for a few seconds"

In practice, you need to spend some time to figure out how item names in your data map to those in the dscore package. Once you’ve completed this mapping, rename the items into the GSED 9-position schema. For example, suppose that your first three gross motor MDAT items are called mot1, mot2, and mot3.

data <- data.frame(
  id = c(1, 1, 2),
  age = c(1, 1.6, 0.9),
  mot1 = c(1, NA, NA),
  mot2 = c(0, 1, 1),
  mot3 = c(NA, 0, 1)
)
data

##   id age mot1 mot2 mot3
## 1  1 1.0    1    0   NA
## 2  1 1.6   NA    1    0
## 3  2 0.9   NA    1    1

Renaming is easy to do by changing the names attribute.

old_names <- names(data)[3:5]
new_names <- get_itemnames(instrument = "mdt", domain = "gm")[1:3]
names(data)[3:5] <- new_names
data

##   id age mdtgmd001 mdtgmd002 mdtgmd003
## 1  1 1.0         1         0        NA
## 2  1 1.6        NA         1         0
## 3  2 0.9        NA         1         1

There may be different versions and revision of the same instrument. Therefore, carefully check whether the item labels match up with the labels in version of the instrument that you administered.

The dscore package assumes that response to milestones are dichotomous (1 = PASS, 0 = FAIL). If necessary, recode your data to match these response categories.

Calculate the D-score and DAZ

Once the data are in proper shape, calculation of the D-score and DAZ is easy.

The milestones dataset in the dscore package contains responses of 27 preterm children measured at various age between birth and 2.5 years on the Dutch Development Instrument (ddi). The dataset looks like:

head(milestones[, c(1, 3, 4, 9:14)])

##    id       age    sex ddigmd053 ddigmd056 ddicmm030 ddifmd002 ddifmd003
## 1 111 0.4873374   male         1         1         1         1         1
## 2 111 0.6570842   male        NA        NA        NA        NA         1
## 3 111 1.1800137   male        NA        NA        NA        NA        NA
## 4 111 1.9055441   male        NA        NA        NA        NA        NA
## 5 177 0.5503080 female         1         1         1         1         1
## 6 177 0.7665982 female        NA        NA        NA        NA         1
##   ddifmm004
## 1         0
## 2         1
## 3        NA
## 4        NA
## 5         1
## 6         1

Each row corresponds to a visit. Most children have three or four visits. Columns starting with ddi hold the responses on DDI-items. A 1 means a PASS, a 0 means a FAIL, and NA means that the item was not administered.

The milestones dataset has properly named columns that identify each item. Calculating the D-score and DAZ is then done by:

ds <- dscore(milestones, population = "dutch", key = "dutch")
dim(ds)

## [1] 100   6

Where ds is a data.frame with the same number of rows as the input data. The first six rows are

head(ds)

##        a  n      p     d      sem    daz
## 1 0.4873 18 0.8333 29.11 1.837552 -1.837
## 2 0.6571 18 0.7222 34.18 1.478156 -1.991
## 3 1.1800 19 0.9474 51.82 2.401714 -0.202
## 4 1.9055 15 0.8667 62.95 1.794096  0.075
## 5 0.5503 18 0.8333 29.41 1.861036 -2.421
## 6 0.7666 18 0.8333 36.76 1.679393 -2.125

In addition, the package calculate the Development-for-Age Z-score (DAZ), which gives the position of the child relative to age peers.

The table below provides the interpretation of the output:

Summarise D-score and DAZ

Combine the milestones data and the result by

md <- cbind(milestones, ds)

We may plot the 27 individual developmental curves by

library(ggplot2)
library(dplyr)

# Prepare the reference ribbon data: sort by age and convert months → years
r <- builtin_references %>%
  filter(population == "dutch" & key == "dutch") %>%
  transmute(age_years = age, SDM2, SD0, SDP2) %>%
  arrange(age_years)

ggplot(md, aes(x = a, y = d, group = id, colour = sex)) +
  theme_light() +
  theme(
    legend.position = c(0.85, 0.15),
    legend.background = element_blank(),
    legend.key = element_blank()
  ) +
  geom_ribbon(
    data = r,
    inherit.aes = FALSE,
    aes(x = age_years, ymin = SDM2, ymax = SDP2),
    fill = "green",
    alpha = 0.1
  ) +
  geom_line(
    data = r,
    inherit.aes = FALSE,
    aes(x = age_years, y = SDM2),
    linewidth = 0.3,
    alpha = 0.6,
    colour = "green"
  ) +
  geom_line(
    data = r,
    inherit.aes = FALSE,
    aes(x = age_years, y = SDP2),
    linewidth = 0.3,
    alpha = 0.6,
    colour = "green"
  ) +
  geom_line(
    data = r,
    inherit.aes = FALSE,
    aes(x = age_years, y = SD0),
    linewidth = 0.5,
    alpha = 0.8,
    colour = "green"
  ) +
  coord_cartesian(xlim = c(0, 2.5)) +
  ylab(expression(italic(D) * "-score")) +
  xlab("Age (years)") +
  scale_color_brewer(palette = "Set1") +
  geom_line(linewidth = 0.1) +
  geom_point(size = 1)

Note that similarity of these curves to growth curves for body height and weight.

The DAZ is an age-standardized D-score with a standard normal distribution with mean 0 and variance 1. We plot the individual DAZ curves relative to the Dutch references by

ggplot(md, aes(x = a, y = daz, group = id, color = factor(sex))) +
  theme_light() +
  theme(legend.position = c(.85, .15)) +
  theme(legend.background = element_blank()) +
  theme(legend.key = element_blank()) +
  scale_color_brewer(palette = "Set1") +
  annotate(
    "rect",
    xmin = -Inf,
    xmax = Inf,
    ymin = -2,
    ymax = 2,
    alpha = 0.1,
    fill = "green"
  ) +
  coord_cartesian(
    xlim = c(0, 2.5),
    ylim = c(-4, 4)
  ) +
  geom_line(lwd = 0.1) +
  geom_point(size = 1) +
  xlab("Age (in years)") +
  ylab("DAZ")

Note that the D-scores and DAZ are a little lower than average. The explanation here is that these all children are born preterm. We can account for prematurity by correcting for gestational age.

The distributions of DAZ for boys and girls show that a large overlap:

ggplot(md) +
  theme_light() +
  scale_fill_brewer(palette = "Set1") +
  geom_density(
    aes(x = daz, group = sex, fill = sex),
    alpha = 0.4,
    adjust = 1.5,
    color = "transparent"
  ) +
  xlab("DAZ")

Under the assumption of independence, we may test whether sex differences are constant in age by a linear regression that includes the interaction between age and sex:

summary(lm(daz ~ age * sex, data = md))

## 
## Call:
## lm(formula = daz ~ age * sex, data = md)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.44533 -0.76002 -0.09713  0.65028  3.11002 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.13455    0.32499  -6.568 2.62e-09 ***
## age          1.15137    0.27197   4.233 5.27e-05 ***
## sexmale      0.07164    0.45039   0.159    0.874    
## age:sexmale -0.12750    0.36137  -0.353    0.725    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.137 on 96 degrees of freedom
## Multiple R-squared:  0.2752, Adjusted R-squared:  0.2525 
## F-statistic: 12.15 on 3 and 96 DF,  p-value: 8.28e-07

This group of children born very preterm starts around -2.5 SD, followed by a catch-up in child development of approximately 1.0 SD per year. The size of the catch-up is equal for boys and girls.

We may account for the clustering effect by including random intercept and age effects, and rerun as

library(Matrix)
library(lme4, quiet = TRUE)
lmer(daz ~ 1 + age + sex + sex * age + (1 + age | id), data = md)

## Linear mixed model fit by REML ['lmerMod']
## Formula: daz ~ 1 + age + sex + sex * age + (1 + age | id)
##    Data: md
## REML criterion at convergence: 304.3713
## Random effects:
##  Groups   Name        Std.Dev. Corr 
##  id       (Intercept) 0.9861        
##           age         0.6386   -0.85
##  Residual             0.9265        
## Number of obs: 100, groups:  id, 27
## Fixed Effects:
## (Intercept)          age      sexmale  age:sexmale  
##     -2.1684       1.2067       0.1080      -0.1719

This analysis yields the same substantive conclusions as before.