Calculate the standard deviation score (SDS) of a pubertal stage

Calculates the SDS for a pubertal stage measurement, given the patient's age and observed stage, by interpolating between the surrounding reference percentiles.

Usage

calculate_sds(age, stage, type, ref = tanner::nl1997)

Arguments

age: Vector of patient ages. The length of age determines the length of the return value (see Value below).
stage: Vector of patient stages, the same length as age (one stage per age; not recycled). For type = "tv" this is the raw testicular volume in **ml**, as read off a Prader orchidometer or otherwise measured; it need not be one of the 12 Prader bead volumes (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 25) — any intermediate value (e.g. 11 or 16 ml) is bracketed between the surrounding reference percentiles. For all other types, stage is the integer Tanner stage (1-5 for "gen", "phb", "bre", "phg"; 1-2 for "men"). A stage shorter or longer than age is not supported: it is silently truncated or padded rather than recycled (e.g. a length-1 stage does not apply to every element of age) and can also produce NAs, a warning, or a "subscript out of bounds" error depending on type – do not rely on any of these behaviors, always pass stage the same length as age.
type: Reference type: one of "gen", "phb", "tv", "bre", "phg" or "men".
ref: Reference data, as produced by nl1997.

Value

A numeric vector of SDS values, the same length as age (one value per element of age).

Details

Implements the mid-P value method of van Buuren & Ooms (2009), equation (6): treating the observed stage c as a coarsened version of a continuous latent variable, uniformly distributed within the stage's probability interval [P(Y<c|X), P(Y<c+1|X)). The mid-P value pi_c = P(Y<c|X) + P(Y=c|X)/2 is the mean of that latent variable, and Z = qnorm(1 - pi_c) = qnorm(1 - (P(Y>=c|X) + P(Y>=c+1|X))/2) converts it to a Z-score/SDS. This is why the SDS averages the surrounding-stage percentiles rather than looking up a single stage's percentile directly: the averaging is the mid-P value itself, not an ad hoc smoothing step. The same formula applies to tv's 12 Prader bead categories, treating each raw ml reading as belonging to the bead-category interval it falls into (see below).

References

van Buuren S, Ooms JCL (2009). Stage line diagram: An age-conditional reference diagram for tracking development. Statistics in Medicine, 28(11), 1569-1579. doi:10.1002/sim.3567

Examples

# a single boy, genital stage 3 at age 12
calculate_sds(age = 12, stage = 3, type = "gen")
#> [1] 1.11302

# a boy's genital-stage trajectory over three visits
calculate_sds(age = c(10, 12, 14), stage = c(1, 3, 4), type = "gen")
#> [1] -0.3655512  1.1130196  0.3941098

# testicular volume in ml, interpolated between Prader beads
calculate_sds(age = 13, stage = 11, type = "tv")
#> [1] 0.4806011