bmidat: Longitudinal study of childhood growth data
In ytalau/eiv: The Study of Measurement Errors in Variables

Description Usage Format Details Source Examples

The bmidat data frame has 3537 rows and 6 columns.

bmidat

This data frame contains the following columns:

id: identifer of child
time: an indicator of age intervals (1 = age 2–7 for childhood BMI z-scores and age 12–17 for obesity in adolescence, 2 = age 7–12 for preadolescence BMI z-scores and age 20–29 for obesity in adulthood)
gender: an indicator of gender (1 = male, 0 = female)
age: child's age
bmi_z: BMI z-score
obes: an indicator of obesity (1 = obese, 0 = none)

Data contains body mass index (BMI) z-scores for 486 subjects from their outpatient visits. Subjects were categorized as obese or non-obese depending on their average BMI z-scores. This dataset can be used to predict obesity in adolescence (age 12–17) and obesity in adulthood (age 20-29) using the childhood (age 2–7) BMI z-scores and preadolescence (age 7–12) BMI z-scores, respectively. Note that the true long term BMI z-scores cannot be measured due to finite measurement and thus they are subject to measurement error.

Wang, C. Y. and Pepe, M. S. (2000). Expected estimating equations to accommodate covariate measurement error. JRSSB, 62, 509-524.

data(bmidata)
## Not run: 
library(data.table)
library(geepack)
dat_cal <- bmidat[order(id, age)]
dat_cal <- dat_cal[, `:=`(
    W_star = bmi_z - shift(bmi_z, n = 1, fill = 0, type = "lag"),
    age_diff = age - shift(age, n = 1, fill = 0, type = "lag")),
    by = .(id, time)
    ][, .(age_diff = tail(age_diff, .N - 1),
          W_star = tail(W_star, .N - 1)), by = .(id, time)]

dat_cal <- dat_cal[, `:=`(W_star2 := W_star * shift(W_star, n = 1, fill = NA,
                                                    type = "lag"),
                          t1 = shift(age_diff, n = 1, fill = NA,
                                     type = "lag"), t2 = age_diff,
                          t3 = shift(age_diff, n = 1, fill = NA,
                                     type = "lag") + age_diff),
                   by = .(id, time)]

dat_cal <- dat_cal[!is.na(W_star2), ]
mome <- function(theta, W = dat_cal$W_star,
                 t = dat_cal$age_diff,
                 W2 = dat_cal[!is.na(W_star2), W_star2],
                 t2 = unique(dat_cal[!is.na(W_star2), .(t1, t2, t3)])) {
    sigma <- theta[1]
    rho <- theta[2]
    mo1 <- sum(W^2 - 2 * sigma^2 * (1 - rho^t))
    mo2 <- sum(W2 - sigma^2 * (rho^t2[, 2] - 1 - rho^t2[, 3] + rho^t2[, 1]))
    c(mo1, mo2)
}

res <- nleqslv::nleqslv(c(0.5, 0.5), fn = mome)

bmidat <- bmidat[, me_sd := sqrt(res$x[1] *
                                     sum(res$x[2]^abs(outer(age, age, FUN = "-"))))/.N,
                 by = .(id, time)]
me_sd2 <- round(mean(bmidat$me_sd), 3)^2

## fitting models

bmidat <- unique(bmidat[, W := mean(bmi_z), by = .(id, time)
                        ][, .(id, time, obes, W, me_sd)])

init <- geepack::geeglm(obes ~ time + time:W -1,
                        family = binomial, data = bmidat,
                        corstr = "ar1", id = id)

cres <- eiv::eivgmm(obes ~ time + time:W - 1,
                    data = bmidat, me.var = c("time1:W", "time2:W"),
                    mcov = list(matrix(c(me_sd2, 0, 0, 0), 2, 2),
                                matrix(c(0, 0, 0, me_sd2), 2, 2)),
                    time.var = "time", id.var = "id",
                    start = init$coefficients,
                    modify_inv = 1,
                    finsam_cor = 0)
summary(cres)

## End(Not run)