I've got repeated measurements data in which patients are measured an irregular amount of times (2 through 6 times per patient) and also with unequally spaced time intervals (some subsequent measures are 6 months apart, some 3 years). Is it possible to model this in a GEE model? For example by specifying a continuous AR1 correlation structure?
I've got some example data:
library(tidyverse)
library(magrittr)
library(geepack)
library(broom)
example_data <- structure(list(pat_id = c(2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4,
4, 7, 7, 8, 8, 8, 13, 13), measurement_number = c(1L, 2L, 3L,
4L, 5L, 6L, 1L, 2L, 1L, 2L, 3L, 4L, 5L, 1L, 2L, 1L, 2L, 3L, 1L,
2L), time = c(0, 0.545, 2.168, 2.68, 3.184, 5.695, 0, 1.892,
0, 0.939, 1.451, 1.955, 4.353, 0, 4.449, 0, 0.465, 4.005, 0,
0.364), age_standardized = c(-0.0941625479695087, -0.0941625479695087,
-0.0941625479695087, -0.0941625479695087, -0.0941625479695087,
-0.0941625479695087, -1.76464003778333, -1.76464003778333, -0.667610044472762,
-0.667610044472762, -0.667610044472762, -0.667610044472762, -0.667610044472762,
0.142696200586183, 0.142696200586183, 0.00556745142236116, 0.00556745142236116,
0.00556745142236116, 0.0554324511182961, 0.0554324511182961),
sex = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("Female",
"Male"), class = "factor"), outcome = c(4241.943359375, 4456.4,
6533.673242397, 7255.561628906, 7594.527875667, 6416.4, 373.782029756049,
614.318359374, 6675.19041238403, 10623.94276368, 10849.01013281,
10627.30859375, 13213, 541.40780090332, 2849.5551411438,
2136.2, 2098.1, 2063.9, 5753.56313232422, 5108.199752386)), class = c("tbl_df",
"tbl", "data.frame"), row.names = c(NA, -20L))
head(example_data)
# A tibble: 6 x 6
pat_id measurement_number time age_standardized sex outcome
<dbl> <int> <dbl> <dbl> <fct> <dbl>
1 2 1 0 -0.0942 Female 4242.
2 2 2 0.545 -0.0942 Female 4456.
3 2 3 2.17 -0.0942 Female 6534.
4 2 4 2.68 -0.0942 Female 7256.
5 2 5 3.18 -0.0942 Female 7595.
6 2 6 5.70 -0.0942 Female 6416.
I actually have also modelled these data with a linear mixed model (using nlme
specifying a continuous AR1), but my supervisor asked me to also explore using a GEE, thats why I ask.
I've read that, using the geepack
package, it is possible to define the correlation structure yourself, but I can't code that well to see if it is possible to define the structure so that rho is adjusted for the time interval in between measurements (by making it rho^s where s is the number of time units).