I have a dataset with some growth measurements pre and post vaccination and 3 different groups (3 different types of vaccine) so there are both a within (pre/post) and between factor (group).
- Problem 1: The number of observations varies between people (some people can have 1 observation and other up to 5)
- Problem 2: Some participants have pre intervention but no post intervention data.
- Problem 3: Time between vaccine and growth measurement varies (ie. some people will have data collected 10 days after vaccination, some other 15 days after etc..)
With all those problems I am a bit confused about how should I answer my questions: Is there a change in BMI z-score between groups after vaccination?
- zBMI: BMI zscore
- tipo_vacuna: vaccine 1, vaccine 2, vaccine 3.
- tiempo_peso_vacuna1: time between first vaccine and zBMI measurement (negative if before -vaccination and positive if after vaccination)
- Index1: number of observation per participants
- study_id: participants The idea was to apply a linear mixed model such as:
df1_lmm =lmer(zBMI ~ tiempo_peso_vacuna1 * tipo_vacuna + (1|study_id), data=df1)
summary(df1_lmm)
anova (df1_lmm)
However I have a lot of doubts:
- Is the model appropriate to answer the research question?
- Does it control for zBMI pre intervention?
- Does the random intercept accounts for the number of observations and their closeness in time to solve the autocorrelation problem? Any insight would be much appreciated, thank you.
Reproducible sample:
df1<-structure(list(study_id = structure(c(3, 3, 3, 3, 3, 3, 4, 4,
4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7,
7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10,
11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13,
13, 13, 14, 14, 14, 14, 14, 14, 16, 16, 16, 16, 16, 16, 18, 18,
18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20,
21, 21, 21, 21), format.spss = "F4.0", display_width = 11L),
ageyear_vacuna1 = structure(c(0.780287474332649, 0.780287474332649,
0.780287474332649, 0.780287474332649, 0.780287474332649,
0.780287474332649, 0.815879534565366, 0.815879534565366,
0.815879534565366, 0.815879534565366, 0.815879534565366,
0.815879534565366, 0.432580424366872, 0.432580424366872,
0.432580424366872, 0.432580424366872, 0.432580424366872,
0.432580424366872, 1.54414784394251, 1.54414784394251, 1.54414784394251,
1.54414784394251, 1.54414784394251, 1.54414784394251, 0.240930869267625,
0.240930869267625, 0.240930869267625, 0.240930869267625,
0.240930869267625, 0.240930869267625, 0.684462696783025,
0.684462696783025, 0.684462696783025, 0.684462696783025,
0.684462696783025, 0.684462696783025, 0.0711841204654346,
0.0711841204654346, 0.0711841204654346, 0.0711841204654346,
0.0711841204654346, 0.0711841204654346, 0.355920602327173,
0.355920602327173, 0.355920602327173, 0.355920602327173,
0.355920602327173, 0.355920602327173, 0.407939767282683,
0.407939767282683, 0.407939767282683, 0.407939767282683,
0.407939767282683, 0.407939767282683, 1.79603011635866, 1.79603011635866,
1.79603011635866, 1.79603011635866, 1.79603011635866, 1.79603011635866,
0.213552361396304, 0.213552361396304, 0.213552361396304,
0.213552361396304, 0.213552361396304, 0.213552361396304,
0.550308008213552, 0.550308008213552, 0.550308008213552,
0.550308008213552, 0.550308008213552, 0.550308008213552,
0.292950034223135, 0.292950034223135, 0.292950034223135,
0.292950034223135, 0.292950034223135, 0.292950034223135,
0.785763175906913, 0.785763175906913, 0.785763175906913,
0.785763175906913, 0.785763175906913, 0.785763175906913,
0.380561259411362, 0.380561259411362, 0.380561259411362,
0.380561259411362, 0.380561259411362, 0.380561259411362,
NA, NA, NA, NA, NA, NA, 0.303901437371663, 0.303901437371663,
0.303901437371663, 0.303901437371663), format.spss = "F8.2", display_width = 17L),
height_m = structure(c(157, 157, 157, 157, 157, 157, 165,
165, 165, 165, 165, 165, 150, 150, 150, 150, 150, 150, 175,
175, 175, 175, 175, 175, 171, 171, 171, 171, 171, 171, 148,
148, 148, 148, 148, 148, 165, 165, 165, 165, 165, 165, 164,
164, 164, 164, 164, 164, 169, 169, 169, 169, 169, 169, 158,
158, 158, 158, 158, 158, 164, 164, 164, 164, 164, 164, 171,
171, 171, 171, 171, 171, 160, 160, 160, 160, 160, 160, 166,
166, 166, 166, 166, 166, 165, 165, 165, 165, 165, 165, 170,
170, 170, 170, 170, 170, 165, 165, 165, 165), label = "height mothers", format.spss = "F6.2", display_width = 14L),
weight_m = structure(c(47.3, 47.3, 47.3, 47.3, 47.3, 47.3,
96, 96, 96, 96, 96, 96, 50, 50, 50, 50, 50, 50, 66, 66, 66,
66, 66, 66, 60, 60, 60, 60, 60, 60, 48, 48, 48, 48, 48, 48,
59, 59, 59, 59, 59, 59, 76.6, 76.6, 76.6, 76.6, 76.6, 76.6,
79, 79, 79, 79, 79, 79, 61, 61, 61, 61, 61, 61, 62, 62, 62,
62, 62, 62, 64, 64, 64, 64, 64, 64, 69, 69, 69, 69, 69, 69,
56, 56, 56, 56, 56, 56, 55, 55, 55, 55, 55, 55, 60, 60, 60,
60, 60, 60, 62, 62, 62, 62), label = "weight mothers", format.spss = "F6.2", display_width = 16L),
weight_m_2 = structure(c(48, 48, 48, 48, 48, 48, 96, 96,
96, 96, 96, 96, 50, 50, 50, 50, 50, 50, 64, 64, 64, 64, 64,
64, 65, 65, 65, 65, 65, 65, 46, 46, 46, 46, 46, 46, 75, 75,
75, 75, 75, 75, 69, 69, 69, 69, 69, 69, 84, 84, 84, 84, 84,
84, 64, 64, 64, 64, 64, 64, 64.5, 64.5, 64.5, 64.5, 64.5,
64.5, 64, 64, 64, 64, 64, 64, 63, 63, 63, 63, 63, 63, 52,
52, 52, 52, 52, 52, 60, 60, 60, 60, 60, 60, 62, 62, 62, 62,
62, 62, 61, 61, 61, 61), format.spss = "F6.2", display_width = 13L),
gwg_m = structure(c(12, 12, 12, 12, 12, 12, 4, 4, 4, 4, 4,
4, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 12, 12, 12,
12, 12, 12, 8, 8, 8, 8, 8, 8, 20, 20, 20, 20, 20, 20, 8,
8, 8, 8, 8, 8, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
15, 12, 12, 12, 12, 12, 12, 18, 18, 18, 18, 18, 18, 7, 7,
7, 7, 7, 7, 17, 17, 17, 17, 17, 17, 20, 20, 20, 20, 20, 20,
10, 10, 10, 10, 10, 10, 9, 9, 9, 9), format.spss = "F4.2", display_width = 15L),
birth_date = structure(c("2020/04/10", "2020/04/10", "2020/04/10",
"2020/04/10", "2020/04/10", "2020/04/10", "2020/04/03", "2020/04/03",
"2020/04/03", "2020/04/03", "2020/04/03", "2020/04/03", "2020/10/19",
"2020/10/19", "2020/10/19", "2020/10/19", "2020/10/19", "2020/10/19",
"2019/06/30", "2019/06/30", "2019/06/30", "2019/06/30", "2019/06/30",
"2019/06/30", "2020/12/06", "2020/12/06", "2020/12/06", "2020/12/06",
"2020/12/06", "2020/12/06", "2020/05/26", "2020/05/26", "2020/05/26",
"2020/05/26", "2020/05/26", "2020/05/26", "2021/01/30", "2021/01/30",
"2021/01/30", "2021/01/30", "2021/01/30", "2021/01/30", "2020/10/20",
"2020/10/20", "2020/10/20", "2020/10/20", "2020/10/20", "2020/10/20",
"2020/11/02", "2020/11/02", "2020/11/02", "2020/11/02", "2020/11/02",
"2020/11/02", "2019/05/11", "2019/05/11", "2019/05/11", "2019/05/11",
"2019/05/11", "2019/05/11", "2020/12/21", "2020/12/21", "2020/12/21",
"2020/12/21", "2020/12/21", "2020/12/21", "2020/09/06", "2020/09/06",
"2020/09/06", "2020/09/06", "2020/09/06", "2020/09/06", "2020/11/21",
"2020/11/21", "2020/11/21", "2020/11/21", "2020/11/21", "2020/11/21",
"2020/05/14", "2020/05/14", "2020/05/14", "2020/05/14", "2020/05/14",
"2020/05/14", "2020/08/29", "2020/08/29", "2020/08/29", "2020/08/29",
"2020/08/29", "2020/08/29", "2020/11/16", "2020/11/16", "2020/11/16",
"2020/11/16", "2020/11/16", "2020/11/16", "2020/11/06", "2020/11/06",
"2020/11/06", "2020/11/06"), format.spss = "A10", display_width = 10L),
sex_infant = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 1L), .Label = c("0", "1"), class = "factor"), delivery_method = structure(c(0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2,
0, 0, 0, 0), format.spss = "F1.0", display_width = 11L),
gestational_age = structure(c(41.4, 41.4, 41.4, 41.4, 41.4,
41.4, 41, 41, 41, 41, 41, 41, 40.86, 40.86, 40.86, 40.86,
40.86, 40.86, 38, 38, 38, 38, 38, 38, 41, 41, 41, 41, 41,
41, 41.29, 41.29, 41.29, 41.29, 41.29, 41.29, 41.14, 41.14,
41.14, 41.14, 41.14, 41.14, 41, 41, 41, 41, 41, 41, 40, 40,
40, 40, 40, 40, 40.14, 40.14, 40.14, 40.14, 40.14, 40.14,
40.71, 40.71, 40.71, 40.71, 40.71, 40.71, 40.71, 40.71, 40.71,
40.71, 40.71, 40.71, 36, 36, 36, 36, 36, 36, 40, 40, 40,
40, 40, 40, 40.71, 40.71, 40.71, 40.71, 40.71, 40.71, 40,
40, 40, 40, 40, 40, 37, 37, 37, 37), format.spss = "F5.2", display_width = 16L),
tipo_vacuna = structure(c(3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 2L, 2L,
2L, 4L, 4L, 4L, 4L, 4L, 4L, 2L, 2L, 2L, 2L, 2L, 2L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 3L, 3L,
3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L), .Label = c("NA", "1", "2", "3"), class = "factor"),
fecha_vacuna_1 = structure(c("2021/01/20", "2021/01/20",
"2021/01/20", "2021/01/20", "2021/01/20", "2021/01/20", "2021/01/26",
"2021/01/26", "2021/01/26", "2021/01/26", "2021/01/26", "2021/01/26",
"2021/03/26", "2021/03/26", "2021/03/26", "2021/03/26", "2021/03/26",
"2021/03/26", "2021/01/14", "2021/01/14", "2021/01/14", "2021/01/14",
"2021/01/14", "2021/01/14", "2021/03/04", "2021/03/04", "2021/03/04",
"2021/03/04", "2021/03/04", "2021/03/04", "2021/01/31", "2021/01/31",
"2021/01/31", "2021/01/31", "2021/01/31", "2021/01/31", "2021/02/25",
"2021/02/25", "2021/02/25", "2021/02/25", "2021/02/25", "2021/02/25",
"2021/02/27", "2021/02/27", "2021/02/27", "2021/02/27", "2021/02/27",
"2021/02/27", "2021/03/31", "2021/03/31", "2021/03/31", "2021/03/31",
"2021/03/31", "2021/03/31", "2021/02/25", "2021/02/25", "2021/02/25",
"2021/02/25", "2021/02/25", "2021/02/25", "2021/03/09", "2021/03/09",
"2021/03/09", "2021/03/09", "2021/03/09", "2021/03/09", "2021/03/26",
"2021/03/26", "2021/03/26", "2021/03/26", "2021/03/26", "2021/03/26",
"2021/03/08", "2021/03/08", "2021/03/08", "2021/03/08", "2021/03/08",
"2021/03/08", "2021/02/25", "2021/02/25", "2021/02/25", "2021/02/25",
"2021/02/25", "2021/02/25", "2021/01/15", "2021/01/15", "2021/01/15",
"2021/01/15", "2021/01/15", "2021/01/15", "", "", "", "",
"", "", "2021/02/25", "2021/02/25", "2021/02/25", "2021/02/25"
), format.spss = "A10", display_width = 10L), fecha_vacuna_2 = structure(c("2021/02/22",
"2021/02/22", "2021/02/22", "2021/02/22", "2021/02/22", "2021/02/22",
"2021/02/18", "2021/02/18", "2021/02/18", "2021/02/18", "2021/02/18",
"2021/02/18", "2021/04/26", "2021/04/26", "2021/04/26", "2021/04/26",
"2021/04/26", "2021/04/26", "2021/02/04", "2021/02/04", "2021/02/04",
"2021/02/04", "2021/02/04", "2021/02/04", "2021/06/02", "2021/06/02",
"2021/06/02", "2021/06/02", "2021/06/02", "2021/06/02", "2021/02/22",
"2021/02/22", "2021/02/22", "2021/02/22", "2021/02/22", "2021/02/22",
"2021/05/29", "2021/05/29", "2021/05/29", "2021/05/29", "2021/05/29",
"2021/05/29", "2021/06/02", "2021/06/02", "2021/06/02", "2021/06/02",
"2021/06/02", "2021/06/02", "2021/07/06", "2021/07/06", "2021/07/06",
"2021/07/06", "2021/07/06", "2021/07/06", "2021/05/30", "2021/05/30",
"2021/05/30", "2021/05/30", "2021/05/30", "2021/05/30", "2021/06/05",
"2021/06/05", "2021/06/05", "2021/06/05", "2021/06/05", "2021/06/05",
"2021/04/23", "2021/04/23", "2021/04/23", "2021/04/23", "2021/04/23",
"2021/04/23", "2021/05/31", "2021/05/31", "2021/05/31", "2021/05/31",
"2021/05/31", "2021/05/31", "2021/05/31", "2021/05/31", "2021/05/31",
"2021/05/31", "2021/05/31", "2021/05/31", "2021/02/09", "2021/02/09",
"2021/02/09", "2021/02/09", "2021/02/09", "2021/02/09", "",
"", "", "", "", "", "2021/03/18", "2021/03/18", "2021/03/18",
"2021/03/18"), format.spss = "A10", display_width = 18L),
Index1 = structure(c(1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6,
1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1,
2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2,
3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3,
4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4,
5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4), format.spss = "F4.0"),
date = structure(c("", "", "", "", "", "", "2020/04/03",
"2020/11/11", "2021/03/03", "2021/04/07", "", "", "2020/10/25",
"2021/02/19", "", "", "", "", "2019/07/05", "2020/07/01",
"2021/01/15", "", "", "", "2020/12/06", "2021/02/11", "2021/03/11",
"", "", "", "2020/06/05", "2021/01/26", "", "", "", "", "2021/01/30",
"2021/02/17", "2021/03/01", "2021/04/07", "", "", "2020/10/20",
"2021/02/22", "2021/03/25", "", "", "", "2020/11/16", "2021/03/09",
"2021/04/08", "", "", "", "2019/05/20", "", "", "", "", "",
"2020/12/21", "2021/02/22", "", "", "", "", "2020/09/06",
"2021/03/04", "", "", "", "", "2020/11/27", "2021/01/25",
"2021/02/23", "2021/03/22", "", "", "2020/05/14", "2020/11/16",
"", "", "", "", "2020/09/08", "2020/12/30", "2021/02/04",
"2021/03/03", "", "", "", "", "", "", "", "", "2020/11/19",
"2021/01/11", "2021/03/08", ""), format.spss = "A10", display_width = 10L),
weight = structure(c(NA, NA, NA, NA, NA, NA, 3.6, 9.7, 10,
11.6, NA, NA, 4.4, 8.2, NA, NA, NA, NA, 2.84, 10.87, 12.5,
NA, NA, NA, 3.56, 6.3, 7.11, NA, NA, NA, 2.84, 8.02, NA,
NA, NA, NA, 3.95, 3.9, 4.97, 6.18, NA, NA, 3.4, 7.7, 8.4,
NA, NA, NA, 4.13, 8.88, 9.2, NA, NA, NA, 3.5, NA, NA, NA,
NA, NA, 3.22, 4.79, NA, NA, NA, NA, 4.6, 8.36, NA, NA, NA,
NA, 1.98, 3.38, 4.32, 5.18, NA, NA, 3.42, 6.12, NA, NA, NA,
NA, 3.28, 6.74, 7.36, 7.68, NA, NA, NA, NA, NA, NA, NA, NA,
3.52, 5.12, 7.2, NA), format.spss = "F5.2", display_width = 12L),
length = structure(c(NA, NA, NA, NA, NA, NA, 49, 68, 72,
73, NA, NA, 52.5, 64, NA, NA, NA, NA, 48.5, 77, 87.5, NA,
NA, NA, 53, 61.5, 65, NA, NA, NA, 48, 68.5, NA, NA, NA, NA,
54, 57, 59.5, 63, NA, NA, 52, 64, 68, NA, NA, NA, 54, 67,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 50, 56.5, NA, NA,
NA, NA, 53, 71.5, NA, NA, NA, NA, NA, 51, NA, 56, NA, NA,
49, 65.5, NA, NA, NA, NA, 51, 63, 64.5, 68, NA, NA, NA, NA,
NA, NA, NA, NA, 51.5, 57, 62, NA), format.spss = "F5.2", display_width = 15L),
headcirc = structure(c(NA, NA, NA, NA, NA, NA, 34.5, 45,
49, 49, NA, NA, 36.5, 42, NA, NA, NA, NA, 34.5, 47.5, 49,
NA, NA, NA, 35, 41, 42, NA, NA, NA, 34, 43, NA, NA, NA, NA,
36, 37.5, 38.5, 41, NA, NA, 35, 42.5, 44, NA, NA, NA, 37,
43.5, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 33, 37.7, NA,
NA, NA, NA, 37.5, 44, NA, NA, NA, NA, NA, 37.5, NA, 40.5,
NA, NA, 33, 41, NA, NA, NA, NA, 35.5, 41.5, NA, 42, NA, NA,
NA, NA, NA, NA, NA, NA, 35, 38, 41, NA), format.spss = "F5.2", display_width = 15L),
zhaz = structure(c(NA, NA, NA, NA, NA, NA, -0.47, -0.73,
-1.08, -1.22, NA, NA, 1.24, 0.84, NA, NA, NA, NA, -1.19,
0.5, 1.72, NA, NA, NA, 1.65, 1.21, 1.58, NA, NA, NA, -1.91,
-0.98, NA, NA, NA, NA, 2.17, 2.11, 2.49, 1.95, NA, NA, 1.12,
-0.06, 0.88, NA, NA, NA, 0.87, 1.31, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, 0.46, -0.38, NA, NA, NA, NA, 1.65, 1.9,
NA, NA, NA, NA, NA, -3.16, NA, -2.79, NA, NA, -0.08, -0.18,
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