Bayesian Network Analysis
bernard-liew
2020-10-21
Last updated: 2020-10-21
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Knit directory: 2020_LBPcausal/
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Load library
# Helper packages
library (tidyverse)
library (tidyselect)
library (arsenal)
library (janitor)
library (magrittr)
library (Rgraphviz)
library (corrr)
library (corrplot)
# Import
library(readxl)
library (xlsx)
# Missing data
library (mice)
library (VIM)
# Modelling
library (bnlearn)
library (caret)
# Parallel
library (doParallel)Introduction
This is a bayesian network analysis where the early change variables are between week 10 and baseline. The late change variables are between week 52 and week 10.
Import data
rm (list = ls())
df_list <- readRDS("output/df_change.RDS")Subset data
df1 <- df_list[["wk10_base"]]
names(df1)[grepl("wk", names (df1))] <- paste0(str_remove(names(df1)[grepl("wk", names (df1))], "wk10_"), "_early")
df2 <- df_list[["wk52_wk10"]]
names(df2)[grepl("wk", names (df2))] <- paste0(str_remove(names(df2)[grepl("wk", names (df2))], "wk52_"), "_late")
df3 <- df_list[["wk52"]]
df3 <- df3 %>%
select (id, grp, subgrp, wk52_lbp, wk52_lp, wk52_osw, wk52_func)
names(df3)[grepl("wk", names (df3))] <- paste0(str_remove(names(df3)[grepl("wk", names (df3))], "wk52_"), "_outcome")
df <- df1 %>%
inner_join (df2, by = c("id", "subgrp", "grp")) %>%
inner_join (df3, by = c("id", "subgrp", "grp")) %>%
#select (-contains ("func_"))%>%
rename (disability_early = osw_early,
disability_late = osw_late,
disability_outcome = osw_outcome)Exploratory analysis
Between group comparisons
tableby (subgrp ~., data = df, digits = 2, digits.p = 2) %>%
summary () | dhr (N=54) | nrdp (N=7) | rdp (N=63) | mfp (N=91) | mtg (N=74) | Total (N=289) | p value | |
|---|---|---|---|---|---|---|---|
| disability_early | 0.35 | ||||||
| N-Miss | 0 | 0 | 1 | 2 | 1 | 4 | |
| Mean (SD) | -12.63 (14.97) | -10.29 (7.16) | -7.97 (10.81) | -9.58 (12.55) | -11.23 (13.56) | -10.25 (12.88) | |
| Range | -42.00 - 30.00 | -16.00 - 4.00 | -34.00 - 14.00 | -36.00 - 38.00 | -44.00 - 30.00 | -44.00 - 38.00 | |
| lbp_early | 0.32 | ||||||
| N-Miss | 0 | 0 | 0 | 0 | 1 | 1 | |
| Mean (SD) | -1.84 (2.47) | -1.86 (1.46) | -2.54 (2.26) | -2.13 (2.31) | -2.62 (2.57) | -2.28 (2.39) | |
| Range | -6.00 - 3.00 | -3.00 - 1.00 | -8.00 - 3.00 | -7.00 - 4.00 | -8.00 - 4.00 | -8.00 - 4.00 | |
| lp_early | 0.68 | ||||||
| N-Miss | 0 | 1 | 14 | 15 | 10 | 40 | |
| Mean (SD) | -2.53 (2.82) | -2.67 (1.86) | -2.20 (2.78) | -1.84 (2.49) | -2.30 (3.04) | -2.20 (2.75) | |
| Range | -8.00 - 3.00 | -5.00 - 0.00 | -8.00 - 3.00 | -6.00 - 5.00 | -9.00 - 5.00 | -9.00 - 5.00 | |
| pain_cope_early | 0.38 | ||||||
| N-Miss | 3 | 0 | 0 | 4 | 3 | 10 | |
| Mean (SD) | -0.96 (2.84) | 0.29 (3.40) | -1.57 (3.14) | -1.12 (3.33) | -1.70 (3.19) | -1.30 (3.17) | |
| Range | -7.00 - 6.00 | -4.00 - 4.00 | -9.00 - 6.00 | -9.00 - 9.00 | -10.00 - 6.00 | -10.00 - 9.00 | |
| anx_early | 0.16 | ||||||
| N-Miss | 3 | 0 | 0 | 3 | 3 | 9 | |
| Mean (SD) | -1.57 (2.95) | -3.86 (2.73) | -1.74 (2.64) | -1.33 (2.93) | -2.00 (2.72) | -1.70 (2.83) | |
| Range | -8.00 - 4.00 | -9.00 - -1.00 | -7.00 - 4.00 | -8.00 - 5.00 | -9.00 - 4.00 | -9.00 - 5.00 | |
| depress_early | 0.12 | ||||||
| N-Miss | 3 | 0 | 2 | 3 | 4 | 12 | |
| Mean (SD) | -1.59 (2.82) | -3.29 (3.50) | -1.20 (2.82) | -0.68 (2.96) | -1.00 (2.88) | -1.11 (2.92) | |
| Range | -8.00 - 5.00 | -9.00 - 1.00 | -8.00 - 6.00 | -7.00 - 8.00 | -8.00 - 6.00 | -9.00 - 8.00 | |
| pain_persist_early | 0.61 | ||||||
| N-Miss | 3 | 0 | 1 | 4 | 3 | 11 | |
| Mean (SD) | -2.08 (3.52) | -3.86 (2.19) | -1.98 (3.48) | -1.93 (2.68) | -2.30 (3.40) | -2.11 (3.20) | |
| Range | -9.00 - 7.00 | -7.00 - -1.00 | -10.00 - 6.00 | -8.00 - 5.00 | -9.00 - 6.00 | -10.00 - 7.00 | |
| work_expect_early | 0.32 | ||||||
| N-Miss | 9 | 0 | 0 | 5 | 3 | 17 | |
| Mean (SD) | -0.35 (2.95) | -0.86 (1.07) | -0.28 (2.40) | 0.34 (2.14) | -0.17 (2.11) | -0.08 (2.33) | |
| Range | -8.00 - 5.51 | -3.00 - 0.00 | -9.11 - 7.00 | -5.00 - 10.00 | -8.00 - 7.13 | -9.11 - 10.00 | |
| sleep_early | 0.28 | ||||||
| N-Miss | 3 | 0 | 0 | 2 | 3 | 8 | |
| Mean (SD) | -2.00 (2.76) | -2.29 (2.69) | -1.05 (2.80) | -1.78 (2.54) | -1.34 (2.81) | -1.56 (2.72) | |
| Range | -9.00 - 4.00 | -7.00 - 1.00 | -6.00 - 10.00 | -8.00 - 4.00 | -9.00 - 8.00 | -9.00 - 10.00 | |
| func_early | 0.18 | ||||||
| N-Miss | 3 | 0 | 0 | 2 | 3 | 8 | |
| Mean (SD) | -6.28 (6.36) | -5.43 (8.60) | -2.63 (8.58) | -5.01 (8.42) | -3.97 (8.88) | -4.46 (8.29) | |
| Range | -26.00 - 7.00 | -18.00 - 11.00 | -23.00 - 27.00 | -29.00 - 14.00 | -24.00 - 25.00 | -29.00 - 27.00 | |
| fear_early | 0.76 | ||||||
| N-Miss | 6 | 1 | 1 | 3 | 4 | 15 | |
| Mean (SD) | -3.15 (7.57) | -5.80 (11.28) | -2.28 (6.39) | -3.32 (6.73) | -2.88 (7.02) | -3.00 (6.97) | |
| Range | -19.00 - 11.00 | -22.00 - 8.00 | -17.00 - 18.00 | -24.00 - 12.00 | -25.00 - 13.00 | -25.00 - 18.00 | |
| grp | 1.00 | ||||||
| advice | 26 (48.1%) | 3 (42.9%) | 30 (47.6%) | 43 (47.3%) | 35 (47.3%) | 137 (47.4%) | |
| individualisedphysio | 28 (51.9%) | 4 (57.1%) | 33 (52.4%) | 48 (52.7%) | 39 (52.7%) | 152 (52.6%) | |
| id | < 0.01 | ||||||
| Mean (SD) | 1526.96 (209.06) | 4573.71 (56.44) | 5529.14 (211.09) | 2514.09 (228.03) | 3515.42 (234.58) | 3293.19 (1403.85) | |
| Range | 1101.00 - 1806.00 | 4501.00 - 4652.00 | 5101.00 - 5903.00 | 2101.00 - 2951.00 | 3101.00 - 3905.00 | 1101.00 - 5903.00 | |
| disability_late | 0.84 | ||||||
| N-Miss | 1 | 0 | 7 | 6 | 3 | 17 | |
| Mean (SD) | -5.72 (14.45) | -4.86 (5.15) | -3.54 (9.44) | -3.97 (12.63) | -3.35 (11.33) | -4.08 (11.92) | |
| Range | -52.00 - 28.00 | -12.00 - 4.00 | -40.00 - 24.00 | -45.12 - 34.00 | -28.00 - 36.00 | -52.00 - 36.00 | |
| lbp_late | 0.24 | ||||||
| N-Miss | 1 | 0 | 6 | 4 | 2 | 13 | |
| Mean (SD) | -0.13 (2.13) | -1.14 (3.39) | 0.05 (1.65) | -0.55 (2.52) | -0.72 (2.32) | -0.40 (2.27) | |
| Range | -7.00 - 5.00 | -7.00 - 4.00 | -4.00 - 4.00 | -7.00 - 6.00 | -8.00 - 5.50 | -8.00 - 6.00 | |
| lp_late | 0.37 | ||||||
| N-Miss | 1 | 1 | 19 | 18 | 11 | 50 | |
| Mean (SD) | -0.77 (2.65) | -0.67 (1.75) | 0.00 (1.67) | -0.76 (2.93) | -0.12 (2.64) | -0.45 (2.58) | |
| Range | -8.00 - 4.00 | -3.00 - 2.00 | -4.00 - 4.00 | -10.00 - 7.00 | -9.00 - 9.00 | -10.00 - 9.00 | |
| pain_cope_late | 0.74 | ||||||
| N-Miss | 4 | 0 | 11 | 18 | 12 | 45 | |
| Mean (SD) | -0.33 (2.93) | -1.55 (1.88) | -0.63 (2.41) | -0.22 (3.45) | -0.08 (3.72) | -0.33 (3.18) | |
| Range | -7.00 - 8.00 | -4.00 - 1.00 | -8.00 - 5.00 | -9.12 - 10.00 | -8.00 - 9.00 | -9.12 - 10.00 | |
| anx_late | 0.71 | ||||||
| N-Miss | 4 | 0 | 11 | 18 | 12 | 45 | |
| Mean (SD) | -0.56 (2.35) | -0.86 (1.86) | 0.18 (2.51) | -0.23 (3.21) | -0.20 (2.95) | -0.22 (2.80) | |
| Range | -7.00 - 4.00 | -4.00 - 1.00 | -8.46 - 6.00 | -9.00 - 9.00 | -6.00 - 7.00 | -9.00 - 9.00 | |
| depress_late | 0.31 | ||||||
| N-Miss | 4 | 0 | 11 | 18 | 12 | 45 | |
| Mean (SD) | -0.16 (2.06) | -1.14 (1.21) | 0.24 (2.18) | 0.20 (2.55) | -0.42 (2.48) | -0.06 (2.34) | |
| Range | -6.00 - 5.00 | -3.00 - 0.00 | -7.00 - 7.00 | -7.00 - 8.00 | -7.00 - 7.00 | -7.00 - 8.00 | |
| pain_persist_late | 0.38 | ||||||
| N-Miss | 4 | 0 | 11 | 18 | 12 | 45 | |
| Mean (SD) | -0.12 (3.90) | -2.43 (2.37) | 0.34 (3.68) | -0.22 (3.76) | 0.33 (3.65) | -0.00 (3.72) | |
| Range | -9.00 - 8.00 | -5.00 - 1.00 | -10.00 - 9.00 | -10.00 - 7.00 | -7.50 - 9.00 | -10.00 - 9.00 | |
| work_expect_late | 0.97 | ||||||
| N-Miss | 4 | 0 | 11 | 18 | 12 | 45 | |
| Mean (SD) | 0.32 (3.55) | 0.00 (0.82) | 0.03 (1.35) | 0.20 (2.31) | 0.13 (1.72) | 0.17 (2.29) | |
| Range | -7.00 - 10.00 | -1.00 - 1.00 | -4.00 - 4.00 | -10.00 - 8.00 | -5.00 - 6.00 | -10.00 - 10.00 | |
| sleep_late | 0.74 | ||||||
| N-Miss | 4 | 0 | 11 | 17 | 12 | 44 | |
| Mean (SD) | 0.12 (2.09) | -0.14 (2.12) | -0.21 (1.35) | 0.03 (2.65) | -0.38 (2.11) | -0.11 (2.15) | |
| Range | -5.00 - 8.00 | -2.00 - 4.00 | -3.00 - 4.00 | -8.00 - 9.00 | -9.00 - 5.00 | -9.00 - 9.00 | |
| func_late | 0.10 | ||||||
| N-Miss | 4 | 0 | 11 | 17 | 12 | 44 | |
| Mean (SD) | -2.37 (6.69) | -4.29 (6.07) | -1.58 (4.38) | 0.63 (7.89) | -1.15 (7.66) | -1.04 (6.98) | |
| Range | -22.00 - 12.00 | -16.00 - 2.00 | -15.00 - 7.00 | -17.00 - 30.00 | -21.00 - 28.00 | -22.00 - 30.00 | |
| fear_late | 0.50 | ||||||
| N-Miss | 4 | 0 | 11 | 17 | 12 | 44 | |
| Mean (SD) | -1.23 (5.71) | 3.26 (3.75) | -0.73 (6.18) | -0.77 (6.94) | -1.27 (6.61) | -0.87 (6.39) | |
| Range | -14.00 - 10.00 | -2.00 - 10.00 | -13.00 - 14.00 | -17.00 - 15.46 | -15.00 - 14.00 | -17.00 - 15.46 | |
| lbp_outcome | 0.06 | ||||||
| N-Miss | 1 | 0 | 6 | 4 | 1 | 12 | |
| Mean (SD) | 2.98 (2.27) | 3.57 (2.70) | 2.47 (2.16) | 3.01 (2.53) | 2.10 (1.88) | 2.67 (2.27) | |
| Range | 0.00 - 8.00 | 1.00 - 7.00 | 0.00 - 8.00 | 0.00 - 9.00 | 0.00 - 8.00 | 0.00 - 9.00 | |
| lp_outcome | 0.35 | ||||||
| N-Miss | 1 | 1 | 19 | 18 | 10 | 49 | |
| Mean (SD) | 2.49 (2.59) | 2.00 (2.10) | 1.98 (2.29) | 2.08 (2.52) | 1.54 (2.36) | 2.01 (2.45) | |
| Range | 0.00 - 8.00 | 0.00 - 5.00 | 0.00 - 8.50 | 0.00 - 9.00 | 0.00 - 9.00 | 0.00 - 9.00 | |
| disability_outcome | 0.11 | ||||||
| N-Miss | 1 | 0 | 6 | 4 | 2 | 13 | |
| Mean (SD) | 18.30 (18.67) | 13.14 (8.71) | 11.58 (12.21) | 16.74 (14.36) | 13.98 (13.11) | 15.16 (14.58) | |
| Range | 0.00 - 70.00 | 2.00 - 26.00 | 0.00 - 70.00 | 0.00 - 54.00 | 0.00 - 60.00 | 0.00 - 70.00 | |
| func_outcome | 0.50 | ||||||
| N-Miss | 2 | 0 | 11 | 17 | 12 | 42 | |
| Mean (SD) | 7.00 (8.14) | 5.57 (4.47) | 5.71 (7.63) | 7.99 (9.45) | 5.88 (7.48) | 6.70 (8.22) | |
| Range | 0.00 - 28.00 | 0.00 - 14.00 | 0.00 - 38.00 | 0.00 - 36.00 | 0.00 - 34.00 | 0.00 - 38.00 |
Correlation plots
col<- colorRampPalette(c("red", "white", "blue"))(20)
df %>%
select_if (is.numeric) %>%
select (-id) %>%
cor (use = "complete.obs") %>%
corrplot(type="upper", tl.col="black", tl.srt=45, col=col)
BN analysis
Create blacklist
df.bn = as.data.frame (df)
df.bn[, grepl ( "id|subgrp|outcome|func",names (df.bn))] <- NULL
tiers_bl = list (colnames (df.bn)[colnames(df.bn) %in% grep ("early",colnames(df.bn), value = TRUE)],
colnames (df.bn)[colnames(df.bn) %in% grep ("late",colnames(df.bn), value = TRUE)])
bl1 = tiers2blacklist(tiers_bl)
tiers_bl = list (colnames (df.bn)[colnames(df.bn) %in% grep ("grp",colnames(df.bn), value = TRUE)],
colnames (df.bn)[colnames(df.bn) %in% grep ("late",colnames(df.bn), value = TRUE)])
bl2 = tiers2blacklist(tiers_bl)
tiers_bl = list (colnames (df.bn)[colnames(df.bn) %in% grep ("grp",colnames(df.bn), value = TRUE)],
colnames (df.bn)[colnames(df.bn) %in% grep ("early",colnames(df.bn), value = TRUE)])
bl3 = tiers2blacklist(tiers_bl)
bl = rbind(bl1, bl2, bl3)Build BN model
doParallel::registerDoParallel(4)
n_boot <- 200
set.seed (20200420)
############
boot_bl_rel <- foreach (B = 1: n_boot) %dopar%{
boot.sample = df.bn[sample(nrow(df.bn),
nrow(df.bn), replace = TRUE), ]
bnlearn::structural.em(boot.sample, impute = "bayes-lw", max.iter = 3,
maximize.args = list(blacklist = bl))
}
#############Performance evaluation using nested cross validation.
Inner is bootstrap resampling for model averaging. Outer is bootstrap resampling k = 25 for performance evaluation.
set.seed (20200420)
flds <- createFolds(1:nrow(df.bn),
k = 10, returnTrain = TRUE)
n_boot = 200
corr.df.list <- list()
for (k in seq_along(flds)) {
train <- df.bn [flds[[k]], ] %>% as.data.frame()
test <- df.bn [-flds[[k]], ] %>% as.data.frame()
doParallel::registerDoParallel(4)
############
boot = foreach (B = 1: n_boot) %dopar%{
boot.sample = train[sample(nrow(train),
nrow(train), replace = TRUE), ]
bnlearn::structural.em(boot.sample, impute = "bayes-lw", max.iter = 3,
maximize.args = list(blacklist = bl))
}
#############
stopImplicitCluster()
bootstr <- custom.strength(boot, nodes = names(train))
avg <- averaged.network(bootstr, threshold = 0.5)
fit <- bn.fit (avg, train, method = "mle")
imp.list = impute (fit, data = test, method = "bayes-lw")
inames = names (imp.list) [!grepl ("grp", names (imp.list))]
corr.df = structure(numeric(length (inames)), names = inames)
for (var in inames) {
corr.df[var] = cor(predict(fit, data = imp.list, var, method = "bayes-lw"),
imp.list[, var])
}
corr.df.list[[k]] <- corr.df
}
corr.df <- bind_cols (corr.df.list) %>%
apply (1, mean)
names (corr.df) <- inames
corr.dfSee results
bootstr = custom.strength(boot_bl_rel, nodes = names(df.bn))
avg = averaged.network(bootstr, threshold = 0.5)
fit = bn.fit (avg, df.bn, method = "mle")
g = strength.plot(avg,
bootstr,
shape = "rectangle",
main = "Figure")
graph::nodeRenderInfo(g) = list(fontsize=18)
renderGraph(g)Save results
save (df,
df.bn,
bl,
boot_bl,
boot_bl_rel,
bootstr,
corr.df,
avg,
fit,
file = "output/results_early2late.RData")
sessionInfo()R version 3.6.2 (2019-12-12)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18363)
Matrix products: default
locale:
[1] LC_COLLATE=English_United Kingdom.1252
[2] LC_CTYPE=English_United Kingdom.1252
[3] LC_MONETARY=English_United Kingdom.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United Kingdom.1252
attached base packages:
[1] grid parallel stats graphics grDevices utils datasets
[8] methods base
other attached packages:
[1] doParallel_1.0.15 iterators_1.0.12 foreach_1.5.0
[4] caret_6.0-86 lattice_0.20-41 bnlearn_4.5
[7] VIM_5.1.1 data.table_1.13.0 colorspace_1.4-1
[10] mice_3.11.0 xlsx_0.6.3 readxl_1.3.1
[13] corrplot_0.84 corrr_0.4.2 Rgraphviz_2.30.0
[16] graph_1.64.0 BiocGenerics_0.32.0 magrittr_1.5
[19] janitor_2.0.1 arsenal_3.5.0 tidyselect_1.1.0
[22] forcats_0.5.0 stringr_1.4.0 dplyr_1.0.1
[25] purrr_0.3.4 readr_1.3.1 tidyr_1.1.1
[28] tibble_3.0.3 ggplot2_3.3.2 tidyverse_1.3.0
[31] workflowr_1.6.2
loaded via a namespace (and not attached):
[1] ellipsis_0.3.1 class_7.3-17 rio_0.5.16
[4] rprojroot_1.3-2 snakecase_0.11.0 fs_1.5.0
[7] rstudioapi_0.11 prodlim_2019.11.13 fansi_0.4.1
[10] lubridate_1.7.9 ranger_0.12.1 xml2_1.3.2
[13] splines_3.6.2 codetools_0.2-16 robustbase_0.93-6
[16] knitr_1.29 jsonlite_1.7.0 pROC_1.16.2
[19] rJava_0.9-12 broom_0.7.0 dbplyr_1.4.4
[22] compiler_3.6.2 httr_1.4.2 backports_1.1.7
[25] assertthat_0.2.1 Matrix_1.2-18 cli_2.0.2
[28] later_1.1.0.1 htmltools_0.5.0 tools_3.6.2
[31] gtable_0.3.0 glue_1.4.1 reshape2_1.4.4
[34] Rcpp_1.0.5 carData_3.0-4 cellranger_1.1.0
[37] vctrs_0.3.2 nlme_3.1-142 lmtest_0.9-37
[40] timeDate_3043.102 gower_0.2.2 xfun_0.16
[43] laeken_0.5.1 xlsxjars_0.6.1 openxlsx_4.1.5
[46] rvest_0.3.6 lifecycle_0.2.0 DEoptimR_1.0-8
[49] MASS_7.3-51.6 zoo_1.8-8 scales_1.1.1
[52] ipred_0.9-9 hms_0.5.3 promises_1.1.1
[55] yaml_2.2.1 curl_4.3 rpart_4.1-15
[58] stringi_1.4.6 highr_0.8 e1071_1.7-3
[61] boot_1.3-25 zip_2.1.0 lava_1.6.7
[64] rlang_0.4.7 pkgconfig_2.0.3 evaluate_0.14
[67] recipes_0.1.13 plyr_1.8.6 R6_2.4.1
[70] generics_0.0.2 DBI_1.1.0 pillar_1.4.6
[73] haven_2.3.1 whisker_0.4 foreign_0.8-72
[76] withr_2.2.0 survival_3.2-3 abind_1.4-5
[79] sp_1.4-2 nnet_7.3-14 modelr_0.1.8
[82] crayon_1.3.4 car_3.0-9 rmarkdown_2.3
[85] blob_1.2.1 git2r_0.27.1 ModelMetrics_1.2.2.2
[88] vcd_1.4-7 reprex_0.3.0 digest_0.6.25
[91] httpuv_1.5.4 stats4_3.6.2 munsell_0.5.0