The goal of spline-pr is to fit poisson regression models with generalized estimating equations (i.e., robust variance estimators for prevalence ratios) that include spline terms. The code in this repo also generates plots that show the estimated spline curve over a domain specified by the user.
This example uses NHANES data to create a spline figure showing the prevalence ratio for blood pressure control as a function of age. Since we are dealing with blood pressure control, we filter the data to include only participants with self-reported antihypertensive medication use. Also, since this is not a ‘survey’ tutorial, we do not engage with the NHANES survey weights.
library(table.glue)
library(tidyverse)
library(splines)
library(geepack)
library(mice)
#> Warning: package 'mice' was built under R version 4.1.1
source("R/functions.R")
data_nhanes <- table.glue::nhanes %>%
as_tibble() %>%
select(age, bp_sys_mmhg, bp_dia_mmhg, meds_bp) %>%
filter(meds_bp == 'yes', age >= 20)
data_nhanes
#> # A tibble: 4,796 x 4
#> age bp_sys_mmhg bp_dia_mmhg meds_bp
#> <dbl> <dbl> <dbl> <chr>
#> 1 72 142 82 yes
#> 2 73 137. 86.7 yes
#> 3 56 157. 82 yes
#> 4 76 127. 66.7 yes
#> 5 60 127. 74 yes
#> 6 65 141. 57.3 yes
#> 7 72 160 71.3 yes
#> 8 80 109. 53.3 yes
#> 9 43 140 82.7 yes
#> 10 65 NA NA yes
#> # ... with 4,786 more rowsAs with almost all data, we have missing values. Thus, we will use multiple imputation and pool our spline estimates from each imputed dataset.
n_imputes <- 5
data_nhanes_impute <- data_nhanes %>%
# remove constant column (all meds_bp == 'yes')
select(-meds_bp) %>%
# run the imputation models
mice(method = 'pmm', m = n_imputes, printFlag = FALSE) %>%
# get the imputed data, action = 'all' means return every imputed data set
complete(action = 'all') %>%
# convert each imputed dataset to a tibble for better printing
map(as_tibble)
# print the first imputed dataset
data_nhanes_impute[[1]]
#> # A tibble: 4,796 x 3
#> age bp_sys_mmhg bp_dia_mmhg
#> <dbl> <dbl> <dbl>
#> 1 72 142 82
#> 2 73 137. 86.7
#> 3 56 157. 82
#> 4 76 127. 66.7
#> 5 60 127. 74
#> 6 65 141. 57.3
#> 7 72 160 71.3
#> 8 80 109. 53.3
#> 9 43 140 82.7
#> 10 65 139. 59.3
#> # ... with 4,786 more rowsLet’s not forget that our outcome is dependent on the two blood pressure variables; i.e., blood pressure control is 1 if systolic blood pressure is < 140 mm Hg and diastolic blood pressure is < 90 mm Hg. .
data_nhanes_impute <- data_nhanes_impute %>%
map(
~ .x %>%
mutate(
bp_control = if_else(
condition = bp_sys_mmhg < 140 & bp_dia_mmhg < 90,
true = 1,
false = 0
)
)
)
data_nhanes_impute[[1]]
#> # A tibble: 4,796 x 4
#> age bp_sys_mmhg bp_dia_mmhg bp_control
#> <dbl> <dbl> <dbl> <dbl>
#> 1 72 142 82 0
#> 2 73 137. 86.7 1
#> 3 56 157. 82 0
#> 4 76 127. 66.7 1
#> 5 60 127. 74 1
#> 6 65 141. 57.3 0
#> 7 72 160 71.3 0
#> 8 80 109. 53.3 1
#> 9 43 140 82.7 0
#> 10 65 139. 59.3 1
#> # ... with 4,786 more rowsNext we fit a geeglm model to each imputed dataset. Note that
fits <- map(
.x = data_nhanes_impute,
.f = ~ geeglm(bp_control ~ ns(age, df = 4),
data = .x,
id = seq(nrow(.x)))
)
summary(fits[[1]])
#>
#> Call:
#> geeglm(formula = bp_control ~ ns(age, df = 4), data = .x, id = seq(nrow(.x)))
#>
#> Coefficients:
#> Estimate Std.err Wald Pr(>|W|)
#> (Intercept) 0.69718 0.06510 114.690 <2e-16 ***
#> ns(age, df = 4)1 -0.04489 0.05971 0.565 0.4522
#> ns(age, df = 4)2 -0.09171 0.05572 2.709 0.0998 .
#> ns(age, df = 4)3 -0.14803 0.14701 1.014 0.3140
#> ns(age, df = 4)4 -0.25158 0.02652 90.018 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Correlation structure = independence
#> Estimated Scale Parameters:
#>
#> Estimate Std.err
#> (Intercept) 0.2268 0.002057
#> Number of clusters: 4796 Maximum cluster size: 1# determine a spline basis function
# the terms used here must match those in geeglm()
bases <- map(
.x = data_nhanes_impute,
.f = ~ ns(.x$age, df = 4)
)
# using the fit and basis function,
# get a predicted spline estimate + SE
spline_preds <- map2(
.x = fits,
.y = bases,
.f = get_spline_preds,
pattern = '^ns\\(',
x_min = 20,
x_max = 80,
x_ref = 50
)
# pool results using Rubin's rules
# V_w = mean of the variance estimates
variance_within <- map_dfc(spline_preds, "se") %>%
apply(MARGIN = 1, function(x) mean(x^2))
# V_b = variance of the predictions
variance_between <- map_dfc(spline_preds, "pred") %>%
apply(MARGIN = 1, var)
# V_total = V_w + V_b * (n_imputes+1) / n_imputes
variance_total <-
variance_within + variance_between + variance_between/n_imputes
se_pooled <- sqrt(variance_total)
spline_pool <- tibble(
x = spline_preds[[1]]$x,
pred = apply(map_dfc(spline_preds, "pred"), 1, mean),
se = se_pooled,
ci_lwr = pred + qnorm(0.025) * se,
ci_upr = pred + qnorm(0.975) * se
)
spline_pool
#> # A tibble: 1,000 x 5
#> x pred se ci_lwr ci_upr
#> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 20 -0.00480 0.0773 -0.156 0.147
#> 2 20.1 -0.00472 0.0770 -0.156 0.146
#> 3 20.1 -0.00464 0.0768 -0.155 0.146
#> 4 20.2 -0.00456 0.0766 -0.155 0.146
#> 5 20.2 -0.00448 0.0764 -0.154 0.145
#> 6 20.3 -0.00440 0.0762 -0.154 0.145
#> 7 20.4 -0.00431 0.0760 -0.153 0.145
#> 8 20.4 -0.00423 0.0757 -0.153 0.144
#> 9 20.5 -0.00415 0.0755 -0.152 0.144
#> 10 20.5 -0.00407 0.0753 -0.152 0.144
#> # ... with 990 more rowsdata_imputed_stack <- bind_rows(data_nhanes_impute)
data_segment <- bin_segments(x = data_imputed_stack$age,
y = data_imputed_stack$bp_control,
x_min = 20,
x_max = 80,
by_y = TRUE,
bin_length = 1,
bin_count = 60,
bin_yintercept = 2/3) %>%
mutate(event_status = factor(event_status,
levels = c(1, 0),
labels = c("Yes", "No")))
fig <- ggplot(spline_pool) +
aes(x = x,
y = exp(pred),
ymin = exp(ci_lwr),
ymax = exp(ci_upr)) +
labs(x = 'age, years',
y = 'Prevalence ratio',
color = 'Blood pressure control') +
geom_line() +
geom_ribbon(alpha = 0.2) +
scale_y_log10() +
geom_segment(data = data_segment,
inherit.aes = FALSE,
size = 2,
mapping = aes(x = x,
y = y,
color = event_status,
xend = xend,
yend = yend)) +
theme_bw() +
geom_hline(yintercept = 1, linetype = 2, color = 'grey') +
theme(panel.grid = element_blank(),
legend.position = c(.2, 0.42)) +
scale_color_manual(values = c("grey", "black"))
fig