Framingham Heart Study
We’ll demonstrate how to use the package with data from the Framingham Heart Study. The following information is from the official Framingham study documentation (https://biolincc.nhlbi.nih.gov/teaching/):
“The Framingham Heart Study is a long term prospective study of the etiology of cardiovascular disease among a population of free living subjects in the community of Framingham, Massachusetts. The Framingham Heart Study was a landmark study in epidemiology in that it was the first prospective study of cardiovascular disease and identified the concept of risk factors and their joint effects. The study began in 1948 and 5,209 subjects were initially enrolled in the study. Participants have been examined biennially since the inception of the study and all subjects are continuously followed through regular surveillance for cardiovascular outcomes. Clinic examination data has included cardiovascular disease risk factors and markers of disease such as blood pressure, blood chemistry, lung function, smoking history, health behaviors, ECG tracings, Echocardiography, and medication use. Through regular surveillance of area hospitals, participant contact, and death certificates, the Framingham Heart Study reviews and adjudicates events for the occurrence of Angina Pectoris, Myocardial Infarction, Heart Failure, and Cerebrovascular disease.
data(cvdd)cvdd is a subset of the data collected as part of the Framingham study from 4,240 participants who conducted a baseline exam and were free of prevalent coronary heart disease when they entered the study. Participant clinic data was collected during three examination periods, approximately 6 years apart, from roughly 1956 to 1968. Each participant was followed for a total of 24 years for the outcome of the following events: Angina Pectoris, Myocardial Infarction, Atherothrombotic Infarction or Cerebral Hemorrhage (Stroke) or death.
NOTE: This is a “teaching” dataset. Specific methods were employed to ensure an anonymous dataset that protects patient confidentiality; therefore, this dataset is inappropriate for publication purposes.” The use of these data for the purposes of this package were approved on 11Mar2019 (request #7161) by NIH/NHLBI.
Binary outcome example
Research question: what is the effect of having diabetes at the beginning of the study on the 24-year risk of cardiovascular disease or death due to any cause?
Here, we will estimate the risk difference, risk ratio, odds ratio,
and number needed to treat, adjusting for patient’s age, sex, body mass
index (BMI), smoking status (current smoker or not), and prevalence of
hypertension (if they are hypertensive or not at baseline). Logistic
regression is used as the underlying parametric model for g-computation.
[NOTE: The CRAN version of this vignette has
reduced the number of bootstraps from 1000 to 200 to comply with CRAN
compile times. If you wish to perfectly recreate results from the
manuscript, change all of the instances of R = 200 to
R = 1000]
## Specify the regression formula
cvdd.formula <- cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE + PREVHYP
## For reproducibility, we should always set the seed since the g-computation uses
## random resampling of the data to calculate confidence intervals and random
## sampling of the distribution when predicting outcomes.
set.seed(1298)
## Call the gComp function
binary.res <- gComp(data = cvdd,
formula = cvdd.formula,
outcome.type = "binary",
R = 200)
binary.res
#> Formula:
#> cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE + PREVHYP
#>
#> Parameter estimates:
#> DIABETES1_v._DIABETES0 Estimate (95% CI)
#> Risk Difference 0.287 (0.198, 0.393)
#> Risk Ratio 1.700 (1.488, 1.968)
#> Odds Ratio 4.550 (2.784, 8.863)
#> Number needed to treat/harm 3.484The result obtained from the gComp function is an object
of class gComp which is a list containing the summary
results, results.df, n, R,
boot.result, contrast, family,
formula, predicted.outcome, and
glm.result (see ?gComp or
help(gComp) for a more detailed explanation of each item in
the list).
class(binary.res)
#> [1] "gComp" "list"
## The names of the different items in the list:
names(binary.res)
#> [1] "summary" "results.df"
#> [3] "n" "R"
#> [5] "boot.result" "contrast"
#> [7] "family" "formula"
#> [9] "predicted.outcome" "glm.result"
## Sample size of the original data:
binary.res$n
#> [1] 4240
## Contrast being compared in the analysis:
binary.res$contrast
#> [1] "DIABETES1 v. DIABETES0"There is also a summary method for objects with class gComp that contains the formula, family and link function, contrast being made, parameter estimates with 95% CIs, and a summary of the underlying glm used for predictions.
summary(binary.res)
#> Formula:
#> cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE + PREVHYP
#>
#> Family: binomial
#> Link function: logit
#>
#> Contrast: DIABETES1 v. DIABETES0
#>
#> Parameter estimates:
#> DIABETES1_v._DIABETES0 Estimate (95% CI)
#> Risk Difference 0.287 (0.198, 0.393)
#> Risk Ratio 1.700 (1.488, 1.968)
#> Odds Ratio 4.550 (2.784, 8.863)
#> Number needed to treat/harm 3.484
#>
#> Underlying glm:
#> Call: stats::glm(formula = formula, family = family, data = working.df,
#> na.action = stats::na.omit)
#>
#> Coefficients:
#> (Intercept) DIABETES1 AGE SEX1
#> -6.25839 1.51501 0.10246 -0.79405
#> BMI CURSMOKE1 PREVHYP1
#> 0.02512 0.58550 0.77804
#>
#> Degrees of Freedom: 4220 Total (i.e. Null); 4214 Residual
#> (19 observations deleted due to missingness)
#> Null Deviance: 5735
#> Residual Deviance: 4697 AIC: 4711Checking model fit
The 95% CIs obtained from the riskCommunicator package represent population-standardized marginal effects obtained with g-computation. To ensure that the parameter estimates from each bootstrap iteration are normally distributed, we can also look at the histogram and Q-Q plots of bootstrapped estimates by calling:
plot(binary.res)
The histograms show the different effect estimates obtained by each
bootstrap resampling of the data and should be normally distributed if
the model is correctly specified. Q-Q plots help to verify that the
bootstrap values are normally distributed by comparing the actual
distribution of bootstrap values against a theoretical normal
distribution of values centered at mean = 0. If the estimates are
normally distributed, the plotted estimates (black circles) should
overlay the diagonal red dashed line.
In the manuscript, we compare the results of gComp to standard regression models. Here, we show how to do that so we can re-create Table 2.
First we obtain the odds ratio using logistic regression.
#>
#> Call: glm(formula = cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE +
#> PREVHYP, family = binomial(link = "logit"), data = cvdd)
#>
#> Coefficients:
#> (Intercept) DIABETES1 AGE SEX1
#> -6.25839 1.51501 0.10246 -0.79405
#> BMI CURSMOKE1 PREVHYP1
#> 0.02512 0.58550 0.77804
#>
#> Degrees of Freedom: 4220 Total (i.e. Null); 4214 Residual
#> (19 observations deleted due to missingness)
#> Null Deviance: 5735
#> Residual Deviance: 4697 AIC: 4711Note the use of confint.default in the above call. The
typical call confint does not return Wald-based CIs, so
we’ve forced it with confint.default. You can read more
about that here: https://stats.stackexchange.com/questions/5304/why-is-there-a-difference-between-manually-calculating-a-logistic-regression-95
Next, we calculate the risk ratio using a Poisson approximation of log-binomial regression with robust variance (sandwich standard errors).
#>
#> Call: glm(formula = cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE +
#> PREVHYP, family = "poisson", data = cvdd %>% mutate(cvd_dth = ifelse(cvd_dth ==
#> "0", 0, ifelse(cvd_dth == "1", 1, NA))))
#>
#> Coefficients:
#> (Intercept) DIABETES1 AGE SEX1
#> -3.86603 0.39673 0.04930 -0.38348
#> BMI CURSMOKE1 PREVHYP1
#> 0.01403 0.26329 0.35452
#>
#> Degrees of Freedom: 4220 Total (i.e. Null); 4214 Residual
#> (19 observations deleted due to missingness)
#> Null Deviance: 3079
#> Residual Deviance: 2539 AIC: 6073We can try to calculate the risk difference using a log-linear regression, but the model won’t converge.
std.reg.rd = glm(formula = cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE + PREVHYP,
data = cvdd %>%
## To use linear regression, we need to change DIABETES from a
## factor to a numeric (0,1) variable
mutate(cvd_dth = ifelse(cvd_dth == "0", 0,
ifelse(cvd_dth == "1", 1, NA))),
family=gaussian(link = 'log'))We can re-create Table 2 from the manuscript now!
# combine standard regression results
std.regression.res = df.std.reg.or %>%
mutate(Parameter = "Odds Ratio",
Std_regression = paste0(round(OR, 2),
" (",
round(LL, 2),
", ",
round(UL, 2),
")")) %>%
bind_rows(df.std.reg.rr %>%
mutate(Parameter = "Risk Ratio",
Std_regression = paste0(round(Estimate, 2),
" (",
round(LL, 2),
", ",
round(UL, 2),
")"))) %>%
select(Parameter, Std_regression) %>%
rename(`Standard regression` = Std_regression)
rownames(std.regression.res) = NULL
(table2 = binary.res$results.df %>%
mutate(riskCommunicator = paste0(format(round(Estimate, 2), 2),
" (",
format(round(`2.5% CL`, 2), 2),
", ",
format(round(`97.5% CL`, 2), 2),
")"),
riskCommunicator = ifelse(Parameter == "Number needed to treat/harm",
round(Estimate, 2), riskCommunicator)) %>%
select(Parameter, riskCommunicator) %>%
left_join(std.regression.res, by = "Parameter"))| Parameter | riskCommunicator | Standard regression |
|---|---|---|
| Risk Difference | 0.29 (0.20, 0.39) | NA |
| Risk Ratio | 1.70 (1.49, 1.97) | 1.49 (1.33, 1.66) |
| Odds Ratio | 4.55 (2.78, 8.86) | 4.55 (2.66, 7.78) |
| Number needed to treat/harm | 3.48 | NA |
Rate outcome example
Research question: what is the effect of having diabetes at the beginning of the study on the rate of cardiovascular disease or death due to any cause?
Here, we will estimate the rate difference and rate ratio, adjusting
for patient’s age, sex, body mass index (BMI), smoking status (current
smoker or not), and prevalence of hypertension (if they are hypertensive
or not at baseline). We have included timeout as the
offset and a rate.multiplier of
365.25*100 so that the estimates are returned with units of
100 person-years. Poisson regression is used as the underlying
parametric model for g-computation. (Note: for overdispersed count/rate
outcomes, the negative binomial distribution can be specified by setting
outcome.type to “count_nb” or
“rate_nb”.)
## Modify the dataset to change the variable cvd_dth from a factor
## to a numeric variable since the outcome for Poisson
## regression must be numeric.
cvdd.t <- cvdd %>%
dplyr::mutate(cvd_dth = as.numeric(as.character(cvd_dth)),
timeout = as.numeric(timeout))
set.seed(6534)
rate.res <- gComp(data = cvdd.t,
Y = "cvd_dth",
X = "DIABETES",
Z = c("AGE", "SEX", "BMI", "CURSMOKE", "PREVHYP"),
outcome.type = "rate",
rate.multiplier = 365.25*100,
offset = "timeout",
R = 200)
rate.res
#> Formula:
#> cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE + PREVHYP + offset(log(timeout_adj))
#>
#> Parameter estimates:
#> DIABETES1_v._DIABETES0 Estimate (95% CI)
#> Incidence Rate Difference 2.189 (1.498, 3.103)
#> Incidence Rate Ratio 1.913 (1.615, 2.324)Rate outcome with subgroups example
Research question: what is the effect of having diabetes at the beginning of the study on the rate of cardiovascular disease or death due to any cause, stratified by sex?
Here, we will estimate the same effects above, but in subgroups defined by sex.
rate.res.subgroup <- gComp(data = cvdd.t,
Y = "cvd_dth",
X = "DIABETES",
Z = c("AGE", "SEX", "BMI", "CURSMOKE", "PREVHYP"),
subgroup = "SEX",
outcome.type = "rate",
rate.multiplier = 365.25*100,
offset = "timeout",
R = 200)
rate.res.subgroup
#> Formula:
#> cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE + PREVHYP + DIABETES:SEX + offset(log(timeout_adj))
#>
#> Parameter estimates:
#> DIABETES1_v._DIABETES0_SEX0 Estimate (95% CI)
#> Incidence Rate Difference 2.488 (1.260, 3.879)
#> Incidence Rate Ratio 1.794 (1.407, 2.243)
#> DIABETES1_v._DIABETES0_SEX1 Estimate (95% CI)
#> Incidence Rate Difference 1.918 (0.990, 3.286)
#> Incidence Rate Ratio 2.044 (1.552, 2.773)The results.df component of the gComp
function output is formatted as a data.frame. This makes it very easy to
immediately plot the results using ggplot2 or your
favorite R plotting functionality. Here’s an example for plotting the
results of the different subgroups (sexes) for the rate example
above.
# Saving the output and modifying the labels of the SEX variable to specify
# male/female instead of 0/1
# Also adding a new variable to show the line indicating no difference found
# (0 for rate difference, 1 for rate ratio)
df = rate.res.subgroup$results.df %>%
mutate(Subgroup = ifelse(Subgroup == "SEX0", "Male", "Female"),
hline = ifelse(Parameter == "Incidence Rate Ratio", 1, 0))
ggplot(df, aes(x = Subgroup, y = Estimate)) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = `2.5% CL`, ymax = `97.5% CL`),
width = 0.2) +
facet_wrap(~Parameter) +
theme_bw() +
labs(x = "", color = "") +
geom_hline(aes(yintercept = hline),
color = "red",
linetype = "dashed",
alpha = 0.3) 
Let’s make a figure comparing the results we got above using riskCommunicator with those we get using standard regression models for this rate example.
First, we need to get the covariate-conditional estimates using standard Poisson regression.
# Standard Poisson regression (spr) for the rate question, across both sexes
spr.rate = glm(
formula = cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE + PREVHYP +
offset(log(timeout+0.001)),
data = cvdd.t,
family = "poisson"
)
# get the parameter estimate and CI from the model object
df.spr.rate = as.data.frame(
exp(cbind(Estimate = coef(spr.rate), confint.default(spr.rate, level = 0.95)))
) %>%
rename(`2.5% CL` = `2.5 %`, `97.5% CL` = `97.5 %`) %>%
filter(rownames(.) == "DIABETES1") %>%
mutate(Subgroup = "All")
# Standard Poisson regression (spr) for the rate question, by subgroup (SEX)
spr.rate.subgroup = glm(
formula = cvd_dth ~ DIABETES + AGE + SEX + BMI + CURSMOKE + PREVHYP +
DIABETES*SEX + offset(log(timeout+0.001)),
data = cvdd.t,
family = "poisson"
)
# Get the variance-covariance matrix so we can calculate standard errors
se.subgroup = vcov(spr.rate.subgroup)
# Get estimates and CIs
df.spr.rate.subgroup = data.frame(
Subgroup = c("Male", "Female"),
raw.est = c(coef(spr.rate.subgroup)[2],
coef(spr.rate.subgroup)[2] + coef(spr.rate.subgroup)[8]),
SE = c(sqrt(se.subgroup[2,2]),
sqrt(se.subgroup[2,2] + se.subgroup[8,8] + 2*se.subgroup[2,8]))) %>%
mutate(Estimate = exp(raw.est),
`2.5% CL` = exp(raw.est - 1.96 * SE),
`97.5% CL` = exp(raw.est + 1.96 * SE))
# Combine the results from the subgroup and full model into a single data.frame
combined.std.reg = df.spr.rate %>%
bind_rows(df.spr.rate.subgroup %>%
select(Subgroup, Estimate:`97.5% CL`)) %>%
mutate(Parameter = "Incidence Rate Ratio",
model = "Standard Poisson Regression")Now, we can plot the same figure shown in the manuscript.
# Combine the riskCommunicator results with the standard Poisson regression results
df.combined = rate.res$results.df %>%
mutate(Subgroup = "All") %>%
bind_rows(df) %>%
mutate(model = "riskCommunicator") %>%
select(-Outcome, -Comparison) %>%
bind_rows(combined.std.reg) %>%
mutate(hline = ifelse(Parameter == "Incidence Rate Ratio", 1, 0))
rate.diff = ggplot(df.combined %>%
filter(Parameter == "Incidence Rate Difference"),
aes(x = Subgroup, y = Estimate, color = model)) +
geom_point(size = 2, position = position_dodge(width = .5)) +
geom_errorbar(aes(ymin = `2.5% CL`, ymax = `97.5% CL`),
width = 0.2,
position = position_dodge(width = .5)) +
scale_color_manual(values = c("#481567FF", "#3CBB75FF")) +
theme_bw() +
labs(x = "",
y = str_wrap('Incidence rate difference of
cardiovascular disease or death
(cases/100 person-years)', width = 32),
color = "") +
geom_hline(aes(yintercept = hline),
color = "red",
linetype = "dashed",
alpha = 0.3) +
theme(legend.position = "none")
rate.ratio = ggplot(df.combined %>%
filter(Parameter == "Incidence Rate Ratio"),
aes(x = Subgroup, y = Estimate, color = model)) +
geom_point(size = 2, position = position_dodge(width = .5)) +
geom_errorbar(aes(ymin = `2.5% CL`, ymax = `97.5% CL`),
width = 0.2,
position = position_dodge(width = .5)) +
scale_y_continuous(trans = "log2") +
scale_color_manual(values = c("#481567FF", "#3CBB75FF")) +
theme_bw() +
labs(x = "",
y = str_wrap('Incidence rate ratio of
cardiovascular disease or death
(shown on natural log scale)', width = 32),
color = "") +
geom_hline(aes(yintercept = hline),
color = "red",
linetype = "dashed",
alpha = 0.3) +
theme(legend.position = "bottom")
ggarrange(rate.ratio, rate.diff, ncol = 2, common.legend = T, legend = "bottom",
labels = c("A", "B"), widths = c(1, 1))
sessionInfo()
#> R version 4.2.0 (2022-04-22)
#> Platform: x86_64-apple-darwin17.0 (64-bit)
#> Running under: macOS Catalina 10.15.7
#>
#> Matrix products: default
#> BLAS: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
#> LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib
#>
#> locale:
#> [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets
#> [6] methods base
#>
#> other attached packages:
#> [1] ggpubr_0.4.0 sandwich_3.0-1
#> [3] formatR_1.12 printr_0.2
#> [5] forcats_0.5.1 stringr_1.4.0
#> [7] dplyr_1.0.9 purrr_0.3.4
#> [9] readr_2.1.2 tidyr_1.2.0
#> [11] tibble_3.1.7 ggplot2_3.3.6
#> [13] tidyverse_1.3.1 riskCommunicator_1.0.1
#>
#> loaded via a namespace (and not attached):
#> [1] lattice_0.20-45 lubridate_1.8.0 zoo_1.8-10
#> [4] assertthat_0.2.1 digest_0.6.29 utf8_1.2.2
#> [7] R6_2.5.1 cellranger_1.1.0 backports_1.4.1
#> [10] reprex_2.0.1 evaluate_0.15 highr_0.9
#> [13] httr_1.4.3 pillar_1.7.0 rlang_1.0.2
#> [16] readxl_1.4.0 rstudioapi_0.13 car_3.0-13
#> [19] jquerylib_0.1.4 rmarkdown_2.14 labeling_0.4.2
#> [22] munsell_0.5.0 broom_0.8.0 compiler_4.2.0
#> [25] modelr_0.1.8 xfun_0.31 pkgconfig_2.0.3
#> [28] htmltools_0.5.2 tidyselect_1.1.2 gridExtra_2.3
#> [31] codetools_0.2-18 fansi_1.0.3 crayon_1.5.1
#> [34] tzdb_0.3.0 dbplyr_2.1.1 withr_2.5.0
#> [37] MASS_7.3-57 grid_4.2.0 jsonlite_1.8.0
#> [40] gtable_0.3.0 lifecycle_1.0.1 DBI_1.1.2
#> [43] magrittr_2.0.3 scales_1.2.0 cli_3.3.0
#> [46] stringi_1.7.6 carData_3.0-5 farver_2.1.0
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#> [67] knitr_1.39 haven_2.5.0 sass_0.4.1