There has been a long relationship between the disciplines of Epidemiology / Public Health and Biostatistics. Students frequently find introductory textbooks explaining statistical methods and the maths behind them, but how to implement those techniques in a computer is most of the time not explained.
One of the most popular statistical software’s in public health
settings is Stata
. Stata
has the advantage of
offering a solid interface with functions that can be accessed via the
use of commands or by selecting the proper input in the graphical unit
interface (GUI). Furthermore, Stata
offers “Grad
Plans” to postgraduate students, making it relatively affordable
from an economic point of view.
R
is a free alternative to Stata
. The use
of R
keeps growing; furthermore, with the relatively high
number of packages and textbooks available, it’s popularity is also
increasing.
In the case of epidemiology, there are already some good packages
available for R
, including: Epi
,
epibasix
, epiDisplay
, epiR
and
epitools
. The pubh
package does not intend to
replace any of them, but to only provide a common syntax for the most
frequent statistical analysis in epidemiology.
Most students and professionals from the disciplines of Epidemiology and Public Health analyse variables in terms of outcome, exposure and confounders. The following table shows the most common names used in the literature to characterise variables in a cause-effect relationships:
Response variable | Explanatory variable(s) |
---|---|
Outcome | Exposure and confounders |
Outcome | Predictors |
Dependent variable | Independent variable(s) |
y | x |
In R
, formulas
are used to declare
relationships between variables. Formulas are common in classic
statistical tests and in regression methods.
Formulas have the following standard syntax:
Where y
is the outcome or response variable,
x
is the exposure or predictor of interest and
my_data
specifies the name of the data frame where
x
and y
can be found.
The symbol ~
is used in R
for formulas. It
can be interpreted as depends on. In the most typical scenario,
y ~ x
means y
depends on x
or
y
is a function of x
:
y = f(x)
Using epidemiology friendly terms:
Outcome = f(Exposure)
Is worth to mention that Stata
requires for variables to
be given in the same order as in formulas: outcome first, predictors
next.
The pubh
package integrates well with other packages of
the tidyverse
which use formulas and the pipe operator
%>%
to add layers over functions. In particular,
pubh
uses ggformula
as a graphical interface
for plotting and takes advantage of variable labels from
sjlabelled
. This versatility allows it to interact also
with tables from moonBook
and effect plots from
sjPlot
.
One way to control for confounders is the use of stratification. In
Stata
stratification is done by including the
by
option as part of the command. In the
ggformula
package, one way of doing stratification is with
a formula like:
Where y
is the outcome or response variable,
x
is the exposure or predictor of interest, z
is the stratification variable (a factor) and my_data
specifies the name of the data frame where x
,
y
and z
can be found.
tidyverse
The tidyverse
has become now the standard in data
manipulation in R
. The use of the pipe function
%>%
from magrittr
allows for cleaner code.
The principle of pipes is to change the paradigm in coding. In standard
codding, when many functions are used, one goes from inner parenthesis
to outer ones.
For example if we have three functions, a common syntax would look like:
f3(f2(f1(..., data), ...), ...)
With pipes, however, the code reads top to bottom and left to right:
Most of the functions from pubh
are compatible with
pipes and the tidyverse
.
pubh
packageThe main contributions of the pubh
package to students
and professionals from the disciplines of Epidemiology and Public Health
are:
glm_coef
that displays coefficients from
most common regression analysis in a way that can be easy interpreted
and used for publications.ggformula
package, introducing
plotting functions with a relatively simple syntax.gtsummary
and
huxtable
packages. The pubh
use huxtables as
standard as they can be easily exported to html, pdf
and doc files when knitting. Tables of descriptive
statistics and of regression coefficients are generated through
functions from gtsummary
and then converted to
huxtable
objects with convenient cosmetics.Many options currently exists for displaying descriptive statistics.
I recommend the function tbl_summary
from the
gtsummary
package for constructing tables of descriptive
statistics where results don’t need to be stratified.
In Public Health and Epidemiology it is common to be interested on
comparing cohorts, categorical variables considered as exposure of
interest. The most classic example are randomised control trials where
we want to compare treatment versus control cohorts. Package
pubh
introduces the function cross_tbl
as a
wrapper to tbl_summary
from gtsummary
. The
idea is to construct these tables, in a simple way and convert them to
huxtables.
The estat
function from the pubh
package
displays descriptive statistics of continuous outcomes; it can use
labels to display nice tables. As a way to aid in the
understanding of the variability, estat
displays also the
relative dispersion (coefficient of variation) which is of particular
interest for comparing variances between groups (factors).
Some examples. We start by loading packages.
rm(list = ls())
library(tidyverse)
library(rstatix)
library(jtools)
library(pubh)
library(sjlabelled)
library(sjPlot)
theme_set(sjPlot::theme_sjplot2(base_size = 10))
theme_update(legend.position = "top")
options('huxtable.knit_print_df' = FALSE)
options('huxtable.autoformat_number_format' = list(numeric = "%5.2f"))
knitr::opts_chunk$set(comment = NA)
We will use a data set about a study of onchocerciasis in Sierra Leone.
# A tibble: 6 × 7
id mf area agegrp sex mfload lesions
<dbl> <fct> <fct> <fct> <fct> <dbl> <fct>
1 1 Infected Savannah 20-39 Female 1 No
2 2 Infected Rainforest 40+ Male 3 No
3 3 Infected Savannah 40+ Female 1 No
4 4 Not-infected Rainforest 20-39 Female 0 No
5 5 Not-infected Savannah 40+ Female 0 No
6 6 Not-infected Rainforest 20-39 Female 0 No
A two-by-two contingency table:
Oncho %>%
mutate(
mf = relevel(mf, ref = "Infected")
) %>%
copy_labels(Oncho) %>%
select(mf, area) %>%
cross_tbl(by = "area") %>%
theme_pubh(2)
Residence | |||
---|---|---|---|
Savannah, N = 548 | Rainforest, N = 754 | Overall, N = 1,302 | |
Infection | |||
Infected | 281 (51%) | 541 (72%) | 822 (63%) |
Not-infected | 267 (49%) | 213 (28%) | 480 (37%) |
Table with all descriptive statistics except id
and
mfload
:
Oncho %>%
select(- c(id, mfload)) %>%
mutate(
mf = relevel(mf, ref = "Infected")
) %>%
copy_labels(Oncho) %>%
cross_tbl(by = "area") %>%
theme_pubh(2)
Residence | |||
---|---|---|---|
Savannah, N = 548 | Rainforest, N = 754 | Overall, N = 1,302 | |
Infection | |||
Infected | 281 (51%) | 541 (72%) | 822 (63%) |
Not-infected | 267 (49%) | 213 (28%) | 480 (37%) |
Age group (years) | |||
5-9 | 93 (17%) | 109 (14%) | 202 (16%) |
10-19 | 72 (13%) | 146 (19%) | 218 (17%) |
20-39 | 208 (38%) | 216 (29%) | 424 (33%) |
40+ | 175 (32%) | 283 (38%) | 458 (35%) |
Sex | |||
Male | 247 (45%) | 369 (49%) | 616 (47%) |
Female | 301 (55%) | 385 (51%) | 686 (53%) |
Severe eye lesions? | 67 (12%) | 134 (18%) | 201 (15%) |
Next, we use a data set about blood counts of T cells from patients
in remission from Hodgkin’s disease or in remission from disseminated
malignancies. We generate the new variable Ratio
and add
labels to the variables.
data(Hodgkin)
Hodgkin <- Hodgkin %>%
mutate(Ratio = CD4/CD8) %>%
var_labels(
Ratio = "CD4+ / CD8+ T-cells ratio"
)
Hodgkin %>% head()
# A tibble: 6 × 4
CD4 CD8 Group Ratio
<int> <int> <fct> <dbl>
1 396 836 Hodgkin 0.474
2 568 978 Hodgkin 0.581
3 1212 1678 Hodgkin 0.722
4 171 212 Hodgkin 0.807
5 554 670 Hodgkin 0.827
6 1104 1335 Hodgkin 0.827
Descriptive statistics for CD4+ T cells:
N | Min | Max | Mean | Median | SD | CV | |
---|---|---|---|---|---|---|---|
CD4+ T-cells | 40.00 | 116.00 | 2415.00 | 672.62 | 528.50 | 470.49 | 0.70 |
In the previous code, the left-hand side of the formula is empty as it’s the case when working with only one variable.
For stratification, estat
recognises the following two
syntaxes:
outcome ~ exposure
~ outcome | exposure
where, outcome
is continuous and exposure
is a categorical (factor
) variable.
For example:
Disease | N | Min | Max | Mean | Median | SD | CV | |
---|---|---|---|---|---|---|---|---|
CD4+ / CD8+ T-cells ratio | Non-Hodgkin | 20.00 | 1.10 | 3.49 | 2.12 | 2.15 | 0.73 | 0.34 |
Hodgkin | 20.00 | 0.47 | 3.82 | 1.50 | 1.19 | 0.91 | 0.61 |
As before, we can report a table of descriptive statistics for all variables in the data set:
Hodgkin %>%
mutate(
Group = relevel(Group, ref = "Hodgkin")
) %>%
copy_labels(Hodgkin) %>%
cross_tbl(by = "Group", bold = FALSE) %>%
theme_pubh(2) %>%
add_footnote("Median (IQR)", font_size = 9)
Disease | |||
---|---|---|---|
Hodgkin, N = 20 | Non-Hodgkin, N = 20 | Overall, N = 40 | |
CD4+ T-cells | 682 (397, 1,131) | 433 (360, 709) | 529 (375, 916) |
CD8+ T-cells | 448 (305, 817) | 232 (150, 323) | 319 (209, 588) |
CD4+ / CD8+ T-cells ratio | 1.19 (0.83, 2.00) | 2.15 (1.58, 2.68) | 1.70 (1.13, 2.30) |
Median (IQR) |
From the descriptive statistics of Ratio we know that the relative dispersion in the Hodgkin group is almost as double as the relative dispersion in the Non-Hodgkin group.
For new users of R
it helps to have a common syntax in
most of the commands, as R
could be challenging and even
intimidating at times. We can test if the difference in variance is
statistically significant with the var.test
command, which
uses can use a formula syntax:
F test to compare two variances
data: Ratio by Group
F = 0.6294, num df = 19, denom df = 19, p-value = 0.3214
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.2491238 1.5901459
sample estimates:
ratio of variances
0.6293991
What about normality? We can look at the QQ-plots against the standard Normal distribution.
Let’s say we choose a non-parametric test to compare the groups:
Wilcoxon rank sum exact test
data: Ratio by Group
W = 298, p-value = 0.007331
alternative hypothesis: true location shift is not equal to 0
For relatively small samples (for example, less than 30 observations
per group) is a standard practice to show the actual data in dot plots
with error bars. The pubh
package offers two options to
show graphically differences in continuous outcomes among groups:
strip_error
bar_error
For our current example:
The error bars represent 95% confidence intervals around mean values.
Is relatively easy to add a line on top, to show that the two groups
are significantly different. The function gf_star
needs the
reference point on how to draw an horizontal line to display statistical
difference or to annotate a plot; in summary, gf_star
:
Thus:
\[ y1 < y2 < y3 \]
In our current example:
Hodgkin %>%
strip_error(Ratio ~ Group) %>%
gf_star(x1 = 1, y1 = 4, x2 = 2, y2 = 4.05, y3 = 4.1, "**")
For larger samples we could use bar charts with error bars. For example:
data(birthwt, package = "MASS")
birthwt <- birthwt %>%
mutate(
smoke = factor(smoke, labels = c("Non-smoker", "Smoker")),
Race = factor(race > 1, labels = c("White", "Non-white")),
race = factor(race, labels = c("White", "Afican American", "Other"))
) %>%
var_labels(
bwt = 'Birth weight (g)',
smoke = 'Smoking status',
race = 'Race',
)
Quick normality check:
The (unadjusted) \(t\)-test:
estimate estimate1 estimate2 .y. group1 group2 n1 n2 statistic p
1 283.7767 3055.696 2771.919 bwt Non-smoker Smoker 115 74 2.729886 0.007
df conf.low conf.high method alternative
1 170.1002 78.57486 488.9786 T-test two.sided
The final plot with annotation to highlight statistical difference (unadjusted):
birthwt %>%
bar_error(bwt ~ smoke) %>%
gf_star(x1 = 1, x2 = 2, y1 = 3400, y2 = 3500, y3 = 3550, "**")
Both strip_error
and bar_error
can generate
plots stratified by a third variable, for example:
The pubh
package includes the function
cosm_reg
, which adds some cosmetics to objects generated by
tbl_regression
and huxtable
. The function
multiple
helps in the analysis and visualisation of
multiple comparisons.
For simplicity, here we show the analysis of the linear model of smoking on birth weight, adjusting by race (and not by other potential confounders).
model_bwt %>%
tbl_regression() %>%
cosm_reg() %>% theme_pubh() %>%
add_footnote(get_r2(model_bwt), font_size = 9)
Variable | Beta | 95% CI | p-value |
---|---|---|---|
Smoking status | <0.001 | ||
Non-smoker | — | — | |
Smoker | -429 | -644, -214 | |
Race | <0.001 | ||
White | — | — | |
Afican American | -450 | -752, -148 | |
Other | -453 | -683, -223 | |
R2 = 0.123 |
Similar results can be obtained with the function
glm_coef
.
model_bwt %>%
glm_coef(labels = model_labels(model_bwt)) %>%
as_hux() %>% theme_pubh() %>%
set_align(everywhere, 2:3, "right") %>%
add_footnote(get_r2(model_bwt), font_size = 9)
Parameter | Coefficient | Pr(>|t|) |
---|---|---|
Constant | 3334.95 (3153.89, 3516.01) | < 0.001 |
Smoking status: Smoker | -428.73 (-643.86, -213.6) | < 0.001 |
Race: Afican American | -450.36 (-752.45, -148.27) | 0.004 |
Race: Other | -452.88 (-682.67, -223.08) | < 0.001 |
R2 = 0.123 |
In the last table of coefficients confidence intervals and p-values
for levels of race are not adjusted for multiple comparisons. We can use
functions from the emmeans
package to make the
corrections.
contrast estimate SE t.ratio p.value lower.CL upper.CL
1 Afican American - White -450.36 153.12 -2.94 0.01 -810.70 -90.02
2 Other - White -452.88 116.48 -3.89 < 0.001 -726.98 -178.77
3 Other - Afican American -2.52 160.59 -0.02 1 -380.44 375.41
The pubh
package offers two wrappers to
epiR
functions.
contingency
calls epi.2by2
and it’s used
to analyse two by two contingency tables.diag_test
calls epi.tests
to compute
statistics related with screening tests.Let’s say we want to look at the effect of ibuprofen on preventing death in patients with sepsis.
# A tibble: 6 × 9
id treat race fate apache o2del followup temp0 temp10
<dbl> <fct> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 Placebo White Dead 27 539. 50 35.2 36.6
2 2 Ibuprofen African American Alive 14 NA 720 38.7 37.6
3 3 Placebo African American Dead 33 551. 33 38.3 NA
4 4 Ibuprofen White Alive 3 1376. 720 38.3 36.4
5 5 Placebo White Alive 5 NA 720 38.6 37.6
6 6 Ibuprofen White Alive 13 1523. 720 38.2 38.2
Let’s look at the table:
Bernard %>%
mutate(
fate = relevel(fate, ref = "Dead"),
treat = relevel(treat, ref = "Ibuprofen")
) %>%
copy_labels(Bernard) %>%
select(fate, treat) %>%
cross_tbl(by = "treat") %>%
theme_pubh(2)
Treatment | |||
---|---|---|---|
Ibuprofen, N = 224 | Placebo, N = 231 | Overall, N = 455 | |
Mortality status | |||
Dead | 84 (38%) | 92 (40%) | 176 (39%) |
Alive | 140 (63%) | 139 (60%) | 279 (61%) |
For epi.2by2
we need to provide the table of counts in
the correct order, so we would type something like:
Outcome + Outcome - Total Inc risk *
Exposed + 84 140 224 37.50 (31.14 to 44.20)
Exposed - 92 139 231 39.83 (33.46 to 46.45)
Total 176 279 455 38.68 (34.18 to 43.33)
Point estimates and 95% CIs:
-------------------------------------------------------------------
Inc risk ratio 0.94 (0.75, 1.19)
Inc odds ratio 0.91 (0.62, 1.32)
Attrib risk in the exposed * -2.33 (-11.27, 6.62)
Attrib fraction in the exposed (%) -6.20 (-33.90, 15.76)
Attrib risk in the population * -1.15 (-8.88, 6.59)
Attrib fraction in the population (%) -2.96 (-15.01, 7.82)
-------------------------------------------------------------------
Uncorrected chi2 test that OR = 1: chi2(1) = 0.260 Pr>chi2 = 0.610
Fisher exact test that OR = 1: Pr>chi2 = 0.631
Wald confidence limits
CI: confidence interval
* Outcomes per 100 population units
For contingency
we only need to provide the information
in a formula:
Outcome
Predictor Dead Alive
Ibuprofen 84 140
Placebo 92 139
Outcome + Outcome - Total Inc risk *
Exposed + 84 140 224 37.50 (31.14 to 44.20)
Exposed - 92 139 231 39.83 (33.46 to 46.45)
Total 176 279 455 38.68 (34.18 to 43.33)
Point estimates and 95% CIs:
-------------------------------------------------------------------
Inc risk ratio 0.94 (0.75, 1.19)
Inc odds ratio 0.91 (0.62, 1.32)
Attrib risk in the exposed * -2.33 (-11.27, 6.62)
Attrib fraction in the exposed (%) -6.20 (-33.90, 15.76)
Attrib risk in the population * -1.15 (-8.88, 6.59)
Attrib fraction in the population (%) -2.96 (-15.01, 7.82)
-------------------------------------------------------------------
Uncorrected chi2 test that OR = 1: chi2(1) = 0.260 Pr>chi2 = 0.610
Fisher exact test that OR = 1: Pr>chi2 = 0.631
Wald confidence limits
CI: confidence interval
* Outcomes per 100 population units
Pearson's Chi-squared test with Yates' continuity correction
data: dat
X-squared = 0.17076, df = 1, p-value = 0.6794
Advantages of contingency
:
contingency
would show the results of the Fisher exact test
at the end of the output.For mhor
the formula has the following syntax:
Thus, mhor
displays the odds ratio of exposure
yes against exposure no on outcome yes for
different levels of stratum, as well as the Mantel-Haenszel
pooled odds ratio.
Example: effect of eating chocolate ice cream on being ill by sex
from the oswego
data set.
data(oswego, package = "epitools")
oswego <- oswego %>%
mutate(
ill = factor(ill, labels = c("No", "Yes")),
sex = factor(sex, labels = c("Female", "Male")),
chocolate.ice.cream = factor(chocolate.ice.cream, labels = c("No", "Yes"))
) %>%
var_labels(
ill = "Developed illness",
sex = "Sex",
chocolate.ice.cream = "Consumed chocolate ice cream"
)
OR Lower.CI Upper.CI Pr(>|z|)
sexFemale:chocolate.ice.creamYes 0.47 0.11 2.06 0.318
sexMale:chocolate.ice.creamYes 0.24 0.05 1.13 0.072
Common OR Lower CI Upper CI Pr(>|z|)
Cochran-Mantel-Haenszel: 0.35 0.12 1.01 0.085
Test for effect modification (interaction): p = 0.5434
Example: We compare the use of lung’s X-rays on the screening of TB against the gold standard test.
Freq <- c(1739, 8, 51, 22)
BCG <- gl(2, 1, 4, labels=c("Negative", "Positive"))
Xray <- gl(2, 2, labels=c("Negative", "Positive"))
tb <- data.frame(Freq, BCG, Xray)
tb <- expand_df(tb)
diag_test(BCG ~ Xray, data = tb)
Outcome + Outcome - Total
Test + 22 51 73
Test - 8 1739 1747
Total 30 1790 1820
Point estimates and 95% CIs:
--------------------------------------------------------------
Apparent prevalence * 0.04 (0.03, 0.05)
True prevalence * 0.02 (0.01, 0.02)
Sensitivity * 0.73 (0.54, 0.88)
Specificity * 0.97 (0.96, 0.98)
Positive predictive value * 0.30 (0.20, 0.42)
Negative predictive value * 1.00 (0.99, 1.00)
Positive likelihood ratio 25.74 (18.21, 36.38)
Negative likelihood ratio 0.27 (0.15, 0.50)
False T+ proportion for true D- * 0.03 (0.02, 0.04)
False T- proportion for true D+ * 0.27 (0.12, 0.46)
False T+ proportion for T+ * 0.70 (0.58, 0.80)
False T- proportion for T- * 0.00 (0.00, 0.01)
Correctly classified proportion * 0.97 (0.96, 0.98)
--------------------------------------------------------------
* Exact CIs
Using the immediate version (direct input):
Outcome + Outcome - Total
Test + 22 51 73
Test - 8 1739 1747
Total 30 1790 1820
Point estimates and 95% CIs:
--------------------------------------------------------------
Apparent prevalence * 0.04 (0.03, 0.05)
True prevalence * 0.02 (0.01, 0.02)
Sensitivity * 0.73 (0.54, 0.88)
Specificity * 0.97 (0.96, 0.98)
Positive predictive value * 0.30 (0.20, 0.42)
Negative predictive value * 1.00 (0.99, 1.00)
Positive likelihood ratio 25.74 (18.21, 36.38)
Negative likelihood ratio 0.27 (0.15, 0.50)
False T+ proportion for true D- * 0.03 (0.02, 0.04)
False T- proportion for true D+ * 0.27 (0.12, 0.46)
False T+ proportion for T+ * 0.70 (0.58, 0.80)
False T- proportion for T- * 0.00 (0.00, 0.01)
Correctly classified proportion * 0.97 (0.96, 0.98)
--------------------------------------------------------------
* Exact CIs