19 Univariate and multivariable regression

This page demonstrates the use of base R regression functions such as glm() and the gtsummary package to look at associations between variables (e.g. odds ratios, risk ratios and hazard ratios). It also uses functions like tidy() from the broom package to clean-up regression outputs.

  1. Univariate: two-by-two tables
  2. Stratified: mantel-haenszel estimates
  3. Multivariable: variable selection, model selection, final table
  4. Forest plots

For Cox proportional hazard regression, see the Survival analysis page.

NOTE: We use the term multivariable to refer to a regression with multiple explanatory variables. In this sense a multivariate model would be a regression with several outcomes - see this editorial for detail

19.1 Preparation

Load packages

This code chunk shows the loading of packages required for the analyses. In this handbook we emphasize p_load() from pacman, which installs the package if necessary and loads it for use. You can also load installed packages with library() from base R. See the page on R basics for more information on R packages.

pacman::p_load(
  rio,          # File import
  here,         # File locator
  tidyverse,    # data management + ggplot2 graphics, 
  stringr,      # manipulate text strings 
  purrr,        # loop over objects in a tidy way
  gtsummary,    # summary statistics and tests 
  broom,        # tidy up results from regressions
  lmtest,       # likelihood-ratio tests
  parameters,   # alternative to tidy up results from regressions
  see          # alternative to visualise forest plots
  )

Import data

We import the dataset of cases from a simulated Ebola epidemic. If you want to follow along, click to download the “clean” linelist (as .rds file). Import your data with the import() function from the rio package (it accepts many file types like .xlsx, .rds, .csv - see the Import and export page for details).

# import the linelist
linelist <- import("linelist_cleaned.rds")

The first 50 rows of the linelist are displayed below.

Clean data

Store explanatory variables

We store the names of the explanatory columns as a character vector. This will be referenced later.

## define variables of interest 
explanatory_vars <- c("gender", "fever", "chills", "cough", "aches", "vomit")

Convert to 1’s and 0’s

Below we convert the explanatory columns from “yes”/“no”, “m”/“f”, and “dead”/“alive” to 1 / 0, to cooperate with the expectations of logistic regression models. To do this efficiently, used across() from dplyr to transform multiple columns at one time. The function we apply to each column is case_when() (also dplyr) which applies logic to convert specified values to 1’s and 0’s. See sections on across() and case_when() in the Cleaning data and core functions page).

Note: the “.” below represents the column that is being processed by across() at that moment.

## convert dichotomous variables to 0/1 
linelist <- linelist %>%  
  mutate(across(                                      
    .cols = all_of(c(explanatory_vars, "outcome")),  ## for each column listed and "outcome"
    .fns = ~case_when(                              
      . %in% c("m", "yes", "Death")   ~ 1,           ## recode male, yes and death to 1
      . %in% c("f", "no",  "Recover") ~ 0,           ## female, no and recover to 0
      TRUE                            ~ NA_real_)    ## otherwise set to missing
    )
  )

Drop rows with missing values

To drop rows with missing values, can use the tidyr function drop_na(). However, we only want to do this for rows that are missing values in the columns of interest.

The first thing we must to is make sure our explanatory_vars vector includes the column age (age would have produced an error in the previous case_when() operation, which was only for dichotomous variables). Then we pipe the linelist to drop_na() to remove any rows with missing values in the outcome column or any of the explanatory_vars columns.

Before running the code, the number of rows in the linelist is nrow(linelist).

## add in age_category to the explanatory vars 
explanatory_vars <- c(explanatory_vars, "age_cat")

## drop rows with missing information for variables of interest 
linelist <- linelist %>% 
  drop_na(any_of(c("outcome", explanatory_vars)))

The number of rows remaining in linelist is nrow(linelist).

19.2 Univariate

Just like in the page on Descriptive tables, your use case will determine which R package you use. We present two options for doing univariate analysis:

  • Use functions available in base R to quickly print results to the console. Use the broom package to tidy up the outputs.
  • Use the gtsummary package to model and get publication-ready outputs

base R

Linear regression

The base R function lm() perform linear regression, assessing the relationship between numeric response and explanatory variables that are assumed to have a linear relationship.

Provide the equation as a formula, with the response and explanatory column names separated by a tilde ~. Also, specify the dataset to data =. Define the model results as an R object, to use later.

lm_results <- lm(ht_cm ~ age, data = linelist)

You can then run summary() on the model results to see the coefficients (Estimates), P-value, residuals, and other measures.

summary(lm_results)
## 
## Call:
## lm(formula = ht_cm ~ age, data = linelist)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -128.579  -15.854    1.177   15.887  175.483 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  69.9051     0.5979   116.9   <2e-16 ***
## age           3.4354     0.0293   117.2   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 23.75 on 4165 degrees of freedom
## Multiple R-squared:  0.7675, Adjusted R-squared:  0.7674 
## F-statistic: 1.375e+04 on 1 and 4165 DF,  p-value: < 2.2e-16

Alternatively you can use the tidy() function from the broom package to pull the results in to a table. What the results tell us is that for each year increase in age the height increases by 3.5 cm and this is statistically significant.

tidy(lm_results)
## # A tibble: 2 x 5
##   term        estimate std.error statistic p.value
##   <chr>          <dbl>     <dbl>     <dbl>   <dbl>
## 1 (Intercept)    69.9     0.598       117.       0
## 2 age             3.44    0.0293      117.       0

You can then also use this regression to add it to a ggplot, to do this we first pull the points for the observed data and the fitted line in to one data frame using the augment() function from broom.

## pull the regression points and observed data in to one dataset
points <- augment(lm_results)

## plot the data using age as the x-axis 
ggplot(points, aes(x = age)) + 
  ## add points for height 
  geom_point(aes(y = ht_cm)) + 
  ## add your regression line 
  geom_line(aes(y = .fitted), colour = "red")

It is also possible to add a simple linear regression straight straight in ggplot using the geom_smooth() function.

## add your data to a plot 
 ggplot(linelist, aes(x = age, y = ht_cm)) + 
  ## show points
  geom_point() + 
  ## add a linear regression 
  geom_smooth(method = "lm", se = FALSE)
## `geom_smooth()` using formula 'y ~ x'

See the Resource section at the end of this chapter for more detailed tutorials.

Logistic regression

The function glm() from the stats package (part of base R) is used to fit Generalized Linear Models (GLM).

glm() can be used for univariate and multivariable logistic regression (e.g. to get Odds Ratios). Here are the core parts:

# arguments for glm()
glm(formula, family, data, weights, subset, ...)
  • formula = The model is provided to glm() as an equation, with the outcome on the left and explanatory variables on the right of a tilde ~.
  • family = This determines the type of model to run. For logistic regression, use family = "binomial", for poisson use family = "poisson". Other examples are in the table below.
  • data = Specify your data frame

If necessary, you can also specify the link function via the syntax family = familytype(link = "linkfunction")). You can read more in the documentation about other families and optional arguments such as weights = and subset = (?glm).

Family Default link function
"binomial" (link = "logit")
"gaussian" (link = "identity")
"Gamma" (link = "inverse")
"inverse.gaussian" (link = "1/mu^2")
"poisson" (link = "log")
"quasi" (link = "identity", variance = "constant")
"quasibinomial" (link = "logit")
"quasipoisson" (link = "log")

When running glm() it is most common to save the results as a named R object. Then you can print the results to your console using summary() as shown below, or perform other operations on the results (e.g. exponentiate).

If you need to run a negative binomial regression you can use the MASS package; the glm.nb() uses the same syntax as glm(). For a walk-through of different regressions, see the UCLA stats page.

Univariate glm()

In this example we are assessing the association between different age categories and the outcome of death (coded as 1 in the Preparation section). Below is a univariate model of outcome by age_cat. We save the model output as model and then print it with summary() to the console. Note the estimates provided are the log odds and that the baseline level is the first factor level of age_cat (“0-4”).

model <- glm(outcome ~ age_cat, family = "binomial", data = linelist)
summary(model)
## 
## Call:
## glm(formula = outcome ~ age_cat, family = "binomial", data = linelist)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -1.339  -1.278   1.024   1.080   1.354  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)   
## (Intercept)   0.233738   0.072805   3.210  0.00133 **
## age_cat5-9   -0.062898   0.101733  -0.618  0.53640   
## age_cat10-14  0.138204   0.107186   1.289  0.19726   
## age_cat15-19 -0.005565   0.113343  -0.049  0.96084   
## age_cat20-29  0.027511   0.102133   0.269  0.78765   
## age_cat30-49  0.063764   0.113771   0.560  0.57517   
## age_cat50-69 -0.387889   0.259240  -1.496  0.13459   
## age_cat70+   -0.639203   0.915770  -0.698  0.48518   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 5712.4  on 4166  degrees of freedom
## Residual deviance: 5705.1  on 4159  degrees of freedom
## AIC: 5721.1
## 
## Number of Fisher Scoring iterations: 4

To alter the baseline level of a given variable, ensure the column is class Factor and move the desired level to the first position with fct_relevel() (see page on Factors). For example, below we take column age_cat and set “20-29” as the baseline before piping the modified data frame into glm().

linelist %>% 
  mutate(age_cat = fct_relevel(age_cat, "20-29", after = 0)) %>% 
  glm(formula = outcome ~ age_cat, family = "binomial") %>% 
  summary()
## 
## Call:
## glm(formula = outcome ~ age_cat, family = "binomial", data = .)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -1.339  -1.278   1.024   1.080   1.354  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.26125    0.07163   3.647 0.000265 ***
## age_cat0-4   -0.02751    0.10213  -0.269 0.787652    
## age_cat5-9   -0.09041    0.10090  -0.896 0.370220    
## age_cat10-14  0.11069    0.10639   1.040 0.298133    
## age_cat15-19 -0.03308    0.11259  -0.294 0.768934    
## age_cat30-49  0.03625    0.11302   0.321 0.748390    
## age_cat50-69 -0.41540    0.25891  -1.604 0.108625    
## age_cat70+   -0.66671    0.91568  -0.728 0.466546    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 5712.4  on 4166  degrees of freedom
## Residual deviance: 5705.1  on 4159  degrees of freedom
## AIC: 5721.1
## 
## Number of Fisher Scoring iterations: 4

Printing results

For most uses, several modifications must be made to the above outputs. The function tidy() from the package broom is convenient for making the model results presentable.

Here we demonstrate how to combine model outputs with a table of counts.

  1. Get the exponentiated log odds ratio estimates and confidence intervals by passing the model to tidy() and setting exponentiate = TRUE and conf.int = TRUE.
model <- glm(outcome ~ age_cat, family = "binomial", data = linelist) %>% 
  tidy(exponentiate = TRUE, conf.int = TRUE) %>%        # exponentiate and produce CIs
  mutate(across(where(is.numeric), round, digits = 2))  # round all numeric columns

Below is the outputted tibble model:

  1. Combine these model results with a table of counts. Below, we create the a counts cross-table with the tabyl() function from janitor, as covered in the Descriptive tables page.
counts_table <- linelist %>% 
  janitor::tabyl(age_cat, outcome)

Here is what this counts_table data frame looks like:

Now we can bind the counts_table and the model results together horizontally with bind_cols() (dplyr). Remember that with bind_cols() the rows in the two data frames must be aligned perfectly. In this code, because we are binding within a pipe chain, we use . to represent the piped object counts_table as we bind it to model. To finish the process, we use select() to pick the desired columns and their order, and finally apply the base R round() function across all numeric columns to specify 2 decimal places.

combined <- counts_table %>%           # begin with table of counts
  bind_cols(., model) %>%              # combine with the outputs of the regression 
  select(term, 2:3, estimate,          # select and re-order cols
         conf.low, conf.high, p.value) %>% 
  mutate(across(where(is.numeric), round, digits = 2)) ## round to 2 decimal places

Here is what the combined data frame looks like, printed nicely as an image with a function from flextable. The Tables for presentation explains how to customize such tables with flextable, or or you can use numerous other packages such as knitr or GT.

combined <- combined %>% 
  flextable::qflextable()

Looping multiple univariate models

Below we present a method using glm() and tidy() for a more simple approach, see the section on gtsummary.

To run the models on several exposure variables to produce univariate odds ratios (i.e. not controlling for each other), you can use the approach below. It uses str_c() from stringr to create univariate formulas (see Characters and strings), runs the glm() regression on each formula, passes each glm() output to tidy() and finally collapses all the model outputs together with bind_rows() from tidyr. This approach uses map() from the package purrr to iterate - see the page on Iteration, loops, and lists for more information on this tool.

  1. Create a vector of column names of the explanatory variables. We already have this as explanatory_vars from the Preparation section of this page.

  2. Use str_c() to create multiple string formulas, with outcome on the left, and a column name from explanatory_vars on the right. The period . substitutes for the column name in explanatory_vars.

explanatory_vars %>% str_c("outcome ~ ", .)
## [1] "outcome ~ gender"  "outcome ~ fever"   "outcome ~ chills"  "outcome ~ cough"   "outcome ~ aches"   "outcome ~ vomit"   "outcome ~ age_cat"
  1. Pass these string formulas to map() and set ~glm() as the function to apply to each input. Within glm(), set the regression formula as as.formula(.x) where .x will be replaced by the string formula defined in the step above. map() will loop over each of the string formulas, running regressions for each one.

  2. The outputs of this first map() are passed to a second map() command, which applies tidy() to the regression outputs.

  3. Finally the output of the second map() (a list of tidied data frames) is condensed with bind_rows(), resulting in one data frame with all the univariate results.

models <- explanatory_vars %>%       # begin with variables of interest
  str_c("outcome ~ ", .) %>%         # combine each variable into formula ("outcome ~ variable of interest")
  
  # iterate through each univariate formula
  map(                               
    .f = ~glm(                       # pass the formulas one-by-one to glm()
      formula = as.formula(.x),      # within glm(), the string formula is .x
      family = "binomial",           # specify type of glm (logistic)
      data = linelist)) %>%          # dataset
  
  # tidy up each of the glm regression outputs from above
  map(
    .f = ~tidy(
      .x, 
      exponentiate = TRUE,           # exponentiate 
      conf.int = TRUE)) %>%          # return confidence intervals
  
  # collapse the list of regression outputs in to one data frame
  bind_rows() %>% 
  
  # round all numeric columns
  mutate(across(where(is.numeric), round, digits = 2))

This time, the end object models is longer because it now represents the combined results of several univariate regressions. Click through to see all the rows of model.

As before, we can create a counts table from the linelist for each explanatory variable, bind it to models, and make a nice table. We begin with the variables, and iterate through them with map(). We iterate through a user-defined function which involves creating a counts table with dplyr functions. Then the results are combined and bound with the models model results.

## for each explanatory variable
univ_tab_base <- explanatory_vars %>% 
  map(.f = 
    ~{linelist %>%                ## begin with linelist
        group_by(outcome) %>%     ## group data set by outcome
        count(.data[[.x]]) %>%    ## produce counts for variable of interest
        pivot_wider(              ## spread to wide format (as in cross-tabulation)
          names_from = outcome,
          values_from = n) %>% 
        drop_na(.data[[.x]]) %>%         ## drop rows with missings
        rename("variable" = .x) %>%      ## change variable of interest column to "variable"
        mutate(variable = as.character(variable))} ## convert to character, else non-dichotomous (categorical) variables come out as factor and cant be merged
      ) %>% 
  
  ## collapse the list of count outputs in to one data frame
  bind_rows() %>% 
  
  ## merge with the outputs of the regression 
  bind_cols(., models) %>% 
  
  ## only keep columns interested in 
  select(term, 2:3, estimate, conf.low, conf.high, p.value) %>% 
  
  ## round decimal places
  mutate(across(where(is.numeric), round, digits = 2))

Below is what the data frame looks like. See the page on Tables for presentation for ideas on how to further convert this table to pretty HTML output (e.g. with flextable).

gtsummary package

Below we present the use of tbl_uvregression() from the gtsummary package. Just like in the page on Descriptive tables, gtsummary functions do a good job of running statistics and producing professional-looking outputs. This function produces a table of univariate regression results.

We select only the necessary columns from the linelist (explanatory variables and the outcome variable) and pipe them into tbl_uvregression(). We are going to run univariate regression on each of the columns we defined as explanatory_vars in the data Preparation section (gender, fever, chills, cough, aches, vomit, and age_cat).

Within the function itself, we provide the method = as glm (no quotes), the y = outcome column (outcome), specify to method.args = that we want to run logistic regression via family = binomial, and we tell it to exponentiate the results.

The output is HTML and contains the counts

univ_tab <- linelist %>% 
  dplyr::select(explanatory_vars, outcome) %>% ## select variables of interest

  tbl_uvregression(                         ## produce univariate table
    method = glm,                           ## define regression want to run (generalised linear model)
    y = outcome,                            ## define outcome variable
    method.args = list(family = binomial),  ## define what type of glm want to run (logistic)
    exponentiate = TRUE                     ## exponentiate to produce odds ratios (rather than log odds)
  )

## view univariate results table 
univ_tab
Characteristic N OR1 95% CI1 p-value
gender 4167 1.00 0.88, 1.13 >0.9
fever 4167 1.00 0.85, 1.17 >0.9
chills 4167 1.03 0.89, 1.21 0.7
cough 4167 1.15 0.97, 1.37 0.11
aches 4167 0.93 0.76, 1.14 0.5
vomit 4167 1.09 0.96, 1.23 0.2
age_cat 4167
0-4
5-9 0.94 0.77, 1.15 0.5
10-14 1.15 0.93, 1.42 0.2
15-19 0.99 0.80, 1.24 >0.9
20-29 1.03 0.84, 1.26 0.8
30-49 1.07 0.85, 1.33 0.6
50-69 0.68 0.41, 1.13 0.13
70+ 0.53 0.07, 3.20 0.5

1 OR = Odds Ratio, CI = Confidence Interval

There are many modifications you can make to this table output, such as adjusting the text labels, bolding rows by their p-value, etc. See tutorials here and elsewhere online.

19.3 Stratified

Stratified analysis is currently still being worked on for gtsummary, this page will be updated in due course.

19.4 Multivariable

For multivariable analysis, we again present two approaches:

  • glm() and tidy()
  • gtsummary package

The workflow is similar for each and only the last step of pulling together a final table is different.

Conduct multivariable

Here we use glm() but add more variables to the right side of the equation, separated by plus symbols (+).

To run the model with all of our explanatory variables we would run:

mv_reg <- glm(outcome ~ gender + fever + chills + cough + aches + vomit + age_cat, family = "binomial", data = linelist)

summary(mv_reg)
## 
## Call:
## glm(formula = outcome ~ gender + fever + chills + cough + aches + 
##     vomit + age_cat, family = "binomial", data = linelist)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -1.383  -1.279   1.029   1.078   1.346  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)
## (Intercept)   0.069054   0.131726   0.524    0.600
## gender        0.002448   0.065133   0.038    0.970
## fever         0.004309   0.080522   0.054    0.957
## chills        0.034112   0.078924   0.432    0.666
## cough         0.138584   0.089909   1.541    0.123
## aches        -0.070705   0.104078  -0.679    0.497
## vomit         0.086098   0.062618   1.375    0.169
## age_cat5-9   -0.063562   0.101851  -0.624    0.533
## age_cat10-14  0.136372   0.107275   1.271    0.204
## age_cat15-19 -0.011074   0.113640  -0.097    0.922
## age_cat20-29  0.026552   0.102780   0.258    0.796
## age_cat30-49  0.059569   0.116402   0.512    0.609
## age_cat50-69 -0.388964   0.262384  -1.482    0.138
## age_cat70+   -0.647443   0.917375  -0.706    0.480
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 5712.4  on 4166  degrees of freedom
## Residual deviance: 5700.2  on 4153  degrees of freedom
## AIC: 5728.2
## 
## Number of Fisher Scoring iterations: 4

If you want to include two variables and an interaction between them you can separate them with an asterisk * instead of a +. Separate them with a colon : if you are only specifying the interaction. For example:

glm(outcome ~ gender + age_cat * fever, family = "binomial", data = linelist)

Optionally, you can use this code to leverage the pre-defined vector of column names and re-create the above command using str_c(). This might be useful if your explanatory variable names are changing, or you don’t want to type them all out again.

## run a regression with all variables of interest 
mv_reg <- explanatory_vars %>%  ## begin with vector of explanatory column names
  str_c(collapse = "+") %>%     ## combine all names of the variables of interest separated by a plus
  str_c("outcome ~ ", .) %>%    ## combine the names of variables of interest with outcome in formula style
  glm(family = "binomial",      ## define type of glm as logistic,
      data = linelist)          ## define your dataset

Building the model

You can build your model step-by-step, saving various models that include certain explanatory variables. You can compare these models with likelihood-ratio tests using lrtest() from the package lmtest, as below:

NOTE: Using base anova(model1, model2, test = "Chisq) produces the same results

model1 <- glm(outcome ~ age_cat, family = "binomial", data = linelist)
model2 <- glm(outcome ~ age_cat + gender, family = "binomial", data = linelist)

lmtest::lrtest(model1, model2)
## Likelihood ratio test
## 
## Model 1: outcome ~ age_cat
## Model 2: outcome ~ age_cat + gender
##   #Df  LogLik Df  Chisq Pr(>Chisq)
## 1   8 -2852.6                     
## 2   9 -2852.6  1 0.0002     0.9883

Another option is to take the model object and apply the step() function from the stats package. Specify which variable selection direction you want use when building the model.

## choose a model using forward selection based on AIC
## you can also do "backward" or "both" by adjusting the direction
final_mv_reg <- mv_reg %>%
  step(direction = "forward", trace = FALSE)

You can also turn off scientific notation in your R session, for clarity:

options(scipen=999)

As described in the section on univariate analysis, pass the model output to tidy() to exponentiate the log odds and CIs. Finally we round all numeric columns to two decimal places. Scroll through to see all the rows.

mv_tab_base <- final_mv_reg %>% 
  broom::tidy(exponentiate = TRUE, conf.int = TRUE) %>%  ## get a tidy dataframe of estimates 
  mutate(across(where(is.numeric), round, digits = 2))          ## round 

Here is what the resulting data frame looks like:

Combine univariate and multivariable

Combine with gtsummary

The gtsummary package provides the tbl_regression() function, which will take the outputs from a regression (glm() in this case) and produce an nice summary table.

## show results table of final regression 
mv_tab <- tbl_regression(final_mv_reg, exponentiate = TRUE)

Let’s see the table:

mv_tab
Characteristic OR1 95% CI1 p-value
gender 1.00 0.88, 1.14 >0.9
fever 1.00 0.86, 1.18 >0.9
chills 1.03 0.89, 1.21 0.7
cough 1.15 0.96, 1.37 0.12
aches 0.93 0.76, 1.14 0.5
vomit 1.09 0.96, 1.23 0.2
age_cat
0-4
5-9 0.94 0.77, 1.15 0.5
10-14 1.15 0.93, 1.41 0.2
15-19 0.99 0.79, 1.24 >0.9
20-29 1.03 0.84, 1.26 0.8
30-49 1.06 0.85, 1.33 0.6
50-69 0.68 0.40, 1.13 0.14
70+ 0.52 0.07, 3.19 0.5

1 OR = Odds Ratio, CI = Confidence Interval

You can also combine several different output tables produced by gtsummary with the tbl_merge() function. We now combine the multivariable results with the gtsummary univariate results that we created above:

## combine with univariate results 
tbl_merge(
  tbls = list(univ_tab, mv_tab),                          # combine
  tab_spanner = c("**Univariate**", "**Multivariable**")) # set header names
Characteristic Univariate Multivariable
N OR1 95% CI1 p-value OR1 95% CI1 p-value
gender 4167 1.00 0.88, 1.13 >0.9 1.00 0.88, 1.14 >0.9
fever 4167 1.00 0.85, 1.17 >0.9 1.00 0.86, 1.18 >0.9
chills 4167 1.03 0.89, 1.21 0.7 1.03 0.89, 1.21 0.7
cough 4167 1.15 0.97, 1.37 0.11 1.15 0.96, 1.37 0.12
aches 4167 0.93 0.76, 1.14 0.5 0.93 0.76, 1.14 0.5
vomit 4167 1.09 0.96, 1.23 0.2 1.09 0.96, 1.23 0.2
age_cat 4167
0-4
5-9 0.94 0.77, 1.15 0.5 0.94 0.77, 1.15 0.5
10-14 1.15 0.93, 1.42 0.2 1.15 0.93, 1.41 0.2
15-19 0.99 0.80, 1.24 >0.9 0.99 0.79, 1.24 >0.9
20-29 1.03 0.84, 1.26 0.8 1.03 0.84, 1.26 0.8
30-49 1.07 0.85, 1.33 0.6 1.06 0.85, 1.33 0.6
50-69 0.68 0.41, 1.13 0.13 0.68 0.40, 1.13 0.14
70+ 0.53 0.07, 3.20 0.5 0.52 0.07, 3.19 0.5

1 OR = Odds Ratio, CI = Confidence Interval

Combine with dplyr

An alternative way of combining the glm()/tidy() univariate and multivariable outputs is with the dplyr join functions.

  • Join the univariate results from earlier (univ_tab_base, which contains counts) with the tidied multivariable results mv_tab_base
  • Use select() to keep only the columns we want, specify their order, and re-name them
  • Use round() with two decimal places on all the column that are class Double
## combine univariate and multivariable tables 
left_join(univ_tab_base, mv_tab_base, by = "term") %>% 
  ## choose columns and rename them
  select( # new name =  old name
    "characteristic" = term, 
    "recovered"      = "0", 
    "dead"           = "1", 
    "univ_or"        = estimate.x, 
    "univ_ci_low"    = conf.low.x, 
    "univ_ci_high"   = conf.high.x,
    "univ_pval"      = p.value.x, 
    "mv_or"          = estimate.y, 
    "mvv_ci_low"     = conf.low.y, 
    "mv_ci_high"     = conf.high.y,
    "mv_pval"        = p.value.y 
  ) %>% 
  mutate(across(where(is.double), round, 2))   
## # A tibble: 20 x 11
##    characteristic recovered  dead univ_or univ_ci_low univ_ci_high univ_pval mv_or mvv_ci_low mv_ci_high mv_pval
##    <chr>              <dbl> <dbl>   <dbl>       <dbl>        <dbl>     <dbl> <dbl>      <dbl>      <dbl>   <dbl>
##  1 (Intercept)          909  1168    1.28        1.18         1.4       0     1.07       0.83       1.39    0.6 
##  2 gender               916  1174    1           0.88         1.13      0.97  1          0.88       1.14    0.97
##  3 (Intercept)          340   436    1.28        1.11         1.48      0     1.07       0.83       1.39    0.6 
##  4 fever               1485  1906    1           0.85         1.17      0.99  1          0.86       1.18    0.96
##  5 (Intercept)         1472  1877    1.28        1.19         1.37      0     1.07       0.83       1.39    0.6 
##  6 chills               353   465    1.03        0.89         1.21      0.68  1.03       0.89       1.21    0.67
##  7 (Intercept)          272   309    1.14        0.97         1.34      0.13  1.07       0.83       1.39    0.6 
##  8 cough               1553  2033    1.15        0.97         1.37      0.11  1.15       0.96       1.37    0.12
##  9 (Intercept)         1636  2114    1.29        1.21         1.38      0     1.07       0.83       1.39    0.6 
## 10 aches                189   228    0.93        0.76         1.14      0.51  0.93       0.76       1.14    0.5 
## 11 (Intercept)          931  1144    1.23        1.13         1.34      0     1.07       0.83       1.39    0.6 
## 12 vomit                894  1198    1.09        0.96         1.23      0.17  1.09       0.96       1.23    0.17
## 13 (Intercept)          338   427    1.26        1.1          1.46      0     1.07       0.83       1.39    0.6 
## 14 age_cat5-9           365   433    0.94        0.77         1.15      0.54  0.94       0.77       1.15    0.53
## 15 age_cat10-14         273   396    1.15        0.93         1.42      0.2   1.15       0.93       1.41    0.2 
## 16 age_cat15-19         238   299    0.99        0.8          1.24      0.96  0.99       0.79       1.24    0.92
## 17 age_cat20-29         345   448    1.03        0.84         1.26      0.79  1.03       0.84       1.26    0.8 
## 18 age_cat30-49         228   307    1.07        0.85         1.33      0.58  1.06       0.85       1.33    0.61
## 19 age_cat50-69          35    30    0.68        0.41         1.13      0.13  0.68       0.4        1.13    0.14
## 20 age_cat70+             3     2    0.53        0.07         3.2       0.49  0.52       0.07       3.19    0.48

19.5 Forest plot

This section shows how to produce a plot with the outputs of your regression. There are two options, you can build a plot yourself using ggplot2 or use a meta-package called easystats (a package that includes many packages).

See the page on ggplot basics if you are unfamiliar with the ggplot2 plotting package.

ggplot2 package

You can build a forest plot with ggplot() by plotting elements of the multivariable regression results. Add the layers of the plots using these “geoms”:

  • estimates with geom_point()
  • confidence intervals with geom_errorbar()
  • a vertical line at OR = 1 with geom_vline()

Before plotting, you may want to use fct_relevel() from the forcats package to set the order of the variables/levels on the y-axis. ggplot() may display them in alpha-numeric order which would not work well for these age category values (“30” would appear before “5”). See the page on Factors for more details.

## remove the intercept term from your multivariable results
mv_tab_base %>% 
  
  #set order of levels to appear along y-axis
  mutate(term = fct_relevel(
    term,
    "vomit", "gender", "fever", "cough", "chills", "aches",
    "age_cat5-9", "age_cat10-14", "age_cat15-19", "age_cat20-29",
    "age_cat30-49", "age_cat50-69", "age_cat70+")) %>%
  
  # remove "intercept" row from plot
  filter(term != "(Intercept)") %>% 
  
  ## plot with variable on the y axis and estimate (OR) on the x axis
  ggplot(aes(x = estimate, y = term)) +
  
  ## show the estimate as a point
  geom_point() + 
  
  ## add in an error bar for the confidence intervals
  geom_errorbar(aes(xmin = conf.low, xmax = conf.high)) + 
  
  ## show where OR = 1 is for reference as a dashed line
  geom_vline(xintercept = 1, linetype = "dashed")

easystats packages

An alternative, if you do not want to the fine level of control that ggplot2 provides, is to use a combination of easystats packages.

The function model_parameters() from the parameters package does the equivalent of the broom package function tidy(). The see package then accepts those outputs and creates a default forest plot as a ggplot() object.

pacman::p_load(easystats)
## Installing package into 'C:/Users/neale/OneDrive - Neale Batra/Documents/Analytics-LAPTOP-RS5P2IBO/R/Projects/R handbook/epiRhandbook_eng/renv/library/R-4.1/x86_64-w64-mingw32'
## (as 'lib' is unspecified)
## Warning: package 'easystats' is not available for this version of R
## 
## A version of this package for your version of R might be available elsewhere,
## see the ideas at
## https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages
## Warning: unable to access index for repository http://www.stats.ox.ac.uk/pub/RWin/bin/windows/contrib/4.1:
##   cannot open URL 'http://www.stats.ox.ac.uk/pub/RWin/bin/windows/contrib/4.1/PACKAGES'
## Warning in p_install(package, character.only = TRUE, ...):
## Warning in library(package, lib.loc = lib.loc, character.only = TRUE, logical.return = TRUE, : there is no package called 'easystats'
## Warning in pacman::p_load(easystats): Failed to install/load:
## easystats
## remove the intercept term from your multivariable results
final_mv_reg %>% 
  model_parameters(exponentiate = TRUE) %>% 
  plot()

19.6 Resources

The content of this page was informed by these resources and vignettes online:

Linear regression in R

gtsummary

UCLA stats page

sthda stepwise regression