Title:	Estimate Risk Ratios and Risk Differences using Regression
Version:	0.4.3
Description:	Risk ratios and risk differences are estimated using regression models that allow for binary, categorical, and continuous exposures and confounders. Implemented are marginal standardization after fitting logistic models (g-computation) with delta-method and bootstrap standard errors, Miettinen's case-duplication approach (Schouten et al. 1993, <doi:10.1002/sim.4780121808>), log-binomial (Poisson) models with empirical variance (Zou 2004, <doi:10.1093/aje/kwh090>), binomial models with starting values from Poisson models (Spiegelman and Hertzmark 2005, <doi:10.1093/aje/kwi188>), and others.
License:	GPL-3
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.2
URL:	https://stopsack.github.io/risks/
BugReports:	https://github.com/stopsack/risks/issues
Suggests:	addreg, covr, knitr, logbin, MASS, rmarkdown, testthat
Imports:	boot, bcaboot, broom, dplyr, purrr, rlang, sandwich, stats, tibble, tidyr
VignetteBuilder:	knitr
Depends:	R (≥ 3.5.0)
NeedsCompilation:	no
Packaged:	2025-05-29 06:00:01 UTC; stopsack
Author:	Konrad Stopsack [aut, cre, cph], Travis Gerke [aut]
Maintainer:	Konrad Stopsack <stopsack@post.harvard.edu>
Repository:	CRAN
Date/Publication:	2025-05-30 20:30:02 UTC

risks: Estimate risk ratios and risk differences using regression

Description

The risks package allows for fitting risk ratio and risk difference models using regression.

risks functions

riskratio: Fit risk ratio models.

riskdiff: Fit risk difference models.

summary.risks: Summarize fitted model.

tidy.risks: Tibble (data frame) of parameters, coefficients, standard errors, confidence intervals.

confint.risks: Confidence intervals.

Author(s)

Maintainer: Konrad Stopsack stopsack@post.harvard.edu (ORCID) [copyright holder]

Authors:

• Travis Gerke tgerke@mail.harvard.edu (ORCID)

See Also

https://github.com/stopsack/risks

Breast Cancer Data

Description

A cohort of women with breast cancer and complete follow-up, as used by Spiegelman and Hertzmark (Am J Epidemiol 2005) and Greenland (Am J Epidemiol 2004).

Usage

breastcancer

Format

breastcancer

A tibble with 192 rows and 3 columns:

death

Death, binary: 0, 1

stage

Cancer stage, 3 categories

receptor

Hormone receptor status, binary: "High", "Low"

...

Source

Newman SC. Biostatistical methods in epidemiology. New York, NY: Wiley, 2001, table 5.3

Confidence Intervals for Model Parameters

Description

Estimates confidence intervals for the fitted risks model. For binomial models, large-sample confidence intervals, not profile likelihood, are used.

Usage

## S3 method for class 'risks'
confint(
  object,
  parm,
  level = 0.95,
  bootrepeats = 1000,
  bootci = "bca",
  jacksd = FALSE,
  ...
)

Arguments

Value

Matrix: First column, lower bound; second column, upper bound.

Examples

confint(
  riskratio(
    formula = death ~ stage + receptor,
    data = breastcancer))

Helper function for logbin and addreg packages

Description

This is a 1:1 copy of a function from logbin that is needed but not exported by logbin and addreg.

Usage

conv.test(theta1, theta2, epsilon)

Arguments

Value

Logical.

Check Risks Class

Description

Check Risks Class

Usage

is.risks(x)

Arguments

Value

Boolean

Print model

Description

Print fitted risks model. The only change, compared to print.glm(), is the addition of the main type of model: relative risk or risk difference. If multiple models were fitted via approach = "all", then the first converged model will be printed.

Usage

## S3 method for class 'risks'
print(x, ...)

Arguments

Value

No return value, called for printing

Print model summary

Description

Print summaries for "risks" models. The printout is the same as for regular summaries of generalized linear models fit via stats::glm(), except that the type of "risks" model is printed first (e.g., "Poisson model with robust covariance") and confidence intervals for model parameters are printed at the end.

Usage

## S3 method for class 'summary.risks'
print(x, ...)

Arguments

Value

No return value, called for printing

Fit risk ratio and risk difference models

Description

riskratio and riskdiff provide a flexible interface to fitting risk ratio and risk difference models.

In cohort studies with a binary outcome, risk ratios and risk differences are typically more appropriate to report than odds ratios from logistic regression, yet such models have historically been difficult to implement in standard software.

The risks package selects an efficient way to fit risk ratio or risk difference models successfully, which will converge whenever logistic models converge. Optionally, a specific approach to model fitting can also be requested. Implemented are Poisson models with robust covariance, binomial models, logistic models with case duplication, binomial models aided in convergence by starting values obtained through Poisson models or logistic models with case duplication, binomial models fitted via combinatorial expectation maximization (optionally also with Poisson starting values), and estimates obtained via marginal standardization after logistic regression with bootstrapped or delta method for confidence intervals.

Adjusting for covariates (e.g., confounders) in the model specification (formula =) is possible.

Usage

riskratio(
  formula,
  data,
  approach = c("auto", "all", "robpoisson", "duplicate", "glm", "glm_startp",
    "glm_startd", "glm_cem", "glm_cem_startp", "margstd_boot", "margstd_delta",
    "logistic", "legacy"),
  variable = NULL,
  at = NULL,
  ...
)

riskdiff(
  formula,
  data,
  approach = c("auto", "all", "robpoisson", "glm", "glm_startp", "glm_cem",
    "glm_cem_startp", "margstd_boot", "margstd_delta", "legacy"),
  variable = NULL,
  at = NULL,
  ...
)

Arguments

Value

Fitted model. This object can be passed on to post-processing functions:

• summary.risks: an overview of results (risks-specific S3 methods: summary.robpoisson, summary.margstd_boot, summary.margstd_delta).

• tidy.risks: a tibble of coefficients and confidence intervals.

Standard post-processing functions can also be used:

• coef: a vector of coefficients.

• confint.risks: a matrix of confidence intervals

• predict.glm(type = "response"): fitted values (predictions).

• residuals: residuals.

If model fitting using all possible approaches was requested via approach = "all", then their results can be retrieved from the list all_models in the returned object (e.g., fit$all_models[[1]], fit$all_models[[2]], etc.).

Functions

• riskratio(): Fit risk ratio models

• riskdiff(): Fit risk difference models

References

Wacholder S. Binomial regression in GLIM: Estimating risk ratios and risk differences. Am J Epidemiol 1986;123:174-184. (Binomial regression models; approach = "glm")

Spiegelman D, Hertzmark E. Easy SAS Calculations for Risk or Prevalence Ratios and Differences. Am J Epidemiol 2005;162:199-200. (Binomial models fitted used starting values from Poisson models; approach = "glm_start")

Zou G. A modified Poisson regression approach to prospective studies with binary data. Am J Epidemiol 2004;159:702-706. (Poisson model with robust/sandwich standard errors; approach = "robpoisson")

Schouten EG, Dekker JM, Kok FJ, Le Cessie S, Van Houwelingen HC, Pool J, Vandenbroucke JP. Risk ratio and rate ratio estimation in case-cohort designs: hypertension and cardiovascular mortality. Stat Med 1993;12:1733–45; (Logistic model with case duplication and cluster-robust standard errors, approach = "duplicate").

Donoghoe MW, Marschner IC. logbin: An R Package for Relative Risk Regression Using the Log-Binomial Model. J Stat Softw 2018;86(9). (Log-binomial models fitted via combinatorial expectation maximization; riskratio(approach = "glm_cem")

Donoghoe MW, Marschner IC. Stable computational methods for additive binomial models with application to adjusted risk differences. Comput Stat Data Anal 2014;80:184-96. (Additive binomial models fitted via combinatorial expectation maximization; riskdiff(approach = "glm_cem"))

Localio AR, Margolis DJ, Berlin JA. Relative risks and confidence intervals were easily computed indirectly from multivariable logistic regression. J Clin Epidemiol 2007;60(9):874-82. (Marginal standardization after fitting a logistic model; approach = "margstd_boot")

Examples

data(breastcancer)  # Cohort study with binary outcome
                    # See for details: help(breastcancer)

# Risk ratio model
fit_rr <- riskratio(formula = death ~ stage + receptor, data = breastcancer)
fit_rr
summary(fit_rr)

# Risk difference model
fit_rd <- riskdiff(formula = death ~ stage + receptor, data = breastcancer)
fit_rd
summary(fit_rd)

Risk Ratios and Risk Differences from Mantel-Haenszel Estimators

Description

This function implements the Mantel-Haenszel estimators for risk ratio and risk differences for a binary or categorical exposure and one or more categorical confounder(s). Compare to estimates from regression models.

Usage

rr_rd_mantel_haenszel(
  data,
  exposure,
  outcome,
  confounders,
  estimand = c("rr", "rd"),
  conf.level = 0.95
)

Arguments

Value

Tibble in tidy format with

• term the (non-reference) exposure levels

• estimate Risk ratio (on log scale) or risk difference

• std.error, conf.low, and conf.high Square-root of M-H variance estimate, and the corresponding confidence limits (on log scale for RR)

• model always "mh"

• estimand "rr" or "rd"

References

Greenland S, Rothman KJ. Introduction to Stratified Analysis. In: Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd edn. Lippincott Williams & Wilkins: Philadelphia, PA 2008. Page 275. Risk ratios: formulae 15-18, -20, -22. Risk differences: formulae 15-18, -19, -21.

Examples

# Newman SC. Biostatistical methods in epidemiology. New York, NY:
# Wiley, 2001, table 5.3

library(tibble)  # used to set up example data
dat <- tibble(
  death    = c(rep(1, 54), rep(0, 138)),
  stage    = c(rep("Stage I", 7),  rep("Stage II", 26), rep("Stage III", 21),
               rep("Stage I", 60), rep("Stage II", 70), rep("Stage III", 8)),
  receptor = c(rep("Low", 2),  rep("High", 5),  rep("Low", 9),  rep("High", 17),
               rep("Low", 12), rep("High", 9),  rep("Low", 10), rep("High", 50),
               rep("Low", 13), rep("High", 57), rep("Low", 2),  rep("High", 6)))

# Risk difference
rr_rd_mantel_haenszel(
  data = dat,
  exposure = stage,
  outcome = death,
  confounders = receptor,
  estimand = "rd")

# Risk ratio, log scale:
result <- rr_rd_mantel_haenszel(
  data = dat,
  exposure = stage,
  outcome = death,
  confounders = receptor,
  estimand = "rr")
result

# Risk ratio, exponentiated:
result %>%
  dplyr::mutate(dplyr::across(.cols = c(estimate, conf.low, conf.high),
                              .fns = exp))

Summary for logistic model with case duplication and cluster-robust covariance

Description

Summarize results from fitting a logistic model with case duplication and cluster-robust covariance. The output is the same as for a regular summary(glm(...)), except for using cluster-robust standard errors.

Usage

## S3 method for class 'duplicate'
summary(
  object,
  dispersion = NULL,
  correlation = FALSE,
  symbolic.cor = FALSE,
  ...
)

Arguments

Value

Model summary (list)

Summary for models using marginal standardization

Description

Summary for models using marginal standardization

Usage

## S3 method for class 'margstd_boot'
summary(
  object,
  dispersion = NULL,
  correlation = FALSE,
  symbolic.cor = FALSE,
  level = 0.95,
  bootrepeats = 1000,
  bootci = c("bca", "normal", "nonpar"),
  ...
)

Arguments

Value

Model summary (list)

Summary for models using marginal standardization with delta method SEs

Description

Summary for models using marginal standardization with delta method SEs

Usage

## S3 method for class 'margstd_delta'
summary(
  object,
  dispersion = NULL,
  correlation = FALSE,
  symbolic.cor = FALSE,
  level = 0.95,
  ...
)

Arguments

Value

Model summary (list)

Generate model summary

Description

Determine type of risks model fitted and generate appropriate summary.

Usage

## S3 method for class 'risks'
summary(object, conf.int = TRUE, default = TRUE, ...)

Arguments

Details

If multiple models were fitted (approach = "all"), then the first converged model is displayed. Other models can be accessed via the returned list $all_models.

Value

Model summary (list)

Summary for Poisson model with robust covariance

Description

Summarize results from fitting a Poisson model with robust/empirical/sandwich covariance. The output is the same as for a regular summary(glm(...)), except for using robust standard errors.

Usage

## S3 method for class 'robpoisson'
summary(
  object,
  dispersion = NULL,
  correlation = FALSE,
  symbolic.cor = FALSE,
  ...
)

Arguments

Value

Model summary (list)

Tidy model summaries for risks models

Description

Obtain a tibble (data frame) with parameters, coefficients, standard errors, confidence limits, and p-values. A column with the type of model fitted is added.

Usage

## S3 method for class 'risks'
tidy(
  x,
  conf.int = TRUE,
  conf.level = 0.95,
  bootrepeats = 1000,
  bootci = c("bca", "normal", "nonpar"),
  bootverbose = FALSE,
  exponentiate = FALSE,
  default = TRUE,
  ...
)

Arguments

Details

If multiple types of models are fitted, tidy() can be used to parameters for all models at once, in one tibble. The last column of the tibble includes the name of the model. See examples.

Value

tibble

Examples

# Define example data
library(broom)  # provides tidy() function

# Fit and tidy the model
fit_rr <- riskratio(
  formula = death ~ stage + receptor,
  data = breastcancer)
tidy(fit_rr)

# Marginal standardization,
# increase number of bootstrap repeats:

fit_rr <- riskratio(
  formula = death ~ stage + receptor,
  data = breastcancer,
  approach = "margstd_boot")
tidy(fit_rr, bootrepeats = 2000)


# Multiple types of models fitted:

fit_rr <- riskratio(
  formula = death ~ stage + receptor,
  data = breastcancer,
  approach = "all")
tidy(fit_rr)