Package 'prLogistic'

Title: Estimation of Prevalence Ratios via Logistic Regression Models
Description: Estimates adjusted prevalence ratios (PR) and their confidence intervals from logistic regression models, addressing the well-known limitation of odds ratios (OR) as approximations to PR in cross-sectional studies with common outcomes. Supports independent observations (glm()), clustered/multilevel data (glmer() from 'lme4'), longitudinal data via Generalised Estimating Equations (geeglm() from 'geepack'), and complex survey designs (svyglm() from 'survey'). Inference is available via the delta method (conditional and marginal standardisation) and via bootstrap (normal-approximation and percentile intervals). Continuous covariates are handled through user-specified or median-based reference values; flexible baseline specification allows any reference category to be chosen for factor predictors. Based on the methodology described in Amorim & Ospina (2021) <doi:10.1590/0001-3765202120190316>.
Authors: Raydonal Ospina [aut, cre] (ORCID: <https://orcid.org/0000-0002-9884-9090>), Leila D. Amorim [aut] (ORCID: <https://orcid.org/0000-0002-1112-2332>)
Maintainer: Raydonal Ospina <[email protected]>
License: GPL (>= 2)
Version: 2.0.2
Built: 2026-06-19 16:43:33 UTC
Source: https://github.com/cran/prLogistic

Help Index

Extract prevalence ratio point estimates

Description

Extract prevalence ratio point estimates

Usage

## S3 method for class 'prLogistic'
coef(object, ...)

Arguments

object

A prLogistic object.
...

Currently ignored.

Value

Named numeric vector of PR estimates.

Extract confidence intervals for prevalence ratios

Description

Extract confidence intervals for prevalence ratios

Usage

## S3 method for class 'prLogistic'
confint(object, parm, level, type = "percentile", ...)

Arguments

object

A prLogistic object.
parm

Ignored (all parameters returned).
level

Ignored (level is stored in the object).
type

For bootstrap objects: "normal" or "percentile".
...

Currently ignored.

Value

Numeric matrix with lower and upper bounds.

Downer Cow Survival Data

Description

Veterinary study of downer cows (cattle unable to rise after calving). The outcome is whether the animal survived to discharge.

Usage

downer

Format

A data frame with 216 rows and 5 variables:

AST

Aspartate aminotransferase (enzyme marker): 0 = normal, 1 = elevated.

CK

Creatine kinase (enzyme marker): 0 = normal, 1 = elevated.

Calving

Whether the downer condition was related to calving: 0 = No, 1 = Yes.

Myopathy

Presence of myopathy: factor with levels "No", "Yes".

Survival

Outcome: factor with levels "Died", "Survived". Binary outcome.

Source

Dohoo, I., Martin, W. & Stryhn, H. (2003). Veterinary Epidemiologic Research. AVC Inc., Prince Edward Island, Canada.

Examples

data(downer)
prop.table(table(downer$Survival))

fit <- glm(as.integer(Survival == "Survived") ~ Myopathy + AST + CK + Calving,
           family = binomial, data = downer)
prLogisticDelta(fit)

Low Birth Weight – Longitudinal Study (Salvador, Brazil)

Description

Data from a longitudinal study of 244 mothers followed during two pregnancies in Salvador, Bahia, Brazil. The outcome is whether the newborn had low birth weight (< 2500 g). The study illustrates clustered binary data (two births per mother) and is the primary motivating example in Amorim & Ospina (2021).

Usage

LBW

Format

A data frame with 488 rows and 6 variables:

ID

Mother identifier (integer).

birth

Birth order within mother: 1 or 2.

smoke

Maternal smoking during pregnancy: factor with levels "No", "Yes".

race

Maternal race: factor with levels "White", "Non-white".

age

Maternal age at delivery (years, centred).

low

Birth weight category: factor with levels "Normal" (>= 2500 g), "Low" (< 2500 g). This is the binary outcome of interest.

Details

The dataset contains repeated observations: each mother contributes two records (one per birth). Models should account for this clustering – either with a random intercept (glmer) or via GEE (geeglm).

Prevalence of low birth weight across both births: approximately 18%.

Source

Amorim, L. D. & Ospina, R. (2021). Prevalence ratio estimation using R. Anais da Academia Brasileira de Ciencias, 93(4), e20190316. doi:10.1590/0001-3765202120190316

Examples

data(LBW)
table(LBW$low, LBW$smoke)

# GEE model accounting for within-mother correlation

library(geepack)
fit_gee <- geeglm(as.integer(low == "Low") ~ smoke + race + age,
                  family = binomial, id = ID,
                  corstr = "exchangeable", data = LBW)
prLogisticGEE(fit_gee)

Forest plot of prevalence ratios

Description

Produces a simple forest plot (no external dependencies beyond base R).

Usage

## S3 method for class 'prLogistic'
plot(
  x,
  main = NULL,
  xlab = "Prevalence Ratio",
  col = "steelblue",
  ci_col = "steelblue",
  ref_line = TRUE,
  type = "percentile",
  ...
)

Arguments

x

A prLogistic object.
main

Plot title. If NULL, a default is used.
xlab

x-axis label.
col

Color for the point estimates.
ci_col

Color for the CI lines.
ref_line

Logical: draw a vertical reference line at PR = 1?
type

For bootstrap objects: "normal" or "percentile".
...

Further graphical parameters passed to plot().

Value

No return value, called for its side effect of drawing a forest plot of the prevalence ratio estimates and their confidence intervals.

Print a prLogistic object

Description

Print a prLogistic object

Usage

## S3 method for class 'prLogistic'
print(x, digits = 4, ...)

Arguments

x

A prLogistic object.
digits

Number of significant digits (default 4).
...

Currently ignored.

Value

Invisibly returns the prLogistic object x. Called for its side effect of printing a formatted summary of the prevalence ratio estimates and confidence intervals to the console.

Bootstrap CI for Prevalence Ratios – Conditional Standardisation

Description

Estimates adjusted prevalence ratios (PR) using conditional standardisation and obtains confidence intervals via bootstrap resampling (normal- approximation and percentile methods).

Usage

prLogisticBootCond(
  fit,
  data,
  conf = 0.95,
  R = 999L,
  ref_values = NULL,
  ref_continuous = c("median", "mean")
)

Arguments

fit

A fitted model object of class glm (binomial family), glmerMod (from lme4::glmer()), geeglm (from geepack::geeglm()), or svyglm (from survey::svyglm()). Must use the logit link.
data

Data frame used to fit fit. Required for bootstrapping.
conf

Numeric scalar in (0, 1): confidence level. Default 0.95.
R

Integer: number of bootstrap replicates. Default 999.
ref_values

Named list of reference values for specific predictors, e.g. list(age = 40, bmi = 25). Overrides automatic reference-value selection. For factor/dummy predictors the value should be 0 (the default) or 1.
ref_continuous

Character string: how to compute the reference value for continuous predictors when not supplied in ref_values. Either "median" (default) or "mean".

Details

At each bootstrap replicate the model is refitted on a resampled dataset and conditional PRs are computed. Two CI types are returned:

Normal

Bootstrap normal-approximation interval.

Percentile

Empirical quantiles of the bootstrap distribution.

Use confint.prLogistic() with type = "normal" or type = "percentile" to extract a single CI type.

Value

An object of class "prLogistic" with components:

table

Numeric matrix with columns Estimate, lower and upper CI.

conf

Confidence level used.

method

"delta".

standardisation

"conditional" or "marginal".

model_type

Class of the fitted model.

call

The matched call.

References

Amorim, L. D. & Ospina, R. (2021). An Acad Bras Cienc, 93(4). doi:10.1590/0001-3765202120190316

Davison, A. C. & Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press.

See Also

prLogisticDelta(), prLogisticBootMarg()

Examples

fit_glm <- glm(case ~ induced + spontaneous + parity,
               family = binomial, data = infert)

set.seed(42)
res <- prLogisticBootCond(fit_glm, data = infert, R = 199)
print(res)
plot(res)

Bootstrap CI for Prevalence Ratios – Marginal Standardisation

Description

Estimates adjusted prevalence ratios (PR) using marginal standardisation (population-averaged) and obtains confidence intervals via bootstrap resampling.

Usage

prLogisticBootMarg(
  fit,
  data,
  conf = 0.95,
  R = 999L,
  ref_values = NULL,
  ref_continuous = c("median", "mean")
)

Arguments

fit

A fitted model object of class glm (binomial family), glmerMod (from lme4::glmer()), geeglm (from geepack::geeglm()), or svyglm (from survey::svyglm()). Must use the logit link.
data

Data frame used to fit fit. Required for bootstrapping.
conf

Numeric scalar in (0, 1): confidence level. Default 0.95.
R

Integer: number of bootstrap replicates. Default 999.
ref_values

Named list of reference values for specific predictors, e.g. list(age = 40, bmi = 25). Overrides automatic reference-value selection. For factor/dummy predictors the value should be 0 (the default) or 1.
ref_continuous

Character string: how to compute the reference value for continuous predictors when not supplied in ref_values. Either "median" (default) or "mean".

Details

Marginal standardisation averages counterfactual predicted probabilities over the empirical covariate distribution, giving a population-averaged PR. At each bootstrap replicate the model is refitted and marginal PRs are recomputed.

Value

An object of class "prLogistic" with components:

table

Numeric matrix with columns Estimate, lower and upper CI.

conf

Confidence level used.

method

"delta".

standardisation

"conditional" or "marginal".

model_type

Class of the fitted model.

call

The matched call.

See Also

prLogisticDelta(), prLogisticBootCond()

Examples

fit_glm <- glm(case ~ induced + spontaneous + parity,
               family = binomial, data = infert)

set.seed(42)
res <- prLogisticBootMarg(fit_glm, data = infert, R = 199)
print(res)

Estimate Prevalence Ratios via Logistic Regression – Delta Method

Description

Estimates adjusted prevalence ratios (PR) and confidence intervals using the delta method, from a fitted logistic regression model. Supports four model types covering independent, clustered, longitudinal and complex-survey data.

Usage

prLogisticDelta(
  fit,
  standardisation = c("conditional", "marginal"),
  conf = 0.95,
  ref_values = NULL,
  ref_continuous = c("median", "mean")
)

Arguments

fit

A fitted model object of class glm (binomial family), glmerMod (from lme4::glmer()), geeglm (from geepack::geeglm()), or svyglm (from survey::svyglm()). Must use the logit link.
standardisation

Character string: "conditional" (default) or "marginal". See Details.
conf

Numeric scalar in (0, 1): confidence level. Default 0.95.
ref_values

Named list of reference values for specific predictors, e.g. list(age = 40, bmi = 25). Overrides automatic reference-value selection. For factor/dummy predictors the value should be 0 (the default) or 1.
ref_continuous

Character string: how to compute the reference value for continuous predictors when not supplied in ref_values. Either "median" (default) or "mean".

Details

Standardisation procedures

Conditional standardisation fixes all covariates at their reference values (median/mean for continuous, 0 for binary/dummy) and computes the PR for each predictor by contrasting exposed (predictor = 1) vs unexposed (predictor = 0) profiles:

PR^j=expit(β^0+β^j+∑k≠jβ^krk)expit(β^0+∑k≠jβ^krk)\widehat{PR}_j = \frac{\mathrm{expit}(\hat\beta_0 + \hat\beta_j + \sum_{k \neq j} \hat\beta_k r_k)} {\mathrm{expit}(\hat\beta_0 + \sum_{k \neq j} \hat\beta_k r_k)}

where rkr_k are the reference values of the remaining covariates.

Marginal standardisation computes counterfactual prevalences using the observed covariate distribution of the entire sample:

PR^j=n−1∑iexpit(η^i(1))n−1∑iexpit(η^i(0))\widehat{PR}_j = \frac{n^{-1}\sum_i \mathrm{expit}(\hat\eta_i^{(1)})} {n^{-1}\sum_i \mathrm{expit}(\hat\eta_i^{(0)})}

where η^i(1)\hat\eta_i^{(1)} and η^i(0)\hat\eta_i^{(0)} are the linear predictors with predictor jj set to 1 and 0, respectively.

Variance estimates use the delta method (first-order Taylor expansion) as described in Oliveira et al. (1997) and Amorim & Ospina (2021).

Baseline / reference category

By default, the reference level of each factor predictor is determined by the contrasts of the fitted model (typically the first level of the factor()). You can override this using ref_values for any predictor column present in the model matrix.

Supported model types

Class Package Use case
glm stats Independent observations
glmerMod lme4 Clustered / multilevel data
geeglm geepack Longitudinal / GEE
svyglm survey Complex survey designs

Value

An object of class "prLogistic" with components:

table

Numeric matrix with columns Estimate, lower and upper CI.

conf

Confidence level used.

method

"delta".

standardisation

"conditional" or "marginal".

model_type

Class of the fitted model.

call

The matched call.

References

Amorim, L. D. & Ospina, R. (2021). Prevalence ratio estimation using R. Anais da Academia Brasileira de Ciencias, 93(4), e20190316. doi:10.1590/0001-3765202120190316

Oliveira, N. F., Santana, V. S. & Lopes, A. A. (1997). Razoes de proporcoes e uso da regressao log?stica em estudos transversais. Revista de Sa?de P?blica, 31, 90-99.

Wilcosky, T. C. & Chambless, L. E. (1985). A comparison of direct adjustment and regression adjustment of epidemiologic measures. Journal of Chronic Diseases, 38, 849-856.

See Also

prLogisticBootCond(), prLogisticBootMarg(), prLogisticGEE(), prLogisticSurvey()

Examples

# --- Independent observations (glm) --- infert is a built-in dataset ----
# outcome: case (spontaneous abortion), prevalence ~33%
fit_glm <- glm(case ~ induced + spontaneous + parity,
               family = binomial, data = infert)

# Conditional PR (continuous covariates at median)
prLogisticDelta(fit_glm, standardisation = "conditional")

# Marginal PR
prLogisticDelta(fit_glm, standardisation = "marginal")

# Custom reference values
prLogisticDelta(fit_glm,
                standardisation = "conditional",
                ref_values = list(parity = 2))


# --- Clustered data (glmer) ---------------------------------------------
library(lme4)
fit_glmer <- glmer(case ~ induced + spontaneous + (1 | stratum),
                   family = binomial, data = infert)
prLogisticDelta(fit_glmer, standardisation = "marginal")

# --- Longitudinal / GEE -------------------------------------------------
library(geepack)
data(ohio, package = "geepack")
fit_gee <- geeglm(resp ~ smoke + age,
                  family  = binomial,
                  id      = id,
                  corstr  = "exchangeable",
                  data    = ohio)
prLogisticDelta(fit_gee, standardisation = "marginal")

# --- Complex survey design ----------------------------------------------
library(survey)
data(api, package = "survey")
dclus2 <- svydesign(id = ~dnum + snum, fpc = ~fpc1 + fpc2, data = apiclus2)
fit_svy <- svyglm(sch.wide ~ meals + stype,
                  design = dclus2, family = quasibinomial)
prLogisticDelta(fit_svy, standardisation = "conditional")

Prevalence Ratios for Longitudinal Data – GEE Models

Description

A convenience wrapper around prLogisticDelta() for models fitted with geepack::geeglm(). GEE provides population-averaged (marginal) estimates suitable for longitudinal or clustered binary outcomes.

Usage

prLogisticGEE(
  fit,
  standardisation = c("marginal", "conditional"),
  conf = 0.95,
  method = c("delta", "bootstrap"),
  data = NULL,
  R = 999L,
  ref_values = NULL,
  ref_continuous = c("median", "mean")
)

Arguments

fit

A geeglm object fitted with family = binomial and link = "logit" (or family = binomial(link = "logit")).
standardisation

Character: "marginal" (default, recommended for GEE) or "conditional".
conf

Confidence level. Default 0.95.
method

Inference method: "delta" (default) or "bootstrap".
data

Data frame (required when method = "bootstrap").
R

Number of bootstrap replicates (only used when method = "bootstrap"). Default 999L.
ref_values

Named list of reference values. See prLogisticDelta().
ref_continuous

"median" (default) or "mean".

Details

GEE accounts for within-subject correlation through a working correlation structure (corstr argument of geeglm()). Common choices:

"independence"

No correlation assumed (equivalent to GLM).

"exchangeable"

Constant correlation across time points.

"ar1"

First-order autoregressive; suitable for ordered time.

"unstructured"

Estimates all pairwise correlations freely.

The robust (sandwich) variance-covariance matrix returned by vcov() on a geeglm object is used automatically, giving valid inference even when the working correlation structure is misspecified.

Value

A "prLogistic" object. See prLogisticDelta().

References

Zeger, S. L. & Liang, K.-Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42, 121-130.

H?jsgaard, S., Halekoh, U. & Yan, J. (2006). The R package geepack for generalised estimating equations. Journal of Statistical Software, 15(2), 1-11.

Amorim, L. D. & Ospina, R. (2021). An Acad Bras Cienc, 93(4). doi:10.1590/0001-3765202120190316

See Also

prLogisticDelta(), geepack::geeglm()

Examples

library(geepack)
data(ohio, package = "geepack")

# Model respiratory symptoms over time with exchangeable correlation
fit_gee <- geeglm(
  resp  ~ smoke + age,
  family = binomial,
  id     = id,
  corstr = "exchangeable",
  data   = ohio
)

# Marginal PR (recommended for GEE)
prLogisticGEE(fit_gee)

# With bootstrap CIs (small R for a fast example; use R >= 999 in practice)
prLogisticGEE(fit_gee, method = "bootstrap", data = ohio, R = 25)

Prevalence Ratios for Complex Survey Data

Description

A convenience wrapper around prLogisticDelta() for logistic regression models fitted on complex survey data using survey::svyglm().

Usage

prLogisticSurvey(
  fit,
  standardisation = c("conditional", "marginal"),
  conf = 0.95,
  ref_values = NULL,
  ref_continuous = c("median", "mean")
)

Arguments

fit

A svyglm object fitted with family = quasibinomial (or binomial) and the logit link.
standardisation

Character: "conditional" (default) or "marginal".
conf

Confidence level. Default 0.95.
ref_values

Named list of reference values. See prLogisticDelta().
ref_continuous

"median" (default) or "mean".

Details

svyglm() incorporates sampling weights and complex design features (stratification, clustering, finite-population corrections) into parameter estimation. The design-consistent variance-covariance matrix is extracted automatically via vcov() and used in the delta-method calculations.

Note: bootstrap resampling for survey data requires design-aware resampling (e.g., survey bootstrap, balanced repeated replication). This is currently not automated; use prLogisticDelta() with a bootstrap-replicate survey design if needed.

Value

A "prLogistic" object. See prLogisticDelta().

References

Lumley, T. (2004). Analysis of complex survey samples. Journal of Statistical Software, 9(1), 1-19.

Lumley, T. (2010). Complex Surveys: A Guide to Analysis Using R. Wiley, New Jersey.

Amorim, L. D. & Ospina, R. (2021). An Acad Bras Cienc, 93(4). doi:10.1590/0001-3765202120190316

See Also

prLogisticDelta(), survey::svyglm()

Examples

library(survey)
data(api, package = "survey")

# Create binary outcome
apiclus2$target_met <- as.numeric(apiclus2$sch.wide == "Yes")

# Stratified two-stage cluster sample
dclus2 <- svydesign(
  id   = ~dnum + snum,
  fpc  = ~fpc1 + fpc2,
  data = apiclus2
)

fit_svy <- svyglm(
  target_met ~ meals + stype,
  design = dclus2,
  family = quasibinomial
)

prLogisticSurvey(fit_svy, standardisation = "conditional")
prLogisticSurvey(fit_svy, standardisation = "marginal")

Summarise a prLogistic object

Description

Summarise a prLogistic object

Usage

## S3 method for class 'prLogistic'
summary(object, ...)

Arguments

object

A prLogistic object.
...

Currently ignored.

Value

Invisibly returns the prLogistic object. Called for its side effect of printing the model call followed by the formatted estimates.

Thailand Education Study – Clustered Binary Data

Description

Data from a survey of primary school students in Thailand. The outcome is whether the student repeated a grade (rgi). Students are nested within schools, making this a clustered binary outcome dataset.

Usage

Thailand

Format

A data frame with 8582 rows and 4 variables:

schoolid

School identifier (integer). There are 411 schools.

sex

Student sex: factor with levels "Girl", "Boy".

pped

Pre-primary education: factor with levels "No", "Yes".

rgi

Repeated a grade: factor with levels "No", "Yes". Binary outcome of interest.

Details

Prevalence of grade repetition is approximately 16%, making PR a more appropriate measure than OR. The clustering by school should be accounted for with glmer or geeglm.

Source

Raudenbush, S. W. & Bryk, A. S. (2002). Hierarchical Linear Models, 2nd ed. Sage.

Amorim, L. D. & Ospina, R. (2021). An Acad Bras Cienc, 93(4). doi:10.1590/0001-3765202120190316

Examples

data(Thailand)
prop.table(table(Thailand$rgi))

# Mixed model (random intercept per school)

library(lme4)
fit_ml <- glmer(as.integer(rgi == "Yes") ~ sex + pped + (1 | schoolid),
                family = binomial, data = Thailand)
prLogisticDelta(fit_ml, standardisation = "marginal")

Titanic Passenger Survival

Description

Survival data for 1307 passengers aboard the RMS Titanic. The outcome is whether the passenger survived.

Usage

titanic

Format

A data frame with 1307 rows and 4 variables:

pclass

Passenger class: factor with levels "1", "2", "3".

survived

Survived: factor with levels "No", "Yes". Binary outcome.

sex

Sex: factor with levels "Female", "Male".

embarked

Port of embarkation: 0 = Southampton, 1 = Cherbourg/ Queenstown.

Details

Overall survival rate is approximately 38%, making this a common outcome – a setting where OR meaningfully diverges from PR.

Source

Harrell, F. E. (2001). Regression Modeling Strategies. Springer, New York.

Examples

data(titanic)
prop.table(table(titanic$survived, titanic$sex), margin = 2)

fit <- glm(as.integer(survived == "Yes") ~ sex + pclass,
           family = binomial, data = titanic)

# OR vs PR comparison
OR <- exp(coef(fit))
PR <- prLogisticDelta(fit, standardisation = "marginal")
print(PR)

Toenail Infection Trial – Longitudinal Binary Outcome

Description

Data from a randomised clinical trial comparing two oral antifungal treatments (itraconazole vs terbinafine) for toenail dermatophyte infection. Patients were measured at up to 7 visits over 18 months.

Usage

Toenail

Format

A data frame with 1908 rows and 5 variables:

ID

Patient identifier. There are 294 patients.

Response

Presence of moderate or severe onycholysis (nail separation): factor with levels "Not moderate/severe", "Moderate/severe". Binary outcome.

Treatment

Antifungal treatment: factor with levels "Itraconazole", "Terbinafine".

Month

Time since randomisation (months, continuous).

Visit

Visit number (1 to 7, integer).

Details

The dataset illustrates a longitudinal binary outcome with dropout (not all patients have 7 visits). GEE with an unstructured or exchangeable correlation is commonly used.

Source

De Backer, M. et al. (1998). Twelve weeks of continuous oral therapy for toenail onychomycosis caused by dermatophytes. Journal of the American Academy of Dermatology, 38, S57-S63.

Examples

data(Toenail)
table(Toenail$Response, Toenail$Treatment)


library(geepack)
Toenail$resp_bin <- as.integer(Toenail$Response == "Moderate/severe")
fit_gee <- geeglm(resp_bin ~ Treatment + Month,
                  family = binomial, id = ID,
                  corstr = "exchangeable", data = Toenail)
prLogisticGEE(fit_gee)

UIS Drug Treatment Study

Description

Data from the University of Massachusetts AIDS Research Unit (UMARU) Impact Study, a 5-year study comparing two residential treatment programmes for drug abuse.

Usage

UIS

Format

A data frame with 575 rows and 7 variables:

ID

Patient identifier.

Age

Age at enrolment (years, centred).

DrugUse

History of intravenous drug use: factor with levels "Short" (<= 3 years), "Long" (> 3 years).

race

Race: factor with levels "White", "Other".

trt

Treatment assignment: factor with levels "Short" (3-month), "Long" (6-month).

site

Treatment site: factor with levels "A", "B".

drugFree

Drug-free at 6 months: factor with levels "No", "Yes". Binary outcome.

Source

Hosmer, D. W. & Lemeshow, S. (2000). Applied Logistic Regression, 2nd ed. Wiley, New York.

Examples

data(UIS)
prop.table(table(UIS$drugFree))

fit <- glm(as.integer(drugFree == "Yes") ~ trt + Age + DrugUse + race + site,
           family = binomial, data = UIS)
prLogisticDelta(fit, standardisation = "conditional")