prLogistic (version 1.0)

prLogisticDelta: Estimation of Prevalence Ratios using Logistic Models and Confidence Intervals with Delta Method

Description

This function estimates prevalence ratios (PRs) and their confidence intervals using logistic models. The estimation of standard errors for PRs is obtained through use of delta method. Confidence intervals of (1-alpha)% for PRs are available for standard logistic regression and for random-effects logistic models (Santos et al, 2008). The function prLogisticDelta allows estimation of PRs using two standardization procedures: conditional or marginal (Wilcosky and Chambless, 1985).

glm, lmer, prLogisticBootCond, prLogisticBootMarg

Usage

prLogisticDelta(formula, cluster = FALSE, 
		pattern = c("conditional", "marginal"), 
		conf = 0.95, dataset, ...)

Arguments

formula

a symbolic description of the model to be fitted. The details of model specification are given below.

cluster

logical argument specifying data clustering. The default is cluster=FALSE. If data is clustered or longitudinal, it should be set to cluster=TRUE.

pattern

the standardization procedure. If pattern is missing then conditional standardization is used. The standardization is set to be the marginal if pattern="marginal".

conf

scalar or vector specifying confidence level(s) for estimation. The default is conf = 0.95.

dataset

a required data frame containing the variables named in formula

...

optional additional arguments. Currently none are used in any methods.

Value

• Returns prevalence ratio and its 95% confidence intervals.

Details

A typical form used with glm() function is included in the formula argument as response ~ terms where response is the (binary) response vector and terms is a series of terms which specifies a linear predictor for response. The prLogisticDelta assumes a binomial family associated to the model. The lmer() function is used when a vertical bar character "|" separates an expression for a model matrix and a grouping factor. Currently only binary predictors are allowed. If categorization for predictors is other than (0,1), factor() should be considered.

References

Localio AR, Margolis DJ, Berlin JA (2007). Relative risks and confidence intervals were easily computed indirectly from multivariate logistic regression. Journal of Clinical Epidemiology, 60, 874-882.

Oliveira NF, Santana VS, Lopes AA (1997). Ratio of proportions and the use of the delta method for confidence interval estimation in logistic regression. Journal of Public Health, 31(1), 90-99.

Santos CAST et al (2008). Estimating adjusted prevalence ratio in clustered cross-sectional epidemiological data. BMC Medical Research Methodology, 8 (80). Available from http://www.biomedcentral.com/1471-2280/8/80.

Wilcosky TC, Chambless LE (1985). A comparison of direct adjustment and regression adjustment of epidemiologic measures. Journal of Chronic Diseases, 34, 849-856.

See Also

glm, lmer, prLogisticBootCond,prLogisticBootMarg

Examples

### For independent observations:
# Estimates from logistic regression with conditional standardization - 
# delta method
 data("titanic", package = "prLogistic")
 attach(titanic)
 prLogisticDelta(survived~ sex + pclass + embarked, data = titanic)

# Estimates from logistic regression with marginal standardization - 
# delta method
 prLogisticDelta(survived~ sex + pclass + embarked, 
 data = titanic, pattern="marginal")


### For clustered data
# Estimates from random-effects logistic regression with conditional 
# standardization - delta method
 data("Thailand", package = "prLogistic")
 prLogisticDelta(rgi~  sex + pped + (1|schoolid), 
 data = Thailand, cluster=TRUE)


# Estimates from random-effects logistic regression with marginal 
# standardization -  delta method
prLogisticDelta(rgi ~  sex + pped + (1|schoolid), data = Thailand,
 pattern="marginal", cluster=TRUE)