# flac: FLAC - Firth's logistic regression with added covariate In logistf: Firth's Bias-Reduced Logistic Regression

## Description

flac implements Firth's bias-reduced penalized-likelihood logistic regression with added covariate.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 flac(...) ## Default S3 method: flac( formula, data, model = TRUE, control, modcontrol, weights, offset, na.action, ... ) ## S3 method for class 'logistf' flac(lfobject, data, model = TRUE, ...) 

## Arguments

 ... Further arguments passed to the method or logistf-call. formula A formula object, with the response on the left of the operator, and the model terms on the right. The response must be a vector with 0 and 1 or FALSE and TRUE for the outcome, where the higher value (1 or TRUE) is modeled. data A data frame containing the variables in the model. model If TRUE the corresponding components of the fit are returned. control Controls iteration parameter. Taken from logistf-object when specified. Otherwise default is control= logistf.control(). modcontrol Controls additional parameter for fitting. Taken from logistf-object when specified. Otherwise default is logistf.mod.control(). weights specifies case weights. Each line of the input data set is multiplied by the corresponding element of weights offset a priori known component to be included in the linear predictor na.action a function which indicates what should happen when the data contain NAs lfobject A fitted logistf object.

## Details

FLAC is a simple modification of Firth's logistic regression which provides average predicted probabilities equal to the observed proportion of events, while preserving the ability to deal with separation. It has been described by Puhr et al (2017).

The modified score equations to estimate coefficients for Firth's logistic regression can be interpreted as score equations for ML estimates for an augmented data set. This data set can be created by complementing each original observation i with two pseudo-observations weighted by h_i/2 with unchanged covariate values and with response values set to y=0 and y=1 respectively. The basic idea of FLAC is to discriminate between original and pseudo-observations in the alternative formulation of Firth's estimation as an iterative data augmentation procedure. The following generic methods are available for ' flac's output object: print, summary, coef, confint, anova, extractAIC, add1, drop1, profile, terms, nobs, predict. Furthermore, forward and backward functions perform convenient variable selection. Note that anova, extractAIC, add1, drop1, forward and backward are based on penalized likelihood ratio tests.

## Value

A flac object with components:

 coefficients The coefficients of the parameter in the fitted model. predict A vector with the predicted probability of each observation linear.predictors A vector with the linear predictor of each observation. prob The p-values of the specific parameters ci.lower The lower confidence limits of the parameter. ci.upper The upper confidence limits of the parameter. call The call object. alpha The significance level: 0.95 var The variance-covariance-matrix of the parameters. loglik A vector of the (penalized) log-likelihood of the restricted and the full models. n The number of observations. formula The formula object. augmented.data The augmented dataset used df The number of degrees of freedom in the model. method depending on the fitting method 'Penalized ML' or Standard ML'.} \item{method.ci}{the method in calculating the confidence intervals, i.e. profile likelihood' or ‘Wald’, depending on the argument pl and plconf. control a copy of the control parameters. modcontrol a copy of the modcontrol parameters. terms the model terms (column names of design matrix). model if requested (the default), the model frame used.

## Methods (by class)

• default: With formula and data

• logistf: With logistf object

## References

Puhr R, Heinze G, Nold M, Lusa L, Geroldinger A (2017). Firth's logistic regression with rare events: accurate effect estimates and predictions? Statistics in Medicine 36: 2302-2317.

logistf() for Firth's bias-Reduced penalized-likelihood logistic regression.
 1 2 3 4 5 6 7 #With formula and data: data(sex2) flac(case ~ age + oc + vic + vicl + vis + dia, sex2) #With a logistf object: lf <- logistf(formula = case ~ age + oc + vic + vicl + vis + dia, data = sex2) flac(lf, data=sex2)