blm (version 2012.2.4)

lexpit: Fit a linear-expit regression model

Description

A direct probability model for regression with a binary outcome from observational data. Covariate effects are the sum of additive terms and an expit term, which allows some explanatory variables to be additive and others non-linear.

Usage

lexpit(formula.linear,formula.expit,data,na.action=na.omit,
					weights=NULL,strata=NULL,par.init=NULL,
					warn = FALSE,
					control.lexpit=list(max.iter=1000,tol=1E-7),...)

Arguments

formula.linear

formula for linear model for binary outcome, event~x1+x2+...

formula.expit

formula for expit model, linear in expit, event~z1+z2+...

data

data.frame containing the variables of formula.linear and formula.expit

na.action

function specifying how missing data should be handled, na.action

weights

Vector of weights equal to the number of observations. For population-based case-control study, weights are the inverse sampling fractions for controls.

strata

vector indicating the stratification for weighted regression with stratified observational data

par.init

list (optional) of initial parameters for linear and expit terms.

warn

logical indicator whether to include warnings during algorithm fitting. Default of FALSE suppresses warnings when testing for feasible parameters.

control.lexpit

list with control parameters for optimization algorithm

...

Additional arguments passed to constrOptim

Value

• Returns an object of class lexpit.

Details

lexpit model uses a two-stage optimization procedure. At the first stage linear terms the solutions to the maximum of a pseudo log-likelihood using a constrained optimization algorithm with an adaptive barrier method, constrOptim (Lange, 2010). The second stage maximizes the pseudo log-likelihood with respect to the expit terms using iterative reweighted least squares with an offset term for the linear component of the model.

Variance estimates are based on Taylor linearization (Shah, 2002). When weights are not NULL, it is assumed that the study is a case-control design.

References

Lange, K. (2010) Numerical Analysis for Statisticians, Springer.

Shah, BV. (2002) Calculus of Taylor deviations. Joint Statistical Meetings.

See Also

constrOptim, nlm

Examples

data(ccdata)

fit <- lexpit(y~female,y~packyear,weights = ccdata$w,
       		strata=ccdata$strata,data=ccdata)

summary(fit)

# LEXPIT MODEL FOR BLADDER CANCER RISK BY AGE 70
formula.linear <- bladder70~female * smoke_status
formula.expit <- bladder70~redmeat+fiber.centered+I(fiber.centered^2)

# ADDITIVE EFFECTS FOR GENDER AND SMOKING
# LOGISTIC EFFECTS FOR FIBER AND REDMEAT CONSUMPTION
data(aarp)

fit <- lexpit(formula.linear, formula.expit, aarp, weight=aarp$w)

# SUMMARY
summary(fit)
confint(fit)

# FITTED ABSOLUTE RISK PER 1,000 PERSONS
head(predict(fit)*1000)