zibreg(
  formula,
  formula.p = ~1,
  data,
  family = stats::binomial(),
  offset = NULL,
  start,
  var = "hessian",
  ...
)

## Simulation
n <- 2e3
x <- runif(n,0,20)
age <- runif(n,10,30)
z0 <- rnorm(n,mean=-1+0.05*age)
z <- cut(z0,breaks=c(-Inf,-1,0,1,Inf))
p0 <- lava:::expit(model.matrix(~z+age) %*% c(-.4, -.4, 0.2, 2, -0.05))
y <- (runif(n)<lava:::tigol(-1+0.25*x-0*age))*1
u <- runif(n)<p0
y[u==0] <- 0
d <- data.frame(y=y,x=x,u=u*1,z=z,age=age)
head(d)

## Estimation
e0 <- zibreg(y~x*z,~1+z+age,data=d)
e <- zibreg(y~x,~1+z+age,data=d)
compare(e,e0)
e
PD(e0,intercept=c(1,3),slope=c(2,6))

B <- rbind(c(1,0,0,0,20),
           c(1,1,0,0,20),
           c(1,0,1,0,20),
           c(1,0,0,1,20))
prev <- summary(e,pr.contrast=B)$prevalence

x <- seq(0,100,length.out=100)
newdata <- expand.grid(x=x,age=20,z=levels(d$z))
fit <- predict(e,newdata=newdata)
plot(0,0,type="n",xlim=c(0,101),ylim=c(0,1),xlab="x",ylab="Probability(Event)")
count <- 0
for (i in levels(newdata$z)) {
  count <- count+1
  lines(x,fit[which(newdata$z==i)],col="darkblue",lty=count)
}
abline(h=prev[3:4,1],lty=3:4,col="gray")
abline(h=prev[3:4,2],lty=3:4,col="lightgray")
abline(h=prev[3:4,3],lty=3:4,col="lightgray")
legend("topleft",levels(d$z),col="darkblue",lty=seq_len(length(levels(d$z))))