fitfrail {frailtySurv}

Fit a shared frailty model

Description

Fit an extended Cox proportional hazards model with unobserved shared frailty variate and unspecified baseline hazard function, using a semiparametric estimation technique. See Gorfine et al.~(2006) and Zucker et al.~(2008) for details.

Usage

fitfrail(formula, dat, control, frailty, weights = NULL, se = FALSE, ...)

Arguments

formula

a formula object, where the lhs is the response as a Surv object and rhs contain the terms, including a cluster term for the cluster identifier

dat

data.frame that provides context for the formula

control

control parameters in the form of a fitfrail.control object

frailty

string name of the shared frailty distribution

weights

vector of cluster weights

se

logical value, whether the standard errors of the regression coefficient and frailty distribution parameter estimates should be calculated. These are obtained using the vcov.fitfrail function

...

additional arguments will be passed to fitfrail.control

Value

A fitfrail object representing the shared frailty model.

beta

the estimated regression coefficients

theta

the estimated frailty distribution parameters

Lambda

a data.frame with the estimated baseline hazard at each failure time

Lambda

a data.frame with the estimated baseline hazard at all observed times

Lambda.fun

a function of time that returns the estimated baseline

loglik

the log-likelihood

iter

the number of iterations performed

trace

the parameter trace during estimation

Convergence

The initial values of the regression coefficients are provided by coxph. Convergence is reached when either the relative reduction or absolute reduction in loglikelihood or score equations (depending on the fitmethod used) are below a threshold. If the maxit iterations are performed before convergence, then the algorithm terminates with a warning.

Author(s)

The estimation method was developed by Malka Gorfine, Li Hsu, and David Zucker; implemented by John V. Monaco.

References

Gorfine M, Zucker DM, Hsu L (2006) Prospective survival analysis with a general semiparametric shared frailty model: A pseudo full likelihood approach. Biometrika, 93(3), 735-741.

Monaco JV, Gorfine M, Hsu L (2018) General Semiparametric Shared Frailty Model: Estimation and Simulation with frailtySurv Journal of Statistical Software, 86(4), 1-42

Zucker DM, Gorfine M, Hsu L (2008) Pseudo-full likelihood estimation for prospective survival analysis with a general semiparametric shared frailty model: Asymptotic theory. Journal of Statistical Planning and Inference, 138(7), 1998-2016.

See Also

vcov.fitfrail, genfrail, simfrail, survfit, coxph

Examples

## Not run: 
# 
# Generate synthetic survival data with regression coefficients 
# beta = c(log(2),log(3)) and theta = 2, where the shared frailty 
# values from a gamma distribution with expectation 1 and variance theta.
# 
dat <- genfrail(N=300, K=2, beta=c(log(2),log(3)), 
                frailty="gamma", theta=2,
                censor.rate=0.35,
                Lambda_0=function(t, tau=4.6, C=0.01) (C*t)^tau)

# Fit a shared frailty model
fit <- fitfrail(Surv(time, status) ~ Z1 + Z2 + cluster(family), 
                dat, frailty="gamma")
fit

# The Lambda.fun function can give the estimated cumulative baseline hazard at
# any time
fit$Lambda.fun(seq(0, 100, by=10))

# Fit the DRS data, clustered on patient
data(drs)
fit.drs <- fitfrail(Surv(time, status) ~ treated + cluster(subject_id), 
                    drs, frailty="gamma")
fit.drs

## End(Not run)

# 
# A small example with c(log(2),log(3)) coefficients, Gamma(2) frailty, and
# 0.10 censorship.
# 
dat <- genfrail(N=30, K=2, beta=c(log(2),log(3)), 
                frailty="gamma", theta=2,
                censor.rate=0.10,
                Lambda_0=function(t, tau=4.6, C=0.01) (C*t)^tau)

# Fit a shared frailty model
fit <- fitfrail(Surv(time, status) ~ Z1 + Z2 + cluster(family), 
                dat, frailty="gamma", se=TRUE)
fit

# Summarize the survival curve
head(summary(fit))