FamEvent (version 1.3)

penf: Penetrance function

Description

Calculates the penetrance for a given age, gender and mutation status based on the assumed penetrance model.

Usage

penf(est, age, sex, mut, base.dist, frailty.dist=NULL, agemin)

Arguments

est

Parameter estimates for the assumed penetrance model including the transformed baseline parameters (\(\lambda, \rho\)), regression coefficients for gender and mutation status (\(\beta_s, \beta_g\)) and a frailty parameter (\(\kappa\)) if frailty.dist is specified.

age

Vector of ages or a single value of age at which the penetrance function is evaluated.

sex

1 for male, 0 for female.

mut

1 for mutation carrier, 0 for mutation noncarrier.

base.dist

Choice of baseline hazard distribution for the penetrance function. Possible choices are "Weibull", "loglogistic", "Gompertz", "lognormal", or "gamma". Default is "Weibull".

frailty.dist

Choice of frailty distribution, either "gamma" or "lognormal", if the penetrance function is based on a shared frailty model. Otherwise, frailty.dist = NULL is set as default.

agemin

Minimum age that the pentrance function starts.

Value

Returns a penetrance value evaluated at given age, gender and mutation status based on the specified penetrance model.

Details

The penetrance function is defined as the probability of developing disease by time \(t\) given gender (\(x_s\)) and mutation status (\(x_g\)), $$ P(T < t|x_s, x_g) = 1 - S(t; x_s, x_g) , $$ where \(S(t; x_s, x_g)\) is the survival distribution based on a proportional hazards model with a specified baseline hazard distribution or based on a shared frailty mode with specified frailty and baseline hazard distributions.

Proportional hazards model:

$$ h(t|x_s, x_g) = h_0(t) \exp(\beta_s x_s+\beta_g x_g) $$ where \(h_0(t)\) is the baseline hazards function specified by base.dist, which depends on the shape and scale parameters, \(\lambda\) and \(\rho\); \(x_s\) indicates male (1) and female (0) and \(x_g\) indicates carrier (1) or non-carrier (0) of a gene of interest (major gene).

Shared frailty model:

$$ h(t|z, x_s, x_g) = z h_0(t) \exp(\beta_s x_s+\beta_g x_g) $$ where \(z\) is the shared frailty whose distribution is specified by frailty.dist with associated parameter \(\kappa\). The marginal survival function is obtained by integrating the conditional survival distribution, \(S(s; z, x_s, x_g) \), over frailty distribution, i.e., $$S(t; x_s, x_g) = \int_0^\infty S(s; z, x_s, x_g) dG(s) $$ where \(G(s)\) is the cumulative distribution function for the frailty.

See Also

penmodelEM, penmodel, penplot, print.penmodel,summary.penmodel,

print.summary.penmodel, plot.penmodel, penci

Examples

# NOT RUN {
  
  # Family data simulated from population-based design using a Weibull baseline hazard 
  
  fam <- simfam(N.fam=300, design="pop+", variation="none", base.dist="Weibull", 
                base.parms=c(0.01,3), vbeta=c(-1.13, 2.35), agemin=20, allelefreq=0.02)
  
  # Penetrance model fit for simulated family data
  
  fit <- penmodel(parms=c(0.01, 3), vbeta=c(-1.13, 2.35), data=fam, 
                  design="pop+", base.dist="Weibull")
  
  # Computing the penetrance at age 50 for male (sex=1) carriers (mut=1) from the assumed 
  # penetrance model based on Weibull baseline hazard.
  
  penf(fit$coefficients, age=50, sex=1, mut=1, base.dist="Weibull", agemin=20)
  
  
# }