Plot the penetrance function

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Description

This function plots the penetrance function given the baseline parameter and regression coefficients' values and choices of baseline and frailty distributions.

Usage

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penplot(base.parms, vbeta, variation="none", base.dist="Weibull", 
       frailty.dist="gamma", depend=1, agemin=20)

Arguments

base.parms

Vector of parameter values for baseline hazard function.

base.parms=c(lambda, rho), where lambda and rho are the shape and scale parameters, respectively.

vbeta

Vector of regression coefficients for gender and majorgene

vbeta=c(beta.s, beta.g). If variation="secondgene", specify regression coefficient for second gene in vbeta=c(beta.s, beta.g1, beta.g2).

base.dist

Choice of baseline hazard distribution. Possible choices are: "Weibull", "loglogistic", "Gompertz", "lognormal", or "gamma". Default is "Weibull".

frailty.dist

Choice of frailty distribution. Possible choices are "gamma" for gamma distribution or "lognormal" for log normal distributions. Default is "gamma".

variation

Source of residual familial correlation. Possible choices are "frailty" for frailty shared within families, "secondgene" for second gene shared within families, or "none" for no residual familial correlation. Default is "none"

depend

Variance of the frailty distribution. Dependence within families increases with depend value. Default value is 1.

agemin

Minimum age of disease onset. Default is 20 years of age.

Details

The penetrance model conditional on the frailty Z and covariates X=(x_s, x_g) is assumed to have the following hazard function

h(t|X,Z) = h_0(t-t_0) Z \exp(β_s x_s+β_g x_g),

where h_0(t) is the baseline hazard function, t_0 is a minimum age of disease onset, x_s and x_g indicate male (1) or female (0) and carrier (1) or non-carrier (0) of a main gene of interest, respectively.

For example, when using a Weibull distribution for baseline hazard and a gamma distribution for frailty, the penetrance function has the form

1-≤ft\{1+\frac{λ^ρ (t-t_0)^ρ \exp(β_s x_s+β_g x_g)}{κ}\right\}^{-κ} .

The penetrance curve for the second gene model is generated by

1-\exp\{-λ^ρ (t-t_0)^ρ \exp (β_g x_g+β_{g1} x_{g1} + β_{g2} x_{g2})\}

where x_{g1} indicates carrior (1) or non-carrior (0) of a major gene and x_{g2} indicates carrior (1) or non-carrior (0) of a second gene.

Value

Returns plots of the penetrance functions and penetrance estimates by age 70 called pen70 specific to gender and mutation-status. When plotting with the second gene model, the plot will generate separate curves for mutation carriers and noncarriers, and seperate curves for the second gene carriers and noncarriers.

Author(s)

Yun-Hee Choi

See Also

simfam

Examples

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# Penetrance function curves based on Weibull baseline hazard function

penplot(base.parms=c(0.01,3), vbeta=c(0.5, 2), base.dist="Weibull", agemin=20)