penplot_cmp: Plot penetrance functions from competing risk models

Description

Plots the penetrance functions from competing risk models given the values of baseline parameters and regression coefficients and choices of baseline and frailty distributions.

Usage

penplot_cmp(event, base.parms, vbeta, cuts = NULL, variation = "none", 
          base.dist = "Weibull", frailty.dist = NULL, depend = c(1, 1), 
          agemin = 20, agemax = 80, print = TRUE, 
          col = c("blue","red","blue","red"),  lty = c(1, 1, 2, 2), 
          add.legend = TRUE, add.title = TRUE, x = "topleft", 
          y = NULL, xlab = "Age at onset", ylab = "Penetrance", 
          ylim = NULL, main = NULL, ...)

Value

Displays plots of the penetrance functions and returns the following values:

pen70: Penetrance estimates by age 70 specific to gender and mutation-status subgroups.
x.age: Vector of ages of onset ranging from agemin to agemax years
pen: Penetrance estimates computed at each age of x.age; if variation = "none" or "frailty", it includes subgroups specific to gender and mutation status for major gene. If variation = "secondgene", it includes subgroups specific to gender and both mutation statuses for major gene and second gene.

Arguments

event: Event of interest for penetrance function: either 1 or 2. Default is 1.
base.parms: List of vectors of parameter values for the specified baseline hazard functions for both events. For example, base.parms = list(c(lambda1, rho1), c(lambda2, rho2)) should be specified when base.dist = c("Weibull", "Weibull").
vbeta: List of vectors of regression coefficients for gender and majorgene, vbeta = list(c(beta1.s, beta1.g), c(beta2.s, beta2.g)) for both events. If variation = "secondgene", regression coefficients for gender, major gene and second gene, vbeta = list(c(beta1.s, beta1.g1, beta1.g2), c(beta2.s, beta2.g1, beta2.g2)), should be specified for each event.
cuts: Vector of cut points defining the intervals when base.dist = "piecewise" is specified and must be strictly positive and finite and greater than agemin. Default is NULL.
variation: Source of residual familial correlation. Possible choices are: "frailty" for frailty shared within families, "secondgene" for second gene variation, or "none" for no residual familial correlation. Default is "none".
base.dist: Vector of two baseline hazard distributions chosen for competing events. Possible choices are: "Weibull", "loglogistic", "Gompertz", "lognormal", "gamma", or "piecewise".If only one distribution is specified, the same distribution will be assumed for both events. A vector of two distributions should be specified if different baseline distributions are assumed for different events. Default is c("Weibull", "Weibull").
frailty.dist: Choice of frailty distribution. Possible choices are "gamma" for independent gamma, "lognormal" for independent log-normal, "cgamma" for correlated gamma, "clognormal" for correlated log-normal distribution when variation = "frailty" or "none" or NULL when no frailty distribution is assumed. Default is NULL.
depend: Vector of frailty parameter values assumed for specified frailty distribution. They corresponds inverse of variance of the frailty distribution. Dependence within families decreases with depend value. Default value is c(1,1).
agemin: Minimum age of disease onset. Default is 20 years of age.
agemax: Maximum age of disease onset. Default is 80 years of age.
print: Logical; if TRUE, prints the penetrance values by age 70 obtained from the assumed model for male carriers, female carriers, male noncarrers, and female noncarriers. Default is TRUE.
col: Colors of lines for male carriers, female carriers, male noncarrers, and female noncarriers. Default is c("blue", "red", "blue", "red").
lty: Types of lines for male carriers, female carriers, male noncarriers, and female noncarriers. Default is c(1, 1, 2, 2).
add.legend: Logical; if TRUE, displays legend in the plot. Default is TRUE.
add.title: Logical; if TRUE, displays title in the plot. Default is TRUE.
x, y: Position of legend; see legend. Defaults are x = "topleft", y = NULL.
xlab: Title for the x-axis. Default is "Age at Onset".
ylab: Title for the y-axis. Default is "Penetrance".
ylim: Limits of the y-axis. Default is NULL. If NULL, ylim will be automatically determined.
main: Main title of the plot. Default is NULL. If NULL, the title will be automatically created.
...: Other parameters to be passed through to plotting functions.

Author

Yun-Hee Choi

Details

Cause-specific proportional hazard models The penetrance models for competing events conditional on the covariates X = c(x_s, x_g) are assumed to have the following hazard functions for event \(j = 1, 2\): h_j(t|X) = h_0j(t - t₀) exp(β_js * x_s + β_jg * x_g), where h_0j(t) is the baseline hazard function for event \(j\), \(j=1,2\), t_0j 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 major gene of interest, respectively.

The penetrance function for the penetrance model has the form, 1 - exp(- H⁰(t - t₀) * exp(β_s * x_s + β_g * x_g )), where H₀(t) is the cumulative baseline hazard function.

Shared frailty models

The penetrance model conditional on the frailty \(Z\) and covariates X = c(x_s, x_g) is assumed to have the following hazard function: h(t|X,Z) = h₀(t - t₀) Z exp(β_s * x_s + β_g * x_g), where h₀(t) is the baseline hazard function, t₀ is a minimum age of disease onset, x_x 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 - (1 + λ^ρ * (t - t₀)^ρ * exp(β_s * x_s + β_g * x_g)/κ)^-κ.

Two-gene models

The penetrance curve for the two-gene model is generated by 1 - exp(- H⁰(t - t₀) * exp(β_s * x_s + β₁ * x₁ + β₂ * x₂)), where H₀(t) is the cumulative baseline hazard function, x₁ indicates carrior (1) or non-carrior (0) of a major gene and x₂ indicates carrior (1) or non-carrior (0) of a second gene. When plotting with the two-gene model, the plot will generate separate curves for mutation carriers and noncarriers, and separate curves for the second gene carriers and noncarriers.

Examples

Run this code

# Penetrance function curves for event 1 
# based on Weibull baselines (no frailty)
penplot_cmp(event=1, base.parms = list(c(0.01,3), c(0.01, 3)), 
        vbeta = list(c(-1, 2), c(-1, 1)), variation = "none", 
        base.dist = "Weibull", agemin = 20, ylim = c(0,1))

# Penetrance function curves for event 1 
# based on gamma frailty and Weibull baselines
penplot_cmp(event=1, base.parms = list(c(0.01,3), c(0.01, 3)), 
        vbeta = list(c(-1, 2), c(-1, 1)), depend=c(2, 2), 
        variation = "frailty", frailty.dist="gamma", base.dist = "Weibull", 
        agemin = 20, ylim = c(0,1))

# Penetrance function curves for event 1 
# based on correlated gamma frailty and Weibull baselines
penplot_cmp(event=1, base.parms = list(c(0.01,3), c(0.01, 3)), 
        vbeta = list(c(-1, 2), c(-1, 1)), depend=c(2, 2, 0.2), 
        variation = "frailty", frailty.dist="cgamma", 
        base.dist = "Weibull", agemin = 20, ylim = c(0,1))

# Penetrance function curves for event 1 
# based on correlated lognormal frailty and Weibull baselines
penplot_cmp(event=1, base.parms = list(c(0.01,3), c(0.01, 3)), 
        vbeta = list(c(-1, 2), c(-1, 1)), depend=c(2, 2, 0.2), 
        variation = "frailty", frailty.dist="clognormal", 
        base.dist = "Weibull", agemin = 20, ylim = c(0,1))

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