survHE (version 2.0.5)

plot_transformed_km: Plot to assess suitability of parametric model

Description

Perform an exploratory investigation for linearity of transformed survival models.

Usage

plot_transformed_km(fit, mod = 1, add_legend = FALSE, graph = "base", ...)

Value

Diagnostic plot

Arguments

fit

An object of class survHE.

mod

Index or name of a model in fit. Defaults to 1.

add_legend

If TRUE, labels assumptions. Defaults to FALSE.

graph

Type of plot: base or ggplot2.

...

Further arguments, passed on to plot.

Author

William Browne, Nathan Green

Details

For the Weibull, twice taking logs of the survivor function

$$log(-log S(t)) = log \lambda + \gamma log t$$

A plot of \(log(-log S(t))\) against \(log(t)\) would give an approximately straight line if the Weibull assumption is reasonable. The plot could also be used to give a rough estimate of the parameters.

Similarly, for the log-logistic distribution

$$logS(t)/(1 - S(t)) = \theta - \kappa log t$$

For the log-normal distribution

$$\Phi^{-1} (1 - S(t)) = (log t - \mu) / \sigma$$

We can also check the assumption made with using the Cox regression model of proportional hazards by inspecting the log-cumulative hazard plot.

$$log H_i(t) = \beta x_i + log H_0(t)$$

The transformed curves for different values of the explanatory variables will be parallel if PH holds.

References

Collett (2015) Modelling Survival Data in Medical Research, CRC Press

Examples

data(bc)
form <- formula("Surv(recyrs, censrec) ~ group")

# exponential distribution
fit_exp <- fit.models(form, data = bc,
                  distr = "exp", method = "mle")
plot_transformed_km(fit_exp)
plot_transformed_km(fit_exp, graph = "ggplot2")
                 
# weibull distribution
fit_wei <- fit.models(form, data = bc,
                  distr = "weibull", method = "mle")
plot_transformed_km(fit_wei)
plot_transformed_km(fit_wei, graph = "ggplot2")
                 
# loglogistic distribution
fit_llog <- fit.models(form, data = bc,
                  distr = "loglogistic", method = "mle")
plot_transformed_km(fit_llog)
plot_transformed_km(fit_llog, graph = "ggplot2")
                 
# lognormal distribution
fit_lnorm <- fit.models(form, data = bc,
                  distr = "lognormal", method = "mle")
plot_transformed_km(fit_lnorm)
plot_transformed_km(fit_lnorm, graph = "ggplot2")

## for only one group
form <- formula("Surv(recyrs, censrec) ~ 1")

fit_exp <- fit.models(form, data = bc,
                  distr = "exp", method = "mle")
plot_transformed_km(fit_exp)
plot_transformed_km(fit_exp, graph = "ggplot2")