gof {tranSurv}

Goodness of fit based on left-truncated regression model

Description

Provide goodness-of-fit diagnostics for the transformation model.

Usage

gof(x, B = 200, P = 1)

Arguments

x

an object of class trSurvfit returned by the trSurvfit() or the trReg() function or a survival object returned by the Surv().

B

an integer value specifies the bootstrap size for the left-truncated regression model. A value greater than 2 is required.

P

an integer value specifies number of breakpoints to test the linearity of the transformation model. When P > 0, P breakpoints divides the event times into P equal spaced segments. Piecewise linear function constructed from those segments of event times are used in the left-truncated regression model, and the overall significance testing if the coefficient estimates are equal is reported. Default value for P is 1. See Details for a description of the goodness of fit procedure.

Details

The googness of fit assessment of the transformation model focus on the structure of the transformation model, which has the form:

h(U) = (1 + a)^{-1} \times (h(T) + ah(X)),

where T is the truncation time, X is the observed failure time, U is the transformed truncation time that is quasi-independent from X and h(\cdot) is a monotonic transformation function. With the condition, T < X, assumed to be satisfied, the structure of the transformation model implies

X - T = -(1 + a) E(U) + (1 + a) X - (1 + a) \times [U - E(U)] := \beta_0 + \beta_1X + \epsilon.

The regression estimates can be obtained by the left-truncated regression model (Karlsson and Lindmark, 2014). To evaluate the goodness of fit of the transformation model, the gof() function directly test the inearity in X by considering larger model that are nonlinear in X. In particular, we expand the covariates X to P piecewise linearity terms and test for equality of the associated coefficients.

Value

A list containing the following elements

coefficients

the regression coefficients of the left-truncated regression model.

pval

the p-value for the equality of the piecewise linearity terms in the expanded model. See Details.

References

Karlsson, M., Lindmark, A. (2014) truncSP: An R Package for Estimation of Semi-Parametric Truncated Linear Regression Models, Journal of Statistical Software, 57 (14), pp 1–19.

Examples

data(channing, package = "boot")
chan <- subset(channing, entry < exit)
fit <- trReg(Surv(entry, exit, cens) ~ sex, data = chan)
gof(fit, B = 10)