proprate2.neyman {surv2sample} | R Documentation |
Checks the assumption of proportional rates (proportional hazards, proportional odds) in two samples of right-censored data using (possibly data-driven) Neyman's smooth test.
proprate2.neyman(x, group, model = 0, data.driven = TRUE, d = ifelse(data.driven, 5, 3), basis = "legendre", time.transf = "F", beta.init = 0, maxiter = 20, eps = 1e-09, choltol = 1e-07) ## S3 method for class 'proprate2.neyman': summary(object, ...)
x |
a "Surv" object, as returned by the Surv
function. |
group |
a vector indicating to which group each observation belongs. May contain values 1 and 2 only. |
model |
the type of model. Possible values are 0 for proportional hazards, 1 for proportional odds. |
data.driven |
Should the test be data-driven? |
d |
the number of basis functions for the test with fixed dimension, the maximum number of basis functions for the data-driven test. |
basis |
the basis of functions. Possible values are "legendre"
for Legendre polynomials and "cos" for cosines. |
time.transf |
the time transformation for basis functions.
Possible values are "F" for the
distribution function (F(t)/F(tau)) estimated from the
pooled sample (recommended), "A" for the
cumulative hazard (A(t)/A(tau)) and "I"
for no transformation (the linear transformation t/tau). |
beta.init |
the initial parameter value for iteration in the simplified partial likelihood estimation. |
maxiter |
the maximum number of iterations. |
eps |
the convergence tolerance parameter. The convergence criterion
is |(l-l_old)/l|<eps . |
choltol |
a tolerance parameter for the Cholesky decomposition. |
object |
an object of class "proprate2.neyman" , as returned
by proprate2.neyman . |
... |
further parameters for printing. |
This function tests the hypothesis that transformation rates (currently hazard rates or odds functions) are proportional (their ratio is constant in time) in two samples of censored survival data.
The proportional rate model is estimated by a two-sample simplification of the partial likelihood. Then Neyman's smooth test of fit is performed. In general, Neyman's smooth tests are based on embedding the null hypothesis in a d-dimensional alternative. Here it consists of expressing the logarithm of the possibly time-varying ratio of rates as a linear combination of d basis functions (Legendre polynomials or cosines) in transformed time. Their significance is tested by a score test. The score is derived from the simplified partial likelihood. See Kraus (2007a) for details. The quadratic test statistic is asymptotically chi-square distributed with d degrees of freedom.
A data-driven choice of the number of basis functions is possible. The selection is based on a Schwarz-type criterion which is the maximiser of penalised score statistics for dimensions 1,...,d. For the p-value of the data-driven test a two-term approximation is used (see Kraus (2007b), eq. (12)), as the asymptotic chi-square with 1 d.f. is inaccurate.
If the test is data-driven, the summary
method prints details
on the selection procedure (statistics and penalised statistics for
each dimension). This is equivalent to print(x, detail=TRUE, ...)
.
proprate2.neyman
returns a list of class "proprate2.neyman"
and "neyman.test"
. Its main components are:
stat |
the test statistic. |
pval |
the p-value (based on the chi-square distribution for the fixed-dimension test and on the two-term approximation for the data-driven test). |
stats, stats.penal |
statistics and penalised statistics for dimensions 1,...,d (only for data-driven tests). |
S.dim |
the selected dimension (only for data-driven tests). |
Most input parameters and some further components are included.
David Kraus (http://www.davidkraus.net/)
Bagdonavicius, V. and Nikulin, M. (2000) On goodness-of-fit for the linear transformation and frailty models. Statist. Probab. Lett. 47, 177–188.
Kraus, D. (2007a) Checking proportional rates in the two-sample transformation model. Research Report 2203, Institute of Information Theory and Automation, Prague. Available at http://www.davidkraus.net/surv2sample/.
Kraus, D. (2007b) Data-driven smooth tests of the proportional hazards assumption. Lifetime Data Anal. 13, 1–16.
proprate2.ks
, proprate2.gs
for other
tests of the proportional rate assumption
proprate2
for estimation
## chronic active hepatitis data data(hepatitis) ## Neyman's test of proportional odds ## test with fixed dimension proprate2.neyman(Surv(hepatitis$time, hepatitis$status), hepatitis$treatment, model = 1, data.driven = FALSE) ## data-driven test print(a <- proprate2.neyman(Surv(hepatitis$time, hepatitis$status), hepatitis$treatment, model = 1, data.driven = TRUE)) ## details of the selection procedure summary(a)