# isurvdiff.smax: Maximum values of s for which the IDP test returns a... In IDPSurvival: Imprecise Dirichlet Process for Survival Analysis

## Description

Search for the maximum values of parameter s for which the IDP test `isurvdiff(formula,...)` issues a determinate decision. The function test values of s up to the parameter smax. If for smax the IDP test is still determinate, `isurvdiff.smax` returns list(smax,testout). If for s=0 the test is already indeterminate, `isurvdiff.smax` returns list(-1,testout), where testout is the last executed test.

## Usage

 `1` ```isurvdiff.smax(formula, ..., verbose=FALSE, accuracy=0.05, smax=12) ```

## Arguments

 `formula` a formula expression of the form `Surv(time, status) ~ predictor`. A single predictor is admitted. `verbose` whether to display each value of s that is tried `accuracy` to which precision s should be computed `smax` to which maximum value s should be tried `...` All arguments of `isurvdiff.smax` are passed to `isurvdiff` to perform the test. Refer to the help of `isurvdiff` for more details about the arguments.

## Value

A list with components:

 `s` The maximum value of s for which the test returns a determinate decision (H=0 or H=1). `test0` The value returned by `isurvdiff(formula,...)` for the last test performed. Refer to the help of `isurvdiff` for more details.

## METHOD

This function implements the IDP sum-rank test describe in Mangili and others (2014).

## References

Benavoli, A., Mangili, F., Zaffalon, M. and Ruggeri, F. (2014). Imprecise Dirichlet process with application to the hypothesis test on the probability that X < Y. ArXiv e-prints, http://adsabs.harvard.edu/abs/2014arXiv1402.2755B.

Mangili, F., Benavoli, A., Zaffalon, M. and de Campos, C. (2014). Imprecise Dirichlet Process for the estimate and comparison of survival functions with censored data.

`Surv`, `isurvdiff`.
 ```1 2 3 4 5 6 7 8 9``` ```data(lung,package='survival') lung <- lung[1:40,] # reduced data set just to ensure that the # example is very fast to run for building the package test <-isurvdiff.smax(Surv(time,status)~sex,lung,groups=c(1,2), alternative = 'two.sided', nsamples=1000) # better to use larger value of nsamples # this small value is to run it quickly print(test\$test0) cat("Maximum s giving the same decision: ",test\$s) ```