GSSE (version 0.1)

Permutation_Test: Permutation Test

Description

Permutation test for the Sieve-NPMLE switch method with null hypothesis $H_0$: F_carr = F_non and alternative hypothesis $H_1$: F_carr is not equal to F_non.

Usage

Permutation_Test (Grid, F_carr, F_non, OY, ODelta, Op0G, nperm)

Arguments

Grid

time points at which the distribution function values are estimated.

F_carr

a vector of distribution function values at given grid points of the carrier group.

F_non

a vector of distribution function values at given grid points of the non-carrier group.

OY

observed event times.

ODelta

observed indicators of right censoring.

Op0G

observed probability values of carrier and non-carrier groups.

nperm

replication number used in permutation.

Value

This function returns a list of prediction values for classes,

Test_Stat

value of the Kolmogorov-Smirnov statistic with observed data.

Pvalues

p-value of the permutation test.

Permutation.value

values of Kolmogorov-Smirnov statistics under all permutations.

Details

Technical details can be found in Wang et al. (2015).

References

Wang, Y., Liang, B., Tong, X., Marder, K., Bressman, S., Orr-Urtreger, A., Giladi, N. & Zeng, D. (2015). Efficient estimation of nonparametric genetic risk function with censored data. Biometrika, 102(3), 515-532.

See Also

test_stat() and Sieve_NPMLE_Switch().

Examples

data("Simulated_data");

OY = Simulated_data[,2];
ind = order(OY);
ODelta = Simulated_data[,3];
Op0G = Simulated_data[,4];

Y = OY[ind];
Delta = ODelta[ind];
p0G = Op0G[ind];

Grid = seq(0.2, 3.65, 0.05);
fix_t1 = c(0.288, 0.693, 1.390);
fix_t2 = c(0.779, 1.860, 3.650);
px = seq(0.1, 3, 0.1);

SieveNPMLE_result = Sieve_NPMLE_Switch( Y=Y, Delta=Delta, p0G=p0G,
                                        px=px, Grid=Grid, Knot=7,
                                        degree=3 );

Lambda_1.hat = cumsum( SieveNPMLE_result$lamb1.hat );
Lambda_2.hat = cumsum( SieveNPMLE_result$lamb2.hat );

F_carr_func = function(x){ 1 - exp( max( Lambda_1.hat[Y <= x] ) ) }
F_non_func  = function(x){ 1 - exp( max( Lambda_2.hat[Y <= x] ) ) }

F_carr = apply( matrix(px, ncol=1), 1, F_carr_func );
F_non = apply( matrix(px, ncol=1), 1, F_non_func );

# Permutation test #

Permutation_Test( Grid=Grid, F_carr=F_carr, F_non=F_non,
                  OY=OY, ODelta=ODelta, Op0G=Op0G,
                  nperm=10 );