GSSE (version 0.1)

Sieve_NPMLE_Switch: Sieve_NPMLE_Switch function

Description

This function is used to estimate the genotype-specific distribution of time-to-event outcomes with the Sieve-NPMLE switch algorithm.

Usage

Sieve_NPMLE_Switch (Y, p0G, Delta, px, Grid, Knot, degree, maxiter=400, ep=1e-05)

Arguments

Y

observed event times or censoring times.

p0G

probabilities of being a carrier.

Delta

indicators of event.

px

grid points at which the distribution function values are estimated.

Grid

grid points used for plots. Grid could be either exactly the same as px or different from px.

Knot

number of knots.

degree

degree of the B-spline base functions.

maxiter

maximum number of iterations.

ep

convergence criterion, default is ep= 1e-05.

Value

This function returns a list of prediction values for classes

lamb1.hat

estimated values of hazard function for the carrier group.

lamb2.hat

estimated values of hazard function for the non-carrier group.

Lamb1

estimated values of cumulative hazard function for the carrier group.

Lamb2

estimated values of cumulative hazard function for the non-carrier group.

Converge

convergence status.

Details

This function is used to estimate the distribution of the age-at-onset of Parkinsons disease for carriers' and non-carriers' mutations in the leucine-rich repeat kinase 2, LRRK2, gene. Please refer to Wang et al. (2015) for more details.

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

p0G_Func(), Sieve_NPMLE_Bootstrap() and Permutation_Test().

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(0.01, 3.65, 0.01);

SieveNPMLE_result = Sieve_NPMLE_Switch( Y=Y, Delta=Delta, p0G=p0G,
                                        px=px, Grid=Grid,
                                        Knot=6, degree=3  );

# 'Sieve_NPMLE_Switch' only returns values of hazard function 
# or cumulative hazard function of mutation groups, in practice, we only 
# need to do a little bit more as follows for calculating the 
# cumulative distribution values of mutation groups. 

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] ) ) }

est.f1 = apply(matrix(fix_t1, ncol=1), 1, F_carr_func );
est.f2 = apply(matrix(fix_t2, ncol=1), 1, F_non_func  );

estp = data.frame( fix_t1 = fix_t1, F_carr_t1 = est.f1,
                   fix_t2 = fix_t2, F_non_t2 = est.f2  );

print(estp);

# plot estimated curves

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

plot( px, F_carr, type='s', lty=1, ylim=c(0, 1), xlab="Y",
      ylab="Estimated Cumulative Distribution Function", col='blue' );
lines(px, F_non, type='s', lty=2, col='red');
legend("topleft", legend=c("Carrier group", "Non-Carrier group"),
       lty=c(1,2), col=c("blue","red") );