Package 'GSSE' reference manual

Title:	Genotype-Specific Survival Estimation
Description:	We propose a fully efficient sieve maximum likelihood method to estimate genotype-specific distribution of time-to-event outcomes under a nonparametric model. We can handle missing genotypes in pedigrees. We estimate the time-dependent hazard ratio between two genetic mutation groups using B-splines, while applying nonparametric maximum likelihood estimation to the reference baseline hazard function. The estimators are calculated via an expectation-maximization algorithm.
Authors:	Baosheng Liang, Yuanjia Wang and Donglin Zeng
Maintainer:	Baosheng Liang <[email protected]>
License:	GPL (>= 2)
Version:	0.1
Built:	2024-12-12 06:57:34 UTC
Source:	CRAN

Genotype-Specific Survival Estimation

Description

The package ‘GSSE’ (Genotype-Specific Survival Estimation) is made to implement a fully efficient sieve maximum likelihood method to estimate genotype-specific distribution of time-to-event outcomes under a nonparametric model. The package can handle missing genotypes in pedigrees. We estimate time-dependent hazard ratio between two genetic mutation groups using B-splines and apply nonparametric maximum likelihood estimation to the reference baseline hazard function. The estimators are calculated via an expectation-maximization algorithm.

Details

Package:	GSSE
Type:	Package
Version:	0.1
Date:	2015-10-17
License:	GPL (>= 2)

The main function is Sieve_NPMLE_Switch(). See the documentation file with examples.

Author(s)

Baosheng Liang <[email protected]>, Yuanjia Wang <[email protected]> and Donglin Zeng <[email protected]>

Maintainer: Baosheng Liang <[email protected]>

References

Wang, Y., Clark, L. N., Louis, E. D., Mejia-Santana, H., Harris, J., Cote, L. J., ... & Marder, K. (2008). Risk of Parkinson disease in carriers of parkin mutations: estimation using the kin-cohort method. Archives of neurology, 65(4), 467-474.

Qin, J., Garcia, T., Ma, Y., Tang, M., Marder, K. & Wang, Y. (2014). Combining isotonic regression and EM algorithm to predict genetic risk under monotonicity constraint. The Annals of Applied Statistics 8(2), 1182-1208.

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.

EM-PAVA function

Description

This function is used to estimate the genotype-specific distribution of time-to-event outcomes using EM-PAVA algorithm (Qin et al. 2014).

Usage

EM_PAVA_Func (q, x, delta, timeval, p, ep = 1e-05, maxiter = 400)
EM_PAVA_Func (q, x, delta, timeval, p, ep = 1e-05, maxiter = 400)

Arguments

`q`	matrix of 2 columns, where the first and second columns are the probabilities of belonging to the carrier `p0G` and non-carrier groups `1 - p0G`, respectively.
`x`	observed event time or censoring time.
`delta`	indicator of event.
`timeval`	grid points at which the distribution function values are estimated.
`p`	number of groups.
`ep`	convergence criterion. Here, `ep = 1e-5` is used as the default value.
`maxiter`	maximum number of EM iterations.

Details

Technical details can be found in Qin et al. (2014).

Value

Returns a list of prediction values for classes

`Fest`	estimated values at the points of `timeval`.
`Fest.all`	estimated values of cumulative distribution function on both carrier and non-carrier groups.

References

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(0.01, 3.65, 0.01);
fix_t1 = c(0.288, 0.693, 1.390);
fix_t2 = c(0.779, 1.860, 3.650);

EMpava_result = EM_PAVA_Func ( q = rbind(p0G,1-p0G), x = Y, delta = Delta, 
                               timeval = Grid, p = 2, ep = 1e-4 );

all = sort(c(Grid, Y));

F_carr_func = function(x){  EMpava_result$Fest.all[1, which.max(all[all <= x]) ]  };
F_non_func  = function(x){  EMpava_result$Fest.all[2, which.max(all[all <= x]) ]  };

PAVA_F1.hat_fix_t = apply( matrix(fix_t1, ncol=1), 1, F_carr_func );
PAVA_F2.hat_fix_t = apply( matrix(fix_t2, ncol=1), 1, F_non_func );

PAVA_F.hat_fix_t = data.frame( fix_t1 = fix_t1, PAVA_F1.hat = PAVA_F1.hat_fix_t,
                               fix_t2 = fix_t2, PAVA_F2.hat = PAVA_F2.hat_fix_t  );

print(PAVA_F.hat_fix_t);

# plot estimated curves

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

plot( Grid, F_carr, type = 's', lty = 1, 
      xlab = "Y", ylab = "Estimated Cumulative Distribution Function",
      ylim = c(0,1), col = 'blue' );
lines(Grid, 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") );

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(0.01, 3.65, 0.01);
fix_t1 = c(0.288, 0.693, 1.390);
fix_t2 = c(0.779, 1.860, 3.650);

EMpava_result = EM_PAVA_Func ( q = rbind(p0G,1-p0G), x = Y, delta = Delta, 
                               timeval = Grid, p = 2, ep = 1e-4 );

all = sort(c(Grid, Y));

F_carr_func = function(x){  EMpava_result$Fest.all[1, which.max(all[all <= x]) ]  };
F_non_func  = function(x){  EMpava_result$Fest.all[2, which.max(all[all <= x]) ]  };

PAVA_F1.hat_fix_t = apply( matrix(fix_t1, ncol=1), 1, F_carr_func );
PAVA_F2.hat_fix_t = apply( matrix(fix_t2, ncol=1), 1, F_non_func );

PAVA_F.hat_fix_t = data.frame( fix_t1 = fix_t1, PAVA_F1.hat = PAVA_F1.hat_fix_t,
                               fix_t2 = fix_t2, PAVA_F2.hat = PAVA_F2.hat_fix_t  );

print(PAVA_F.hat_fix_t);

# plot estimated curves

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

plot( Grid, F_carr, type = 's', lty = 1, 
      xlab = "Y", ylab = "Estimated Cumulative Distribution Function",
      ylim = c(0,1), col = 'blue' );
lines(Grid, 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") );

Data Set for Illustration of the ‘p0G’ Calculation

Description

This is a small data set used for illustration of the ‘p0G’ calculation. There are 2 columns, 20 rows in this data set.

Usage

data("p0G_data")data("p0G_data")

Format

A data frame with 20 observations on the following 2 columns with

relative: a factor with levels Child, Parent and Sibling,
proband_pd: a factor with levels No and Yes.

Source

This data set is a tiny subset of the data set of a Parkinson disease research project supported by Michael J. Fox Foundation.

References

Examples

data("p0G_data")
data("p0G_data")

Probability Calculation of Relative's Mutation Status

Description

This function is used to calculate the probability of a relative being a carrier.

Usage

p0G_Func (p, status, relative, model)
p0G_Func (p, status, relative, model)

Arguments

`p`	population frequency of mutation.
`status`	proband's carrier status (`status` = 0, non-carrier; = 1, homozygous; = 2, heterozygous).
`relative`	relative's relationship to the proband (`relative` = 1, parents; = 2, sibling; = 3, offspring).
`model`	assumed genetic model ("dominant" or "recessive").

Details

Technical details can be found in Wang et al. (2008).

Value

The function p0G_Func returns the probability of a relative being a carrier under the given genetic model.

References

Examples


#  Example 1  #

 data("p0G_data");
 attach(p0G_data);

 n = dim(p0G_data)[1];
 Status = as.numeric( proband_pd == "Yes" );
 Relative = rep(1, n) + 1*(relative == "Sibling") + 2*(relative == "Child");

 detach(p0G_data);

 p0G = rep(0, n);

 for(i in 1:n)
 {
  p0G[i] = p0G_Func(p = 0.02, status = Status[i], relative = Relative[i], model="dominant");
 }

 data.frame(pd_status = Status, relatives = Relative, prob = p0G);

#  Example 2  #

 n = 50;
 status = sample(x=c(0,1), size = n, replace = TRUE, prob = c(0.6, 0.4) );
 relative = sample(x=1:3, size = n, replace = TRUE, prob = c(1/3, 1/3, 1/3) );

 p0G = rep(0, n);

 for(i in 1:n)
 {
  p0G[i] = p0G_Func(p = 0.2, status = status[i], relative = relative[i], model="dominant");
 }

 data.frame(status = status, relative = relative, p0G = p0G);

#  Example 1  #

 data("p0G_data");
 attach(p0G_data);

 n = dim(p0G_data)[1];
 Status = as.numeric( proband_pd == "Yes" );
 Relative = rep(1, n) + 1*(relative == "Sibling") + 2*(relative == "Child");

 detach(p0G_data);

 p0G = rep(0, n);

 for(i in 1:n)
 {
  p0G[i] = p0G_Func(p = 0.02, status = Status[i], relative = Relative[i], model="dominant");
 }

 data.frame(pd_status = Status, relatives = Relative, prob = p0G);

#  Example 2  #

 n = 50;
 status = sample(x=c(0,1), size = n, replace = TRUE, prob = c(0.6, 0.4) );
 relative = sample(x=1:3, size = n, replace = TRUE, prob = c(1/3, 1/3, 1/3) );

 p0G = rep(0, n);

 for(i in 1:n)
 {
  p0G[i] = p0G_Func(p = 0.2, status = status[i], relative = relative[i], model="dominant");
 }

 data.frame(status = status, relative = relative, p0G = p0G);

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)
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.

Details

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

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.

References

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 );

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 );

Sieve_NPMLE_Bootstrap function

Description

This function is used for calculating standard error estimates and 95% confidence bands in quantile using the bootstrap method.

Usage

Sieve_NPMLE_Bootstrap ( fam_ID, Y0, Delta0, p0G0, fix_t1, fix_t2,
                        Grid, Knot, degree=3, Bn, maxiter=400, ep=1e-05)
Sieve_NPMLE_Bootstrap ( fam_ID, Y0, Delta0, p0G0, fix_t1, fix_t2,
                        Grid, Knot, degree=3, Bn, maxiter=400, ep=1e-05)

Arguments

`fam_ID`	family ID numbers.
`Y0`	observed event times or censoring times.
`Delta0`	indicators of event.
`p0G0`	probabilities of being a carrier.
`fix_t1`	a vector of fixed points at which the carrier's cumulative distribution function values are estimated.
`fix_t2`	a vector of fixed points at which the non-carrier's cumulative distribution function values are estimated.
`Grid`	a vector of grid points used for plotting the estimated distribution functions of carrier and non-carrier groups.
`Knot`	number of knots of the B-spline base functions.
`degree`	degree of the B-spline base functions.
`Bn`	number of bootstrap samples.
`maxiter`	maximum number of iterations.
`ep`	convergence criterion, default is ep= 1e-05.

Details

Using bootstrap for standard error estimation and 95% confidence bands calculation. We do the Bootstrap resample according to fam_ID.

Value

This function returns a list

`Boot.L1`	estimated cumulative hazard function for the carrier group.
`Boot.L2`	estimated cumulative hazard function for the non-carrier group.
`SE_F1_fix_t`	estimated standard errors for the carrier group at given points `fix_t1`.
`SE_F2_fix_t`	estimated standard errors for the non-carrier group at given points `fix_t2`.

References

Examples


data("Simulated_data");

OID = Simulated_data[,1];
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] ) ) }

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

# ---------------- #
#    Bootstrap     #
# ---------------- #

 Boot = Sieve_NPMLE_Bootstrap( fam_ID=OID, Y0=OY, Delta0=ODelta, p0G0=Op0G,
                               fix_t1=fix_t1, fix_t2=fix_t2, Grid = Grid,
                               Knot=6, degree =3, Bn=10  );

 SE1 = Boot$SE_F1_fix_t;
 SE2 = Boot$SE_F2_fix_t;

 estp = data.frame( fix_t1 = fix_t1, F1.hat = est.f1, SE_F1 = SE1,
                    fix_t2 = fix_t2, F2.hat = est.f2, SE_F2 = SE2  );

 print(estp)

data("Simulated_data");

OID = Simulated_data[,1];
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] ) ) }

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

# ---------------- #
#    Bootstrap     #
# ---------------- #

 Boot = Sieve_NPMLE_Bootstrap( fam_ID=OID, Y0=OY, Delta0=ODelta, p0G0=Op0G,
                               fix_t1=fix_t1, fix_t2=fix_t2, Grid = Grid,
                               Knot=6, degree =3, Bn=10  );

 SE1 = Boot$SE_F1_fix_t;
 SE2 = Boot$SE_F2_fix_t;

 estp = data.frame( fix_t1 = fix_t1, F1.hat = est.f1, SE_F1 = SE1,
                    fix_t2 = fix_t2, F2.hat = est.f2, SE_F2 = SE2  );

 print(estp)

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)
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`.

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.

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.

References

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") );

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") );

Simulated Parkinson's disease data

Description

This is an artificial data set used for the illustration of the current R-package. There are 4 columns, 268 rows in this data set.

Usage

data("Simulated_data")data("Simulated_data")

Format

A data frame with 268 observations on the following 4 columns with.

FamID: a factor with levels Child, Parent and Sibling
Y: a factor with levels No and Yes
delta: a numeric vector
p0G: a numeric vector, probability distribution value.

Source

This is a simulated data set based on the real data analysis results in Wang et al. (2015).

References

Marder, K., Wang, Y., Alcalay, R. N., Mejia-Santana, H., Tang, M. X., Lee, A., ... & Miravite, J. (2015). Age-specific penetrance of LRRK2 G2019S in the Michael J. Fox Ashkenazi Jewish LRRK2 Consortium. Neurology, 85(1), 89–95.

Examples

data("Simulated_data")
data("Simulated_data")

Kolmogorov-Smirnov Test Statistic

Description

This function is used to calculate the Kolmogorov-Smirnov statistic: $D(F_1, F_2) = \sup_{x}|F_1(x) - F_2(x)|$ .

Usage

test_stat (F1, F2)
test_stat (F1, F2)

Arguments

`F1`	vector of one distribution function value.
`F2`	vector of the other distribution function value.

Details

It is necessary to point out that F1 and F2 are based on common grids. Other technical details can be found in Wang et al. (2015).

Value

This function returns a list of prediction values for classes,

out

value of Kolmogorov-Smirnov statistics.

References

Examples


 X = seq(0.01, 1, 0.05);
 Func_1 = function(x){ x + runif(length(x), min=0, max=1) };
 Func_2 = function(x){ x + 2*runif(length(x), min=0, max=1) };
 
 U1 = Func_1(X);
 U2 = Func_2(X);
 
 test_stat (F1 = U1, F2 = U2);

X = seq(0.01, 1, 0.05);
 Func_1 = function(x){ x + runif(length(x), min=0, max=1) };
 Func_2 = function(x){ x + 2*runif(length(x), min=0, max=1) };
 
 U1 = Func_1(X);
 U2 = Func_2(X);
 
 test_stat (F1 = U1, F2 = U2);

Package 'GSSE'

Help Index

Genotype-Specific Survival Estimation

Description

Details

Author(s)

References

EM-PAVA function

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Data Set for Illustration of the ‘p0G’ Calculation

Description

Usage

Format

Source

References

See Also

Examples

Probability Calculation of Relative's Mutation Status

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Permutation Test

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Sieve_NPMLE_Bootstrap function

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Sieve_NPMLE_Switch function

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Simulated Parkinson's disease data

Description

Usage

Format

Source

References

See Also

Examples

Kolmogorov-Smirnov Test Statistic

Description

Usage

Arguments

Details

Value

References

See Also

Examples