Type: Package
Title: Set-Based Inference for Multiple Interval-Censored Outcomes
Version: 0.2.0
Description: Contains tests for association between a set of genetic variants and multiple correlated outcomes that are interval censored. Interval-censored data arises when the exact time of the onset of an outcome of interest is unknown but known to fall between two time points.
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.1.1
Imports: bindata, fastGHQuad, CompQuadForm, stats, ICSKAT
Suggests: knitr, rmarkdown
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2022-11-25 22:49:29 UTC; jaihe2
Author: Jaihee Choi [aut, cre], Ryan Sun [aut]
Maintainer: Jaihee Choi <jaiheechoi01@gmail.com>
Repository: CRAN
Date/Publication: 2022-11-25 23:10:02 UTC

Get_CausalSNPs_bynum()

Description

Matrix of subsetted genetic information.

Usage

Get_CausalSNPs_bynum(gMat, num, Causal.MAF.Cutoff)

Arguments

gMat

Matrix of SNPs.

num

Number of causal variants.

Causal.MAF.Cutoff

Minor allele frequency value cutoff for causal SNPs.

Value

Output is a vector of indices to subset the full genetic matrix.

d/d_theta_l

Description

Calculate the first derivative of the theta terms for outcome l.

Usage

fd_term(l, temp_beta, phen,d, apply_diffs,
   A_i, no_l_all,HL_array, HR_array)

Arguments

l

Outcome of interest.

temp_beta

Vector of fitted coefficients.

phen

list containing the covariate design matrices.

d

Number of quadrature nodes.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

A_i

Product of apply_diffs across all outcomes k summed over all quadrature nodes d.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

Value

The output is a 1 x (p + 2) vector of the first derivative terms for outcome l.

d/d_gamma_l

Description

Calculates the gradient term for U_g for the score statistic.

Usage

gamma_fd(l, HL_array, HR_array, tpos_all, obs_all,
   temp_beta, A_i, no_l_all, gMat, a1, a2, d)

Arguments

l

Index of first outcome of interest.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

tpos_all

n x k matrix containing a indictor for whether that time is left-censored or not.

obs_all

n x k matrix containing a indictor for whether that time is right-censored or not.

temp_beta

Vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes k summed over all quadrature nodes d.

no_l_all

n x (K - 1) matrix containing the product of apply_diffs across all outcomes K excluding the current outcome l.

gMat

n x q matrix of genetic information.

a1

First shape parameter of beta parameter.

a2

Second shape parameter of beta parameter.

d

Number of quadrature nodes.

Value

The output is a vector containing the first derivative with respect to gamma.

d^2/d_gamma_ldgamma_m

Description

Calculates the [off-diagonal] Information matrix term for I_gamma gamma with respect to outcome l and outcome m.

Usage

gamma_off(l, m, HL_array, HR_array,
   tpos_all, obs_all, temp_beta, A_i,
   no_l_all, no_two_all, gMat, a1, a2, k, d)

Arguments

l

Index of first outcome of interest.

m

Index of second outcome of interest.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

tpos_all

n x k matrix containing a indictor for whether that time is left-censored or not.

obs_all

n x k matrix containing a indictor for whether that time is right-censored or not.

temp_beta

Vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes k summed over all quadrature nodes d.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

no_two_all

n x (k - 2) matrix containing the product of apply_diffs across all outcomes k excluding the outcomes l and m.

gMat

n x q matrix of genetic information.

a1

First shape parameter of beta parameter.

a2

Second shape parameter of beta parameter.

k

Total number of outcomes.

d

Number of quadrature nodes.

Value

The output is a matrix containing the component of the information matrix of the gamma parameter for outcomes l and m.

d^2/d_gamma_ldgamma_l

Description

Calculates the [on-diagonal] Information matrix term for I_gamma gamma with respect to outcome l.

Usage

gamma_on(l, HL_array, HR_array, tpos_all, obs_all,
   temp_beta, A_i, no_l_all, gMat, a1, a2, d)

Arguments

l

Index of first outcome of interest.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

tpos_all

n x k matrix containing a indictor for whether that time is left-censored or not.

obs_all

n x k matrix containing a indictor for whether that time is right-censored or not.

temp_beta

Vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes k summed over all quadrature nodes d.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

gMat

n x q matrix of genetic information.

a1

First shape parameter of beta parameter.

a2

Second shape parameter of beta parameter.

d

Number of quadrature nodes.

Value

The output is a matrix containing the component of the information matrix of the gamma parameter for outcome l.

d^2/d_gamma_ldsigma^2

Description

Calculates the Information matrix term of I_eta gamma for one outcome of interest l.

Usage

gammasigma(
  l, HL_array, HR_array, tpos_all, obs_all,
  apply_diffs, temp_beta, A_i, xDats, no_l_all,
  no_two_all, gMat, a1, a2, k, d)

Arguments

l

Index of first outcome of interest.

HL_array

n x K matrix containing all the hazard values for the left times.

HR_array

n x K matrix containing all the hazard values for the right times.

tpos_all

n x k matrix containing a indictor for whether that time is left-censored or not.

obs_all

n x k matrix containing a indictor for whether that time is right-censored or not.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

temp_beta

vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes K summed over all quadrature nodes D.

xDats

List of design matrices.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes K excluding the current outcome l.

no_two_all

n x (k - 2) matrix containing the product of apply_diffs across all outcomes k excluding the outcomes l and m.

gMat

n x q matrix of genetic information.

a1

First shape parameter of beta parameter.

a2

Second shape parameter of beta parameter.

k

Total number of outcomes.

d

Number of quadrature nodes.

Value

The output is a matrix containing the component of the information matrix of the gamma and sigma^2 parameters for outcome l.

d^2/d_gamma_kdtheta_k

Description

Calculates the Information matrix term of I_eta gamma for outcome k.

Usage

gammatheta(l, HL_array, HR_array, tpos_all, obs_all, apply_diffs,
   temp_beta, A_i, xDats, no_l_all, gMat, a1, a2, d)

Arguments

l

Index of first outcome of interest.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

tpos_all

n x k matrix containing a indictor for whether that time is left-censored or not.

obs_all

n x k matrix containing a indictor for whether that time is right-censored or not.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

temp_beta

vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes k summed over all quadrature nodes d.

xDats

List of design matrices for all outcomes.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

gMat

n x q matrix of genetic information.

a1

First shape parameter of beta parameter.

a2

Second shape parameter of beta parameter.

d

Number of quadrature nodes.

Value

The output is a matrix containing the component of the information matrix of the gamma and theta parameters for outcome l.

d^2/d_gamma_ldtheta_m

Description

Calculates the Information matrix term of I_eta gamma for outcomes l and m

Usage

gammatheta_off(l,m, HL_array, HR_array, xAll, apply_diffs, temp_beta,
   A_i, no_l_all, no_two_all, gMat, a1, a2, k, d)

Arguments

l

Index of first outcome of interest.

m

Index of second outcome of interest.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

xAll

List of design matrices and censoring terms.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

temp_beta

vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes K summed over all quadrature nodes d.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

no_two_all

n x (k - 2) matrix containing the product of apply_diffs across all outcomes k excluding the outcomes l and m.

gMat

n x q matrix of genetic information.

a1

First shape parameter of beta parameter.

a2

Second shape parameter of beta parameter.

k

Total number of outcomes.

d

Number of quadrature nodes.

Value

The output is a matrix containing the component of the information matrix of the gamma and theta parameters for outcomes l and m.

Get A vector

Description

Product of difference of survival terms of the left and right interval times, across all outcomes k, summed over all quadrature nodes d.

Usage

get_A(store, weights, d, n)

Arguments

store

Matrix of difference of survival values of the left and right time intervals.

weights

Gaussian quadrature weights.

d

Total number of Gaussian quadrature nodes.

n

Total number of observations.

Value

The output is a vector used to compute the derivative terms.

H_ik(L_ik)

Description

Calculates the hazard function of the left time interval for outcome l.

Usage

haz_left(l, d, temp_beta, phen, r1, k)

Arguments

l

Outcome of interest.

d

Total number of Gaussian quadrature nodes.

temp_beta

vector of fitted coefficients.

phen

list of data matrices containing both left and right information.

r1

Gaussian quadrature nodes.

k

Total number of outcomes.

Value

The output is a vector of the hazard values of the left times.

H_ik(R_ik)

Description

Calculates the hazard function of the right time interval for outcome l.

Usage

haz_right(l, d, temp_beta, phen, r1, k)

Arguments

l

Outcome of interest.

d

Total number of Gaussian quadrature nodes.

temp_beta

vector of fitted coefficients.

phen

list of data matrices containing both left and right information.

r1

Gaussian quadrature nodes.

k

Total number of outcomes.

Value

The output is a vector of the hazard values of the right times.

d^2/d_theta_kdsigma^2

Description

Calculates the Information matrix term of I_theta sigma^2 for outcomes l and m.

Usage

sd_off(l, m, phen_l, phen_m, temp_beta, d, apply_diffs, A_i,
   HL_array, HR_array, no_l_all, no_two_all, tpos_all, obs_all, k)

Arguments

l

Index of first outcome of interest.

m

Index of second outcome of interest.

phen_l

List containing the left and right design matrices and interval times for outcome l.

phen_m

List containing the left and right design matrices and interval times for outcome m.

temp_beta

vector of fitted coefficients.

d

Total number of quadrature nodes.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

A_i

Product of apply_diffs across all outcomes k summed over all quadrature nodes d.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

no_two_all

n x (k - 2) matrix containing the product of apply_diffs across all outcomes K excluding outcomes l and m.

tpos_all

n x k matrix containing a indictor for whether that time is left-censored or not.

obs_all

n x k matrix containing a indictor for whether that time is right-censored or not.

k

Total number of outcomes.

Value

The output is a matrix containing the component of the information matrix of the sigma and theta parameters.

d^2/dsigma^2^2

Description

Calculates the Information matrix term of I_sigma^2 sigma^2 for outcome l.

Usage

sd_on(l, k, temp_beta, phen, d, apply_diffs, A_i,
   no_l_all, HL_array, HR_array)

Arguments

l

Index of first outcome of interest.

k

Total number of outcomes.

temp_beta

vector of fitted coefficients.

phen

List containing the left and right design matrices and interval times for outcome l.

d

Total number of quadrature nodes.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

A_i

Product of apply_diffs across all outcomes K summed over all quadrature nodes D.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

Value

The output is a single value for the second derivative with respect to sigma.

Simulate genetic matrix.

Description

Simulates a n x q genetic matrix with the option to specify the common pairwise correlation.

Usage

sim_gmat(n,q,rho)

Arguments

n

Total number of observations.

q

Total number of SNPs.

rho

Common pairwise correlation parameter.

Value

The result of a n x q genetic matrix of q SNPs.

Examples

# Set sample size
n = 100

# Set number of SNPs
q = 5

# Set common pairwise correlation
rho = 0.1

# Simulate genetic matrix
gMat <- sim_gmat(n, q, rho)

simico_fit_null()

Description

Fit the null model via newton raphson for multiple outcomes interval-censored skat.

Usage

simico_fit_null(init_beta, epsilon, xDats, lt_all, rt_all, k, d)

Arguments

init_beta

Starting values for NR.

epsilon

Stopping criterion for NR.

xDats

List of left and right design matrices.

lt_all

n x k matrix of left times.

rt_all

n x k matrix of right times.

k

Total number of outcomes.

d

Total number of quadrature nodes.

Value

beta_fit

Vector of fitted coefficients.

iter

Number of iterations needed for the Newton-Raphson to converge.

diff

Difference between the current values of temp_beta and the previous iteration of temp_beta.

jmat

Information matrix of the theta parameters.

grad

Vector of the first derivaive of the theta parameters.

Examples

# Set number of outcomes
k = 2

# Set number of observations
n = 100

# Set number of covariates
p = 2

# Set number of SNPs
q = 50

# Set number of causal SNPs
num = 5

# Set number of quadrature nodes
d = 100

# Variance of subject-specific random effect
tauSq = 1

# Define the effect sizes
effectSizes <- c(.03, .15)

# Set MAF cutoff for causal SNPs
Causal.MAF.Cutoff = 0.1

# the baseline cumulative hazard function
bhFunInv <- function(x) {x}

set.seed(1)

# Generate covariate matrix
xMat <- cbind(rnorm(n), rbinom(n=n, size=1, prob=0.5))

# Generate genetic matrix
gMat <- matrix(data=rbinom(n=n*q, size=2, prob=0.1), nrow=n)

# Get indices to specific select causal variants
idx <- Get_CausalSNPs_bynum(gMat, num, Causal.MAF.Cutoff)

# Subset the gMat
gMatCausal <- gMat[,idx]

# Generate the multiple outcomes
exampleDat <- simico_gen_dat(bhFunInv = bhFunInv, obsTimes = 1:3,
                             windowHalf = 0.1, n, p, k, tauSq, gMatCausal,
                             xMat, effectSizes)

# Set the initial estimate values
init_beta <-c (rep(c(0, 0, 0, 1, 0), k), 1)

# Run the Newton-Raphson
nullFit <- simico_fit_null(init_beta = init_beta,
   epsilon = 10^-5, xDats = exampleDat$fullDat$xDats,
   lt_all = exampleDat$leftTimesMat,
   rt_all = exampleDat$rightTimesMat,
   k = k, d = d)

simico_gen_dat()

Description

Generate multiple interval-censored data under proportional hazards model.

Usage

simico_gen_dat(bhFunInv, obsTimes = 1:3, windowHalf = 0.1,
   n, p, k, tauSq, gMatCausal, xMat, effectSizes)

Arguments

bhFunInv

The inverse of the baseline hazard function.

obsTimes

Vector of the intended observation times.

windowHalf

The amount of time before or after the intended obsTimes that a visit might take place.

n

Total number of observations.

p

Total number of covariates.

k

Total number of outcomes.

tauSq

Variance of the subject specific random effect.

gMatCausal

Matrix of subsetted genetic information for only a select causal SNPs.

xMat

Matrix of covariates.

effectSizes

Vector of genetic effect sizes. Should be entered as a vector the same length as the number of outcomes.

Value

exactTimesMat

n x k matrix containing the simulated exact times that the event occurred.

leftTimesMat

n x k matrix containing the left time interval that is observed.

rightTimesMat

n x k matrix containing the right time interval that is observed.

obsInd

n x k matrix containing a indictor for whether that time is right-censored or not.

tposInd

n x k matrix containing a indictor for whether that time is left-censored or not.

fullDat

Data in complete form to enter into SIMICO functions.

Examples

# Set number of outcomes
k = 2

# Set number of observations
n = 100

# Set number of covariates
p = 2

# Set number of SNPs
q = 50

# Set number of causal SNPs
num = 5

# Set number of quadrature nodes
d = 100

# Variance of subject-specific random effect
tauSq = 1

# Define the effect sizes
effectSizes <- c(.03, .15)

# Set MAF cutoff for causal SNPs
Causal.MAF.Cutoff = 0.1

# the baseline cumulative hazard function
bhFunInv <- function(x) {x}

set.seed(1)

# Generate covariate matrix
xMat <- cbind(rnorm(n), rbinom(n=n, size=1, prob=0.5))

# Generate genetic matrix
gMat <- matrix(data=rbinom(n=n*q, size=2, prob=0.1), nrow=n)

# Get indices to specific select causal variants
idx <- Get_CausalSNPs_bynum(gMat, num, Causal.MAF.Cutoff)

# Subset the gMat
gMatCausal <- gMat[,idx]

# Generate the multiple outcomes
exampleDat <- simico_gen_dat(bhFunInv = bhFunInv, obsTimes = 1:3,
                             windowHalf = 0.1, n, p, k, tauSq, gMatCausal,
                             xMat, effectSizes)

Get P-Values

Description

Calculate test statistic and p-values for multiple outcome test and multiple burden test.

Usage

simico_out(nullFit, xDats, lt_all, rt_all, Itt, a1, a2, G, k, d)

Arguments

nullFit

Results of the Newton-Raphson: estimates of the beta coefficients.

xDats

List of design matrices.

lt_all

Matrix containing the generated left interval times.

rt_all

Matrix containing the generated right interval times.

Itt

I_theta theta - Information matrix of theta.

G

n x q matrix of genetic information.

a1

First shape parameter of beta parameter.

a2

Second shape parameter of beta parameter.

k

Total number of outcomes.

d

Number of quadrature nodes.

Value

multQ

Score statistic for multiple outcome test.

multP

P-value for multiple outcome test.

burdQ

Score statistic for multiple burden test.

burdP

P-value for multiple burden test.

Examples

# Set number of outcomes
k = 2

# Set number of observations
n = 100

# Set number of covariates
p = 2

# Set number of SNPs
q = 50

# Set number of causal SNPs
num = 5

# Set number of quadrature nodes
d = 100

# Variance of subject-specific random effect
tauSq = 1

# Define the effect sizes
effectSizes <- c(.03, .15)

# Set MAF cutoff for causal SNPs
Causal.MAF.Cutoff = 0.1

# the baseline cumulative hazard function
bhFunInv <- function(x) {x}

set.seed(1)

# Generate covariate matrix
xMat <- cbind(rnorm(n), rbinom(n=n, size=1, prob=0.5))

# Generate genetic matrix
gMat <- matrix(data=rbinom(n=n*q, size=2, prob=0.1), nrow=n)

# Get indices to specific select causal variants
idx <- Get_CausalSNPs_bynum(gMat, num, Causal.MAF.Cutoff)

# Subset the gMat
gMatCausal <- gMat[,idx]

# Generate the multiple outcomes
exampleDat <- simico_gen_dat(bhFunInv = bhFunInv, obsTimes = 1:3,
                             windowHalf = 0.1, n, p, k, tauSq, gMatCausal,
                             xMat, effectSizes)

# Set the initial estimate values
init_beta <-c (rep(c(0, 0, 0, 1, 0), k), 1)

# Run the newton-raphson
nullFit <- simico_fit_null(init_beta = init_beta,
   epsilon = 10^-5, xDats = exampleDat$fullDat$xDats,
   lt_all = exampleDat$leftTimesMat,
   rt_all = exampleDat$rightTimesMat,
   k = k, d = d)

# Get the test statistics p-values
out <- simico_out(nullFit = nullFit$beta_fit,
   xDats = exampleDat$fullDat$xDats,
   lt_all = exampleDat$leftTimesMat,
   rt_all = exampleDat$rightTimesMat,
   Itt = nullFit$jmat, a1 = 1, a2 = 25,
   G = gMat, k  = k, d = d)

# Print results
# Score statistic
out$multQ

# P-values
out$multP

d/d_sigma^2

Description

Calculates the first derivative term with respect to sigma^2.

Usage

ss_fd(l, phen, HL_array, HR_array, tpos_all, obs_all,
   apply_diffs, temp_beta, A_i, no_l_all, k, d)

Arguments

l

Index of first outcome of interest.

phen

List containing all the left and right design matrices.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

tpos_all

n x k matrix containing a indictor for whether that time is left-censored or not.

obs_all

n x k matrix containing a indictor for whether that time is right-censored or not.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

temp_beta

vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes k summed over all quadrature nodes d.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

k

Total number of outcomes.

d

Number of quadrature nodes.

Value

The output is a single value for the first derivative with respect to sigma.

d^2/d_sigma^2^2

Description

Calculates the second derivative term with respect to sigma^2.

Usage

ss_sd(HL_array, HR_array, xAll, apply_diffs, temp_beta,
   A_i, no_l_all, no_two_all, k, d)

Arguments

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

xAll

List containing the left and right matrices and event times.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

temp_beta

vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes K summed over all quadrature nodes D.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

no_two_all

n x (k - 2) matrix containing the product of apply_diffs across all outcomes k excluding outcomes l and m.

k

Total number of outcomes.

d

Number of quadrature nodes.

Value

The output is a single value for the second derivative with respect to sigma^2.

d^2/d_theta_ldsigma^2

Description

Calculates the Information matrix term of I_eta theta for one outcome of interest l.

Usage

st_off(l, HL_array, HR_array, xAll, apply_diffs,
   temp_beta, A_i, no_l_all, no_two_all, k, d)

Arguments

l

Index of first outcome of interest.

HL_array

n x k matrix containing all the hazard values for the left times.

HR_array

n x k matrix containing all the hazard values for the right times.

xAll

List containing the left and right matrices and event times.

apply_diffs

Matrix containing the differences between survival functions of the left and right time intervals.

temp_beta

vector of fitted coefficients.

A_i

Product of apply_diffs across all outcomes K summed over all quadrature nodes D.

no_l_all

n x (k - 1) matrix containing the product of apply_diffs across all outcomes k excluding the current outcome l.

no_two_all

n x (k - 2) matrix containing the product of apply_diffs across all outcomes k excluding outcomes l and m.

k

Total number of outcomes.

d

Number of quadrature nodes.

Value

The output is a matrix containing the component of the information matrix of the theta eta parameters for outcome l.

S_ik(L_ik) - S_ik(R_ik)

Description

Calculates the difference between the survival functions of the left and right time intervals for outcome k for quadrature node d.

Usage

surv_diff(l, d, temp_beta, phen, r1, k)

Arguments

l

Outcome of interest.

d

Total number of Gaussian quadrature nodes.

temp_beta

Vector of fitted coefficients.

phen

List of data matrices containing both left and right information.

r1

Gaussian quadrature nodes.

k

Total number of outcomes.

Value

The output is a vector of the difference of the survival values of the left times and right times.

S_ik(L_ik)

Description

Calculates the survival function of the left time interval for outcome k for quadrature node d.

Usage

surv_left(l, d, temp_beta, phen, r1, k)

Arguments

l

Outcome of interest.

d

Total number of Gaussian quadrature nodes.

temp_beta

Vector of fitted coefficients.

phen

List of data matrices containing both left and right information.

r1

Gaussian quadrature nodes.

k

Total number of outcomes.

Value

The output is a vector of the survival values of the left times.

S_ik(R_ik)

Description

Calculates the survival function of the right time interval for outcome k for quadrature node d.

Usage

surv_right(l, d, temp_beta, phen, r1, k)

Arguments

l

Outcome of interest.

d

Total number of Gaussian quadrature nodes.

temp_beta

Vector of fitted coefficients.

phen

List of data matrices containing both left and right information.

r1

Gaussian quadrature nodes.

k

Total number of outcomes.

Value

The output is a vector of the survival values of the left times.

Survival Difference Product without Outcome l

Description

Calculate the product of the difference between survival terms excluding that of the outcome of interest.

Usage

without_one_phen(l, k, store)

Arguments

l

Outcome of interest.

k

Total number of outcomes.

store

Array of difference between left and right survival values.

Value

A n x (k-1) matrix where each column is the product of all the differences of left and right survival values across all outcomes excluding the column index outcome.

Survival Difference Product without Outcomes l and m

Description

Differnence of survival functions multiplied across all outcomes excluding outcomes l and m.

Usage

without_two_phen(l, m, k, store, n, d)

Arguments

l

The first outcome of interest.

m

The second outcome of interest.

k

Total number of outcomes.

store

Array of difference between left and right survival values.

n

Total number of observation.

d

Total number of quadrature nodes.

Value

A n x (k-2) matrix containing the product of all the differences of left and right survival values across all outcomes excluding outcomes l and m.