Power Calculations for SNP Studies with Censored Outcomes

Description

This package can be used to conduct asymptotic and empirical power and sample size calculations for Single-nucleotide Polymorphism (SNP) association studies with right censored time to event outcomes.

Details

The functions sim.snp.expsurv.power and survSNP.power.table can be used to conduct power and sample size calculations. The package vignette serves as a tutorial for using this package. The technical details are provided in the reference cited below. It is highly recommended that the vignette along with this are reviewed before using this package. Currently, this package only supports additive risk models.

Author(s)

Kouros Owzar, Zhiguo Li, Nancy Cox, Sin-Ho Jung and Chanhee Yi

References

Kouros Owzar, Zhiguo Li, Nancy Cox and Sin-Ho Jung. Power and Sample Size Calculations for SNP Association Studies with Censored Time-to-Event Outcomes. https://onlinelibrary.wiley.com/doi/full/10.1002/gepi.21645

Examples

# See vignette for examples including details on the example
# considered below

results<-sim.snp.expsurv.power(GHR=1.25, B=0, n=500, raf=0.1, erate=0.75, pilm=0.5, 
                               lm=1, model="additive", test="additive", alpha=0.05)
results[,c("n","erate","alpha","pow0")]


GHRs<-seq(1.05,1.5,by=0.05)
ns<-c(100,500,700)
rafs<-c(0.1,0.3,0.5)
erates<-c(0.5,0.7,0.9)
res<-survSNP.power.table(GHRs,ns,rafs,erates,pilm=0.5,lm=1,model="additive",
                         test="additive",alpha=0.05)

# Create key for illustration
KEY=paste("q=",levels(factor(res$raf)),sep="")
KEY<-list(lines=list(col=1:length(KEY),lty=1:length(KEY)),
          text=list(labels=paste("q=",levels(factor(res$raf)),sep="")),
          column=3)


# Illustrate Power
print(xyplot(pow0~GHR|factor(erate)*factor(n),group=factor(raf),
             data=res,type="l",lty=KEY$lines$lty,col=KEY$lines$col,
             key=KEY,
             xlab="Genotype Hazard Ratio",ylab="Power"))

# Illustrate Power (restricted to n=100)

print(xyplot(pow0~GHR|factor(erate),group=factor(raf),
             data=subset(res,n==ns[1]),
             type="l",lty=KEY$lines$lty,col=KEY$lines$col,
             key=KEY,
             xlab="Genotype Hazard Ratio",ylab="Power",
             sub=paste("n=",ns[1],", alpha=",round(unique(res$alpha),2))))

Calculating the asymptotic power and variance

Description

This function calculates the asymptotic power and variance assuming that the survival distribution is a mixture of exponentials with rates and the censoring distribution is uniform on the interval (a,b).

Usage

asypow(n, theta, a, b, lambda0, q, p, alpha, z,exactvar)

Arguments

Details

This function is called by sim.snp.expsurv.power to calculate the asymptotic variance (exact and approximate) formulas. It is not intended to be called directly by the user. To conduct power calculations, use sim.snp.expsurv.power or the convenience wrapper function survSNP.power.table.

Value

Author(s)

Kouros Owzar, Zhiguo Li, Nancy Cox, Sin-Ho Jung and Chanhee Yi

References

Kouros Owzar, Zhiguo Li, Nancy Cox and Sin-Ho Jung. Power and Sample Size Calculations for SNP Association Studies with Censored Time-to-Event Outcomes. https://onlinelibrary.wiley.com/doi/full/10.1002/gepi.21645

Calculate bound for censoring distribution.

Description

This function computes the bound

Usage

censbnd(lambda, p, crate, rootint = c(0.1, 1000))

Arguments

Details

The time to event distribution T is assumed to be a mixture of exponentials with parameter lambda0, lambda1 and lambda2 with mixing proportion p0,p1 and p2. Suppose that the censoring distribution is uniform on the interval [0,b]. This function calculates b for a desired censoring rate. It is not intended to be called directly by the user. To conduct power calculations, use sim.snp.expsurv.power or the convenience wrapper function survSNP.power.table.

Value

This function returns a list from the uniroot function. The root component of this list in the

Author(s)

Kouros Owzar, Zhiguo Li, Nancy Cox, Sin-Ho Jung and Chanhee Yi

References

Kouros Owzar, Zhiguo Li, Nancy Cox and Sin-Ho Jung. Power and Sample Size Calculations for SNP Association Studies with Censored Time-to-Event Outcomes. https://onlinelibrary.wiley.com/doi/full/10.1002/gepi.21645

Examples

censbnd(0.1,hwe(0.1),0.9)$root

Relative genotypic frequencies under HWE

Description

Compute relative genotypic frequencies for a given relative allelic frequency

Usage

hwe(raf)

Arguments

Details

For a bi-allelic SNP with genotypes AA, AB and BB, with a relative allele frequency q for the B allele, this function returns the corresponding relative genotypic frequencies. It is not intended to be called directly by the user. To conduct power calculations, use sim.snp.expsurv.power or the convenience wrapper function survSNP.power.table.

Value

A vector of length three relative genotypic frequencies.

Author(s)

Kouros Owzar, Zhiguo Li, Nancy Cox, Sin-Ho Jung and Chanhee Yi

References

Kouros Owzar, Zhiguo Li, Nancy Cox and Sin-Ho Jung. Power and Sample Size Calculations for SNP Association Studies with Censored Time-to-Event Outcomes. https://onlinelibrary.wiley.com/doi/full/10.1002/gepi.21645

Examples

censbnd(0.1,hwe(0.1),0.9)

Asymptotic and Empirical Power

Description

This function calculates asymptotic and empirical power for SNP association studies

Usage

sim.snp.expsurv.power(GHR, B, n, raf, erate, pilm, lm, model, test, alpha, 
                      exactvar = FALSE, interval = c(0, 10), rootint = c(0.1, 200))

Arguments

Details

This function calculates asymptotic and empirical power for SNP association studies

Value

This function returns a data.frame with the following columns

Author(s)

Kouros Owzar, Zhiguo Li, Nancy Cox, Sin-Ho Jung and Chanhee Yi

References

Kouros Owzar, Zhiguo Li, Nancy Cox and Sin-Ho Jung. Power and Sample Size Calculations for SNP Association Studies with Censored Time-to-Event Outcomes. https://onlinelibrary.wiley.com/doi/full/10.1002/gepi.21645

See Also

survSNP.power.table

Examples

# See vignette for examples including details on the example
# considered below

results<-sim.snp.expsurv.power(GHR=1.25, B=0, n=500, raf=0.1, erate=0.75, pilm=0.5, 
                               lm=1, model="additive", test="additive", alpha=0.05)
results[,c("n","erate","alpha","pow0")]

Simulation of Cox Score Statistic

Description

This function simulates the asymptotic P-value for the Cox score statistic under a specified genetic risk model

Usage

sim.snp.expsurv.sctest(n, gtprev, lam, a, b, ztest, diag = FALSE)

Arguments

Details

This function simulates the genotypes 0, 1 or 2 from relative genotypic frequencies. Then conditional on genotype, it simulates the time to event from an exponential distribution with parameter lambdag. The censoring time is drawn from a uniform law on the interval [a,b]. It is not intended to be called directly by the user. To conduct power calculations, use sim.snp.expsurv.power or the convenience wrapper function survSNP.power.table.

Value

A vector of length 2 containing the observed event rate and the asymptotic P-value for the Cox score test

Author(s)

Kouros Owzar, Zhiguo Li, Nancy Cox, Sin-Ho Jung and Chanhee Yi

References

Kouros Owzar, Zhiguo Li, Nancy Cox and Sin-Ho Jung. Power and Sample Size Calculations for SNP Association Studies with Censored Time-to-Event Outcomes. https://onlinelibrary.wiley.com/doi/full/10.1002/gepi.21645

Exponential Hazard Rates for a Genetic Risk Model

Description

This function calculates the exponential hazard rates for the conditional survival functions

Usage

surv.exp.gt.model(pilm, lm, gtprev, GRR, zmodel, interval)

Arguments

Details

Determines the time to event distributions in the three component mixture model discussed in the reference below. It is not intended to be called directly by the user. To conduct power calculations, use sim.snp.expsurv.power or the convenience wrapper function survSNP.power.table.

Value

A vector of length three containing the exponential hazard rates

Author(s)

Kouros Owzar, Zhiguo Li, Nancy Cox, Sin-Ho Jung and Chanhee Yi

References

Kouros Owzar, Zhiguo Li, Nancy Cox and Sin-Ho Jung. Power and Sample Size Calculations for SNP Association Studies with Censored Time-to-Event Outcomes. https://onlinelibrary.wiley.com/doi/full/10.1002/gepi.21645

Table for Asymptotic and Empirical Power

Description

This function produces a table with the resulting empirical and asymptotic power over a given range of Genotype Hazard Ratios, relative allelic frequencies, sample sizes, and event rates.

Usage

survSNP.power.table(GHRs, ns, rafs, erates, pilm, lm, model, test, alpha, 
                    exactvar = FALSE, B = 0)

Arguments

Details

This version only supports additive models.

Value

See output of sim.snp.expsurv.power.

Author(s)

Kouros Owzar, Zhiguo Li, Nancy Cox, Sin-Ho Jung and Chanhee Yi

References

Kouros Owzar, Zhiguo Li, Nancy Cox and Sin-Ho Jung. Power and Sample Size Calculations for SNP Association Studies with Censored Time-to-Event Outcomes. https://onlinelibrary.wiley.com/doi/full/10.1002/gepi.21645

Examples

GRRs<-seq(1.5,2,by=0.25)
ns<-c(100,500,1000)
rafs<-c(0.3,0.5,0.7)
erates=c(0.5,0.7,0.9)
res<-survSNP.power.table(GRRs,ns,rafs,erates,pilm=0.5,lm=1,model="additive",
                         test="additive",alpha=0.05)

# Create key for illustration
KEY=paste("q=",levels(factor(res$raf)),sep="")
KEY<-list(lines=list(col=1:length(KEY),lty=1:length(KEY)),
          text=list(labels=paste("q=",levels(factor(res$raf)),sep="")),
          column=3)


# Illustrate Power
print(xyplot(pow0~GHR|factor(erate)*factor(n),group=factor(raf),
             data=res,type="l",lty=KEY$lines$lty,col=KEY$lines$col,
             key=KEY,
             xlab="Genotype Hazard Ratio",ylab="Power"))

# Illustrate Power (restricted to n=100)

print(xyplot(pow0~GHR|factor(erate),group=factor(raf),
             data=subset(res,n==ns[1]),
             type="l",lty=KEY$lines$lty,col=KEY$lines$col,
             key=KEY,
             xlab="Genotype Hazard Ratio",ylab="Power",
             sub=paste("n=",ns[1],", alpha=",round(unique(res$alpha),2))))