estimation {CaseCohortCoxSurvival}

estimation

Description

Estimates the log-relative hazard, baseline hazards at each unique event time, cumulative baseline hazard in a given time interval [Tau1, Tau2] and pure risk in [Tau1, Tau2] and for a given covariate profile x.

Usage

estimation(mod, Tau1 = NULL, Tau2 = NULL, x = NULL, missing.data = NULL, 
riskmat.phase2 = NULL, dNt.phase2 = NULL, status.phase2 = NULL)

Arguments

mod

a Cox model object, result of function coxph.

Tau1

left bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the first event time.

Tau2

right bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the last event time.

x

vector of length p, specifying the covariate profile considered for the pure risk. Default is (0,...,0).

missing.data

was data on the p covariates missing for certain individuals in the phase-two data (i.e., was a third phase of sampling performed)? If missing.data = TRUE, the arguments below need to be provided. Default is FALSE.

riskmat.phase2

at risk matrix for the phase-two data at all of the case event times, even those with missing covariate data. Needs to be provided if missing.data = TRUE.

dNt.phase2

counting process matrix for failures in the phase-two data. Needs to be provided if missing.data = TRUE and status.phase2 = NULL.

status.phase2

vector indicating the case status in the phase-two data. Needs to be provided if missing.data = TRUE and dNt.phase2 = NULL.

Details

estimation returns the log-relative hazard estimates provided by mod, and estimates the baseline hazard point mass at any event time non-parametrically.

estimation works for estimation from a case-cohort with design weights or calibrated weights, when the case-cohort consists of the subcohort and cases not in the subcohort (i.e., case-cohort obtained from two phases of sampling), as well as with design weights when covariate data was missing for certain individuals in the phase-two data (i.e., case-cohort obtained from three phases of sampling).

Value

beta.hat: vector of length p with log-relative hazard estimates.

lambda0.t.hat: vector with baseline hazards estimates at each unique event time.

Lambda0.Tau1Tau2.hat: cumulative baseline hazard estimate in [Tau1, Tau2].

Pi.x.Tau1Tau2.hat: pure risk estimate in [Tau1, Tau2] and for covariate profile x.

References

Breslow, N. (1974). Covariance Analysis of Censored Survival Data. Biometrics, 30, 89-99.

Etievant, L., Gail, M.H. (2023). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Submitted.

See Also

estimation.CumBH, estimation.PR, influences, influences.RH, influences.CumBH, influences.PR, influences.missingdata, influences.RH.missingdata, influences.CumBH.missingdata, and influences.PR.missingdata.

Examples

data(dataexample.missingdata, package="CaseCohortCoxSurvival")
cohort      <- dataexample.missingdata$cohort # a simulated cohort
casecohort  <- dataexample.missingdata$casecohort # a simulated stratified case-cohort
riskmat.phase2  <- dataexample.missingdata$riskmat.phase2
dNt.phase2      <- dataexample.missingdata$dNt.phase2

Tau1    <- 0 # given time interval for the pure risk
Tau2    <- 8
x       <- c(-1, 1, -0.6) # given covariate profile for the pure risk

# Estimation using the whole cohort

mod.cohort <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = cohort, 
                    robust = TRUE)
estimation.cohort <- estimation(mod = mod.cohort, Tau1 = Tau1, Tau2 = Tau2, 
                                x = x)

# print the vector with log-relative hazard estimates
estimation.cohort$beta.hat

# print the cumulative baseline hazard estimate
estimation.cohort$Lambda0.Tau1Tau2.hat

# print the pure risk estimate
estimation.cohort$Pi.x.Tau1Tau2.hat

# Estimation using the stratified case-cohort with known design weights

mod <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort, 
             weight = weights.true, id = id, robust = TRUE)
estimation.casecohort <- estimation(mod = mod, Tau1 = Tau1, Tau2 = Tau2, x = x,
                                    missing.data = TRUE, 
                                    riskmat.phase2 = riskmat.phase2, 
                                    dNt.phase2 = dNt.phase2)

# print the vector with log-relative hazard estimates
estimation.casecohort$beta.hat

# print the cumulative baseline hazard estimate
estimation.casecohort$Lambda0.Tau1Tau2.hat

# print the pure risk estimate
estimation.casecohort$Pi.x.Tau1Tau2.hat