influences.PR {CaseCohortCoxSurvival}

influences.PR

Description

Computes the influences on the pure risk in the time interval [Tau1, Tau2] and for a given covariate profile x, from that on the log-relative hazard and cumulative baseline hazard. Can take calibration of the design weights into account.

Usage

influences.PR(beta, Lambda0.Tau1Tau2, x = NULL, infl.beta, 
infl.Lambda0.Tau1Tau2, calibrated = NULL, infl2.beta = NULL, 
infl2.Lambda0.Tau1Tau2 = NULL)

Arguments

beta

vector of length p with log-relative hazard values.

Lambda0.Tau1Tau2

cumulative baseline hazard in [Tau1, Tau2].

x

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

infl.beta

matrix with the overall influences on the log-relative hazard estimates.

infl.Lambda0.Tau1Tau2

vector with the overall influences on the cumulative baseline hazard estimate in [Tau1, Tau2].

calibrated

are calibrated weights used for the estimation of the parameters? If calibrated = TRUE, the arguments below need to be provided. Default is FALSE.

infl2.beta

matrix with the phase-two influences on the log-relative hazard estimates. Needs to be provided if missing.data = TRUE.

infl2.Lambda0.Tau1Tau2

vector with the phase-two influences on the cumulative baseline hazard estimate in [Tau1, Tau2]. Needs to be provided if missing.data = TRUE.

Details

influences.PR works for estimation from a case-cohort with design weights or calibrated weights (case-cohort consisting of the subcohort and cases not in the subcohort, i.e., case-cohort obtained from two phases of sampling).

If covariate information is missing for certain individuals in the phase-two data (i.e., case-cohort obtained from three phases of sampling), use influences.PR.missingdata.

influences uses the influence formulas provided in Etievant and Gail (2023). More precisely, as in Section 3.2 if calibrated = FALSE, and as in Section 4.3 if calibrated = TRUE.

If calibrated = FALSE, the infuences are only provided for the individuals in the case-cohort. If calibrated = TRUE, the influences are provided for all the individuals in the cohort.

Value

infl.Pi.x.Tau1Tau2.hat: vector with the overall influences on the pure risk estimate in [Tau1, Tau2] and for covariate profile x.

infl2.Pi.x.Tau1Tau2.hat: vector with the phase-two influences on the pure risk estimate in [Tau1, Tau2] and for covariate profile x. Returned if calibrated = TRUE.

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

References

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

Examples

data(dataexample, package="CaseCohortCoxSurvival")
cohort      <- dataexample$cohort # a simulated cohort
casecohort  <- dataexample$casecohort # a simulated stratified case-cohort
A           <- dataexample$A # matrix with auxiliary variables values in the cohort

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

# Estimation using the whole cohort

mod.cohort <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = cohort, 
                    robust = TRUE)
estimation.cohort     <- influences(mod.cohort, Tau1 = Tau1, Tau2 = Tau2, x = x)
beta.hat.cohort       <- estimation.cohort$beta.hat
Lambda0.hat.cohort    <- estimation.cohort$Lambda0.Tau1Tau2.hat
infl.beta.cohort      <- estimation.cohort$infl.beta
infl.Lambda0.cohort   <- estimation.cohort$infl.Lambda0.Tau1Tau2

estimation.cohort2    <- influences.PR(beta = beta.hat.cohort, 
                                       Lambda0.Tau1Tau2 = Lambda0.hat.cohort, 
                                       x = v, infl.beta = infl.beta.cohort, 
                                       infl.Lambda0.Tau1Tau2 = infl.Lambda0.cohort)

# print the influences on the pure risk estimate for profile v
#estimation.cohort2$infl.Pi.x.Tau1Tau2

# Estimation using the stratified case-cohort with weights calibrated on A

mod.calib <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort, 
                   weight = weights.calib, id = id, robust = TRUE)
estimation.calib    <- influences(mod.calib, A = A, calibrated = TRUE, 
                                  Tau1 = Tau1, Tau2 = Tau2, x = x)
beta.hat.calib      <- estimation.calib$beta.hat
Lambda0.hat.calib   <- estimation.calib$Lambda0.Tau1Tau2.hat
infl.beta.calib     <- estimation.calib$infl.beta
infl.Lambda0.calib  <- estimation.calib$infl.Lambda0.Tau1Tau2
infl2.beta.calib    <- estimation.calib$infl2.beta
infl2.Lambda0.calib <- estimation.calib$infl2.Lambda0.Tau1Tau2

estimation.calib2   <- influences.PR(beta = beta.hat.calib,
                                     Lambda0.Tau1Tau2 = Lambda0.hat.calib, 
                                     x = v, infl.beta = infl.beta.calib,
                                     infl.Lambda0.Tau1Tau2 = infl.Lambda0.calib,
                                     calibrated = TRUE, 
                                     infl2.beta = infl2.beta.calib,
                                     infl2.Lambda0.Tau1Tau2 = infl2.Lambda0.calib)

# print the influences on the pure risk estimate for profile v
#estimation.calib2$infl.Pi.x.Tau1Tau2

# print the phase-two influences on the pure risk estimate for profile v
#estimation.calib2$infl2.Pi.x.Tau1Tau2