influences {CaseCohortCoxSurvival}

influences

Description

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

Usage

influences(mod, Tau1 = NULL, Tau2 = NULL, x = NULL, calibrated = NULL, 
A = 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).

calibrated

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

A

n \times q matrix with the values of the auxiliary variables used for the calibration of the weights in the whole cohort. Needs to be provided if calibrated = TRUE.

Details

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

infl.lambda0.t: matrix with the overall influences on the baseline hazards estimates at each unique event time.

infl.Lambda0.Tau1Tau2.hat: vector with the overall influences on the cumulative baseline hazard estimate in [Tau1, Tau2].

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

infl2.beta: matrix with the phase-two influences on the log-relative hazard estimates. Returned if calibrated = TRUE.

infl2.lambda0.t: matrix with the phase-two influences on the baseline hazards estimates at each unique event time. Returned if calibrated = TRUE.

infl2.Lambda0.Tau1Tau2.hat: vector with the phase-two influences on the cumulative baseline hazard estimate in [Tau1, Tau2]. Returned if calibrated = TRUE.

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.

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

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.RH, influences.CumBH, influences.PR, 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

# 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)

# 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

# print the influences on the log-relative hazard estimates
#estimation.cohort$infl.beta

# print the influences on the cumulative baseline hazard estimate
#estimation.cohort$infl.Lambda0.Tau1Tau2

# print the influences on the pure risk estimate
#estimation.cohort$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)

# print the influences on the log-relative hazard estimates
#estimation.calib$infl.beta

# print the influences on the cumulative baseline hazard estimate
#estimation.calib$infl.Lambda0.Tau1Tau2

# print the influences on the pure risk estimate
#estimation.calib$infl.Pi.x.Tau1Tau2

# print the phase-two influences on the log-relative hazard estimates
#estimation.calib$infl2.beta

# print the phase-two influences on the cumulative baseline hazard estimate
#estimation.calib$infl2.Lambda0.Tau1Tau2

# print the phase-two influences on the pure risk estimate
#estimation.calib$infl2.Pi.x.Tau1Tau2