auxiliary.construction {CaseCohortCoxSurvival}

auxiliary.construction

Description

Creates the auxiliary variables proposed by Breslow et al. (Stat. Biosci., 2009), Breslow and Lumley (IMS, 2013), and proposed by Shin et al. (Biometrics, 2020).

Usage

 auxiliary.construction(mod, Tau1=NULL, Tau2=NULL, method="Breslow",
                        time.on.study=NULL, casecohort=NULL)

Arguments

mod

A cox model object, result of function coxph run on the cohort data with imputed covariate values.

Tau1

Left bound of the time interval considered for the cumulative baseline hazard. Default is the first event time.

Tau2

Right bound of the time interval considered for the cumulative baseline hazard. Default is the last event time.

method

"Breslow", "Breslow2013" or "Shin" to specify the algorithm to construct the auxiliary variables. The default is "Breslow".

time.on.study

Total folow-up time in [Tau1, Tau2]. Required for method = "Shin".

casecohort

Data frame containing the casecohort data. It must include columns "weights" containing the design weights and "id" as an id variable. Required for method = "Shin".

Details

Construction of the auxiliary variables can follow Breslow et al. (2009), Breslow and Lumley (2013), or Shin et al. (2020) (method). It relies on predictions of the phase-two covariates for all members of the cohort. The auxiliary variables are given by (i) the influences for the log-relative hazard parameters estimated from the Cox model with imputed cohort data; (ii) the influences for the cumulative baseline parameter estimated from the Cox model with imputed cohort data; (iii) the products of total follow-up time (on the time interval for which pure risk is to be estimated) with the estimated relative hazard for the imputed cohort data, where the log-relative hazard parameters are estimated from the Cox model with case-cohort data and weights calibrated with (i). When method = Breslow, calibration of the design weights is against (i), as proposed by Breslow et al. (2009) to improve efficiency of case-cohort estimates of relative hazard. When method = Breslow2013, calibration of the design weights is against (i) and (ii), as proposed by Breslow and Lumley (2013) to also improve efficiency of case-cohort estimates of cumulative baseline hazard. When method = Shin, calibration is against (i) and (iii), as proposed by Shin et al. (2020) to improve efficiency of relative hazard and pure risk estimates under the nested case-control design. See also Section 4.1 in Etievant and Gail (2023).

Following Etievant and Gail (2023), in function caseCohortCoxSurvival we only provide calibration of the design weight as proposed by Breslow et al. (2009) or Shin et al. (2020).

Value

A.RH.Breslow: matrix with the influences on the log-relative hazard, estimated from the cohort with imputed phase-two covariate values for method = "Breslow" and method = "Breslow2013".

A.CumBH.Breslow: matrix with the influences on the cumulative baseline hazard in [Tau1, Tau2], estimated from the cohort with imputed phase-two covariate values for method = "Breslow2013".

A.RH.Shin: matrix with the influences on the log-relative hazard, estimated from the cohort with imputed phase-two covariate values for method = "Shin".

A.PR.Shin: matrix with the products of total follow-up times in [Tau1, Tau2] and estimated relative hazards, estimated from the cohort with imputed phase-two covariate values for method = "Shin".

References

Breslow, N.E. and Lumley, T. (2013). Semiparametric models and two-phase samples: Applications to Cox regression. From Probability to Statistics and Back: High-Dimensional Models and Processes, 9, 65-78.

Breslow, N.E., Lumley, T., Ballantyne, C.M., Chambless, L.E. and Kulich, M. (2009). Improved Horvitz- Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology. Statistics in Biosciences, 1, 32-49.

Shin Y.E., Pfeiffer R.M., Graubard B.I., Gail M.H. (2020) Weight calibration to improve the efficiency of pure risk estimates from case-control samples nested in a cohort. Biometrics, 76, 1087-1097

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

calibration, influences, influences.RH, influences.CumBH and influences.PR.

Examples

  data(dataexample, package="CaseCohortCoxSurvival")

  cohort <- dataexample$cohort
  Tau1   <- 0
  Tau2   <- 8

  # Running the coxph model on the imputed cohort data 
  mod.imputedcohort <- coxph(Surv(times, status) ~ X1.pred + X2.pred + X3.pred,
                             data = cohort, robust = TRUE)

  # method = Breslow
  ret <- auxiliary.construction(mod.imputedcohort)
  # print auxiliary variables based on the log-relative hazard influences
  ret$A.RH.Breslow[1:5,]

  # Example for method = Shin, variables names must match with fitted model
  casecohort              <- dataexample$casecohort
  casecohort[, "X1.pred"] <- casecohort[, "X1"]
  casecohort[, "X2.pred"] <- casecohort[, "X2"]
  casecohort[, "X3.pred"] <- casecohort[, "X3"]

  time.on.study <- pmax(pmin(Tau2, cohort$times) - Tau1, 0)
  ret <- auxiliary.construction(mod.imputedcohort, method="Shin",
                 time.on.study=time.on.study, casecohort=casecohort)
  ret$A.PR.Shin[1:5]