auxiliary.construction {CaseCohortCoxSurvival} | R Documentation |

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).

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

`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 |

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

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).

`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".

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.

`calibration`

, `influences`

, `influences.RH`

,
`influences.CumBH`

and `influences.PR`

.

```
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]
```

[Package *CaseCohortCoxSurvival* version 0.0.32 Index]