variance {CaseCohortCoxSurvival} | R Documentation |

## variance

### Description

Computes the variance estimate that follows the complete variance decomposition, for a parameter such as log-relative hazard, cumulative baseline hazard or covariate specific pure-risk.

### Usage

```
variance(n, casecohort, weights = NULL, infl, calibrated = NULL,
infl2 = NULL, cohort = NULL, stratified = NULL,
variance.phase2 = NULL)
```

### Arguments

`n` |
number of individuals in the whole cohort. |

`casecohort` |
If |

`weights` |
vector with design weights for the individuals in the case-cohort data. |

`infl` |
matrix with the overall influences on the parameter. |

`calibrated` |
are calibrated weights used for the estimation of the
parameters? If |

`infl2` |
matrix with the phase-two influences on the parameter. Needs to be
provided if |

`cohort` |
If |

`stratified` |
was the sampling of the case-cohort stratified on |

`variance.phase2` |
should the phase-two variance component also be returned?
Default is |

### Details

`variance`

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 `variance.missingdata`

.

`variance`

uses the variance formulas provided in Etievant and Gail
(2023). More precisely, as in Section 3.3 if `calibrated = FALSE`

, and as in
Section 4.3 if `calibrated = TRUE`

.

### Value

`variance`

: variance estimate.

`variance.phase2`

: phase-two variance component.

### 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

`influences`

, `influences.RH`

, `influences.CumBH`

,
`influences.PR`

, `robustvariance`

and `variance.missingdata`

.

### Examples

```
data(dataexample, package="CaseCohortCoxSurvival")
cohort <- dataexample$cohort # a simulated cohort
n <- nrow(cohort)
casecohort <- dataexample$casecohort # a simulated stratified case-cohort
A <- dataexample$A # matrix with auxiliary variables values in the cohort
Tau1 <- 0 # given time interval for the pure risk
Tau2 <- 8
x <- c(-1, 1, -0.6) # given covariate profile for the pure risk
# Estimation using the stratified case-cohort with design weights
mod <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort,
weight = weights, id = id, robust = TRUE)
# parameters and influences estimation
estimation <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x)
beta.hat <- estimation$beta.hat
Lambda0.hat <- estimation$Lambda0.Tau1Tau2.hat
Pi.x.hat <- estimation$Pi.x.Tau1Tau2.hat
infl.beta <- estimation$infl.beta
infl.Lambda0 <- estimation$infl.Lambda0.Tau1Tau2
infl.Pi.x <- estimation$infl.Pi.x.Tau1Tau2
# variance estimate for the log-relative hazard
variance(n = n, casecohort = casecohort, infl = infl.beta, stratified = TRUE)
# variance estimate for the cumulative baseline hazard estimate
variance(n = n, casecohort = casecohort, infl = infl.Lambda0, stratified = TRUE)
# variance estimate for the pure risk estimate
variance(n = n, casecohort = casecohort, infl = infl.Pi.x, stratified = TRUE)
# Estimation using the stratified case-cohort with calibrated weights
mod.calib <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort,
weight = weights.calib, id = id, robust = TRUE)
# Parameters and influences estimation
estimation.calib <- influences(mod.calib, A = A, calibrated = TRUE,
Tau1 = Tau1, Tau2 = Tau2, x = x)
beta.hat.calib <- estimation.calib$beta.hat
Lambda0.hat.calib <- estimation.calib$Lambda0.Tau1Tau2.hat
Pi.x.hat.calib <- estimation.calib$Pi.x.Tau1Tau2.hat
infl.beta.calib <- estimation.calib$infl.beta
infl.Lambda0.calib <- estimation.calib$infl.Lambda0.Tau1Tau2
infl.Pi.x.calib <- estimation.calib$infl.Pi.x.Tau1Tau2
infl2.beta.calib <- estimation.calib$infl2.beta
infl2.Lambda0.calib <- estimation.calib$infl2.Lambda0.Tau1Tau2
infl2.Pi.x.calib <- estimation.calib$infl2.Pi.x.Tau1Tau2
# variance estimate for the log-relative hazard
variance(n = n, casecohort = casecohort, cohort = cohort, calibrated = TRUE,
stratified = TRUE, infl = infl.beta.calib, infl2 = infl2.beta.calib)
# variance estimate for the cumulative baseline hazard estimate
variance(n = n, casecohort = casecohort, cohort = cohort, calibrated = TRUE,
stratified = TRUE, infl = infl.Lambda0.calib,
infl2 = infl2.Lambda0.calib)
# variance estimate for the pure risk estimate
variance(n = n, casecohort = casecohort, cohort = cohort, calibrated = TRUE,
stratified = TRUE, infl = infl.Pi.x.calib, infl2 = infl2.Pi.x.calib)
```

*CaseCohortCoxSurvival*version 0.0.34 Index]