variance.missingdata {CaseCohortCoxSurvival} | R Documentation |

## variance.missingdata

### 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, when covariate information is missing for individuals in the phase-two sample.

### Usage

```
variance.missingdata(n, casecohort, casecohort.phase2, weights,
weights.phase2, weights.p2.phase2, infl2, infl3, stratified.p2 = NULL,
estimated.weights = NULL)
```

### Arguments

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

`casecohort` |
If |

`casecohort.phase2` |
If |

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

`weights.phase2` |
vector with design weights for the individuals in the phase-two sample. |

`weights.p2.phase2` |
vector with phase-two design weights for the individuals in the phase-two sample. |

`infl2` |
matrix with the phase-two influences on the parameter. |

`infl3` |
matrix with the phase-three influences on the parameter. |

`stratified.p2` |
was the second phase of sampling stratified on |

`estimated.weights` |
were the phase-three weights estimated? Default is |

### Details

`variance.missingdata`

works for estimation from a case cohort with design
weights and when covariate information was missing for certain individuals in the
phase-two data (i.e., case cohort obtained from three phases of sampling and
consisting of individuals in the phase-two data without missing covariate
information).

If there are no missing covariates in the phase- two sample, use `variance`

with either design weights or calibrated weights.

`variance.missingdata`

uses the variance formulas provided in Etievant and
Gail (2023). More precisely, as in Section 5.4 if `estimated.weights = TRUE`

, and as in
Web Appendix H.2 if `estimated.weights = FALSE`

.

### Value

`variance`

: variance estimate.

### 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.missingdata`

, `influences.RH.missingdata`

, `influences.CumBH.missingdata`

,

`influences.PR.missingdata`

, `robustvariance`

and `variance`

.

### Examples

```
data(dataexample.missingdata, package="CaseCohortCoxSurvival")
cohort <- dataexample.missingdata$cohort # a simulated cohort
n <- nrow(cohort)
casecohort <- dataexample.missingdata$casecohort # a simulated stratified case cohort
casecohort.phase2 <- dataexample.missingdata$casecohort.phase2
riskmat.phase2 <- dataexample.missingdata$riskmat.phase2
dNt.phase2 <- dataexample.missingdata$dNt.phase2
B.phase2 <- dataexample.missingdata$B.phase2
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 true known design weights
mod <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort,
weight = weights.true, id = id, robust = TRUE)
estimation <- influences.missingdata(mod = mod, riskmat.phase2 = riskmat.phase2,
dNt.phase2 = dNt.phase2, Tau1 = Tau1,
Tau2 = Tau2, x = x)
infl.beta <- estimation$infl.beta
infl.Lambda0 <- estimation$infl.Lambda0.Tau1Tau2
infl.Pi.x <- estimation$infl.Pi.x.Tau1Tau2
infl2.beta <- estimation$infl2.beta
infl2.Lambda0 <- estimation$infl2.Lambda0.Tau1Tau2
infl2.Pi.x <- estimation$infl2.Pi.x.Tau1Tau2
infl3.beta <- estimation$infl3.beta
infl3.Lambda0 <- estimation$infl3.Lambda0.Tau1Tau2
infl3.Pi.x <- estimation$infl3.Pi.x.Tau1Tau2
# variance estimate for the log-relative hazard
variance.missingdata(n = n, casecohort = casecohort,
casecohort.phase2 = casecohort.phase2,
weights = casecohort$weights.true,
weights.phase2 = casecohort.phase2$weights.true,
weights.p2.phase2 = casecohort.phase2$weights.p2.true,
infl2 = infl2.beta, infl3 = infl3.beta,
stratified.p2 = TRUE)
# variance estimate for the cumulative baseline hazard estimate
variance.missingdata(n = n, casecohort = casecohort,
casecohort.phase2 = casecohort.phase2,
weights = casecohort$weights.true,
weights.phase2 = casecohort.phase2$weights.true,
weights.p2.phase2 = casecohort.phase2$weights.p2.true,
infl2 = infl2.Lambda0, infl3 = infl3.Lambda0,
stratified.p2 = TRUE)
# variance estimate for the pure risk estimate
variance.missingdata(n = n, casecohort = casecohort,
casecohort.phase2 = casecohort.phase2,
weights = casecohort$weights.true,
weights.phase2 = casecohort.phase2$weights.true,
weights.p2.phase2 = casecohort.phase2$weights.p2.true,
infl2 = infl2.Pi.x, infl3 = infl3.Pi.x,
stratified.p2 = TRUE)
# Estimation using the stratified case cohort with estimated weights, and
# accounting for the estimation through the influences
mod.est <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort,
weight = weights.est, id = id, robust = TRUE)
estimation.est <- influences.missingdata(mod.est,
riskmat.phase2 = riskmat.phase2,
dNt.phase2 = dNt.phase2,
estimated.weights = TRUE,
B.phase2 = B.phase2, Tau1 = Tau1,
Tau2 = Tau2, x = x)
infl.beta.est <- estimation.est$infl.beta
infl.Lambda0.est <- estimation.est$infl.Lambda0.Tau1Tau2
infl.Pi.x.est <- estimation.est$infl.Pi.x.Tau1Tau2
infl2.beta.est <- estimation.est$infl2.beta
infl2.Lambda0.est <- estimation.est$infl2.Lambda0.Tau1Tau2
infl2.Pi.x.est <- estimation.est$infl2.Pi.x.Tau1Tau2
infl3.beta.est <- estimation.est$infl3.beta
infl3.Lambda0.est <- estimation.est$infl3.Lambda0.Tau1Tau2
infl3.Pi.x.est <- estimation.est$infl3.Pi.x.Tau1Tau2
# variance estimate for the log-relative hazard
variance.missingdata(n = n, casecohort = casecohort,
casecohort.phase2 = casecohort.phase2,
weights = casecohort$weights.est,
weights.phase2 = casecohort.phase2$weights.est,
weights.p2.phase2 = casecohort.phase2$weights.p2.true,
infl2 = infl2.beta.est, infl3 = infl3.beta.est,
stratified.p2 = TRUE, estimated.weights = TRUE)
# variance estimate for the cumulative baseline hazard estimate
variance.missingdata(n = n, casecohort = casecohort,
casecohort.phase2 = casecohort.phase2,
weights = casecohort$weights.est,
weights.phase2 = casecohort.phase2$weights.est,
weights.p2.phase2 = casecohort.phase2$weights.p2.true,
infl2 = infl2.Lambda0.est, infl3 = infl3.Lambda0.est,
stratified.p2 = TRUE, estimated.weights = TRUE)
# variance estimate for the pure risk estimate
variance.missingdata(n = n, casecohort = casecohort,
casecohort.phase2 = casecohort.phase2,
weights = casecohort$weights.est,
weights.phase2 = casecohort.phase2$weights.est,
weights.p2.phase2 = casecohort.phase2$weights.p2.true,
infl2 = infl2.Pi.x.est, infl3 = infl3.Pi.x.est,
stratified.p2 = TRUE, estimated.weights = TRUE)
```

*CaseCohortCoxSurvival*version 0.0.34 Index]