estimation.weights.phase3 {CaseCohortCoxSurvival} | R Documentation |

## estimation.weights.phase3

### Description

Estimates the weights for the third phase of sampling (due to missingness).

### Usage

```
estimation.weights.phase3(B.phase3, total.phase2, gamma0 = NULL, niter.max = NULL,
epsilon.stop = NULL)
```

### Arguments

`B.phase3` |
matrix for the case-cohort (phase-three data), with phase-three
sampling strata indicators. It should have as many columns as phase-three strata
( |

`total.phase2` |
vector of length |

`gamma0` |
vector of length |

`niter.max` |
maximum number of iterations for the iterative optimization
algorithm. Default is |

`epsilon.stop` |
threshold for the difference between the estimated weighted
total and the total in the whole cohort. If this difference is less than the
value of |

### Details

`estimation.weights.phase3`

estimates the phase-three sampling weights by solving in
`\gamma`

```
\sum_{j=1}^J \sum_{i=1}^{n^{(j)}} \lbrace \xi_{i,j} V_{i,j}
\text{exp}( \gamma' B_{i,j}) B_{i,j} - \xi_{i,j} B_{i,j} \rbrace = 0,
```

with `\xi_{i,j}`

the phase-two sampling indicator and `V_{i,j}`

the phase-three
sampling indicator of individual `i`

in stratum `j`

, and with
`\sum_{j=1}^J \sum_{i=1}^{n^{(j)}} \xi_{i,j} B_{i,j}`

the total in the
phase-two data. See Section 5.2 in Etievant and Gail (2023).
The Newton Raphson method is used to solve the optimization problem.

In the end, the estimated weights are given by `\text{exp}(\hat \gamma' B_{i,j})`

,
and `\sum_{j=1}^J \sum_{i=1}^{n^{(j)}} \xi_{i,j} V_{i,j} \text{exp}(\hat \gamma' B_{i,j}) B_{i,j}`

gives the estimated total.

### Value

`gamma.hat`

: vector of length `J^{(3)}`

with final gamma values.

`estimated.weights`

: vector with the estimated phase-three weights for the
individuals in the case-cohort (phase-three data), computed from `B.phase3`

and `gamma.hat`

.

`estimated.total`

: vector with the estimated totals, computed from the
`estimated.weights`

and `B.phase3`

.

### 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`

and `influences.PR.missingdata`

.

### Examples

```
data(dataexample.missingdata, package="CaseCohortCoxSurvival")
casecohort <- dataexample.missingdata$casecohort # a simulated stratified case-cohort
# phase-two data: dataexample.missingdata$casecohort.phase2
B.phase2 <- dataexample.missingdata$B.phase2
B.phase3 <- dataexample.missingdata$B.phase3
total.B.phase2 <- colSums(B.phase2)
J3 <- ncol(B.phase3)
estimation.weights.p3 <- estimation.weights.phase3(B.phase3 = B.phase3,
total.phase2 = total.B.phase2,
gamma0 = rep(0, J3),
niter.max = 10^(4),
epsilon.stop = 10^(-10))
# print estimated phase-three weights
#estimation.weights.p3$estimated.weights
```

*CaseCohortCoxSurvival*version 0.0.34 Index]