Description Usage Arguments Details Value Author(s) References See Also Examples

This function compute the surrogate threshold effect (STE) from the one-step joint frailty
`model`

or joint frailty-copula
`model`

. The STE is defined as the minimum treament effect
on surrogate endpoint, necessary to predict a non-zero effect on
true endpoint (Burzykowski *et al.*, 2006).

1 2 | ```
ste(object, var.used = "error.estim", alpha. = 0.05,
pred.int.use = "up")
``` |

`object` |
An object inheriting from |

`var.used` |
This argument takes two values. The first one is |

`alpha.` |
The confidence level for the prediction interval. The default is |

`pred.int.use` |
A character string that indicates the bound of the prediction interval
to use to compute the STE. Possible values are |

The STE is obtained by solving the equation
`l`

(*α*_{0}) `= 0`

(resp.
`u`

(*α*_{0}) `= 0`

), where
*α*_{0} represents
the corresponding STE, and
`l`

(*α*_{0}) (resp.
`u`

(*α*_{0})) is the lower (resp. upper) bound of the prediction interval
of the treatment effect on the true endpoint (*β* + b_{0}) . Thereby,

where
represents the set of estimates for the fixed-effects and the
variance-covariance parameters of the random effects obtained from the joint surrogate
`model`

(Sofeu *et al.*, 2019).

If the previous equations gives two solutions, STE can be the
minimum (resp. the maximum) value or both of them, according to the shape of the function.
If the concavity of the function is turned upwards, STE is the first value and
the second value represents the maximum (res. the minimum) treament value observable
on the surrogate that can predict a nonzero treatment effect on true endpoint.
If the concavity of the function is turned down, both of the solutions
represent the STE and the interpretation is such that accepted values of the
treatment effects on `S`

predict a nonzero treatment effects on `T`

Given that negative values of treatment effect indicate a reduction of the risk
of failure and are considered beneficial, STE is recommended to be computed from
the upper prediction
limit
`u`

(*α*_{0}).

The details on the computation of STE are described in
Burzykowski *et al.* (2006).

Returns and displays the STE.

Casimir Ledoux Sofeu casimir.sofeu@u-bordeaux.fr, scl.ledoux@gmail.com and Virginie Rondeau virginie.rondeau@inserm.fr

Burzykowski T, Buyse M (2006). "Surrogate threshold effect: an alternative measure for meta-analytic surrogate endpoint validation." Pharmaceutical Statistics, 5(3), 173-186.ISSN 1539-1612.

Sofeu, C. L., Emura, T., and Rondeau, V. (2019). One-step validation method for surrogate endpoints using data from multiple randomized cancer clinical trials with failure-time endpoints. Statistics in Medicine 38, 2928-2942.

Sofeu, C. L. and Rondeau, V. (2020). How to use frailtypack for validating failure-time surrogate endpoints using individual patient data from meta-analyses of randomized controlled trials. PLOS ONE; 15, 1-25.

`jointSurroPenal, jointSurroCopPenal`

, `predict`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
## Not run:
###--- Joint surrogate model ---###
###---evaluation of surrogate endpoints---###
data(dataOvarian)
joint.surro.ovar <- jointSurroPenal(data = dataOvarian, n.knots = 8,
init.kappa = c(2000,1000), indicator.alpha = 0,
nb.mc = 200, scale = 1/365)
# ======STE=====
# Assuming errors on the estimates
ste(joint.surro.ovar, var.used = "error.estim")
# Assuming no errors on the estimates
ste(joint.surro.ovar, var.used = "No.error", pred.int.use = "up")
## End(Not run)
``` |

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