frailtypack (version 3.4.0)

ste: Surrogate threshold effect for the one-step Joint surrogate model for the evaluation of a canditate surrogate endpoint.

Description

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).

Usage

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

Arguments

object

An object inheriting from jointSurroPenal class (output from calling the jointSurroPenal or jointSurroCopPenal function ).

var.used

This argument takes two values. The first one is "error.estim" and indicates if the prediction error takes into account the estimation error of the estimates of the parameters. If the estimates are supposed to be known or if the dataset includes a high number of trials with a high number of subject per trial, value No.error can be used. The default is error.estim, which is highly recommended in practice.

alpha.

The confidence level for the prediction interval. The default is 0.05

pred.int.use

A character string that indicates the bound of the prediction interval to use to compute the STE. Possible values are up for the upper bound (the default) or lw for the lower bound. up when we have a protective treatment effect and lw when we have a deleterious treatment effect (see details).

Value

Returns and displays the STE.

Details

The STE is obtained by solving the equation l(\(\alpha\)) = 0 (resp. u(\(\alpha\)) = 0), where \(\alpha\) represents the corresponding STE, and l(\(\alpha\)) (resp. u(\(\alpha\))) is the lower (resp. upper) bound of the prediction interval of the treatment effect on the true endpoint (\(\beta\) + b) . 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(\(\alpha\)).

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

References

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.

See Also

jointSurroPenal, jointSurroCopPenal, predict

Examples

# NOT RUN {

# }
# 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")

# }
# NOT RUN {

# }