covariance: Covariance between two survival probability estimates.

In InferenceSMR: Inference About the Standardized Mortality Ratio when Evaluating the Effect of a Screening Program on Survival

Covariance between two survival probability estimates.

Description

The function covariance calculates the covariance between two survival probabilty obtained with a Cox proportional hazard model. Follow-up times and covariates may differ for the two survival probabilties. This is mostly an internal function, meant to be used by the function var.expDeath.

Usage

covariance(t_i, delta_i, beta, time1, z1, time2, z2, S0_i, S1_i, S02_i, Omega_1)

Arguments

t_i	All the follow up times.
delta_i	Indicator that the individual was censored: 1 if the individual was censored, 0 otherwise.
beta	The coefficients of the Cox model.
time1	First survival time.
z1	Covariates for first survival.
time2	Second survival time.
z2	Covariates for second survival.
S0_i	Object described in Lin, Flemming and Wei (1994), slightly modified for computationnal efficiency. It is obtained with function1.
S1_i	Object described in Lin et al. (1994), slightly modified for computationnal efficiency. It is obtained with function1.
S02_i	Object described in Lin et al. (1994), slightly modified for computationnal efficiency. It is obtained with function1.
Omega_1	Inverse of the asymptotic variance-covariance matrix of the estimated parameters of the Cox model. It is obtained with function1.

Details

This function was built to be an internal function, only used by the function var.expDeath.

Value

The covariance between the two estimated survival probability.

Author(s)

Denis Talbot, Thierry Duchesne, Jacques Brisson, Nathalie Vandal.

References

Lin D.Y., Fleming T.R., Wei L.J. (1994) Confidence bands for survival curves under the proportional hazards model, Biometrika, 81 (1): 73-81.

Talbot, D., Duchesne, T., Brisson, J., Vandal, N. (2011) Variance estimation and confidence intervals for the standardized mortality ratio with application to the assessment of a cancer screening program, Statistics in Medicine, 30, 3024-3037.

See Also

var.expDeath, function1

InferenceSMR documentation built on May 29, 2024, 5:30 a.m.