lambda(t | z) = lambda_0(t) exp(beta z) with lambda_0 ~ BP and beta
normal. Because the covariate acts multiplicatively on the hazard,
the ratio of cumulative hazards between two covariate values is
exp(beta ) FOR EVERY t – proportional hazards holds by construction,
independently of whatever the baseline turns out to be, which is why
the baseline can be left nonparametric.
Usage
Ghosalcoxmodel(beta = 0.7, z = c(0, 1), t = 1, c = 2)
Arguments
- beta
Log hazard ratio.
- z
Two covariate values.
- t
Time point.
- c
Beta-process concentration (does not enter the mean ratio).
Value
List with estimate (the hazard ratio),
cum_hazards, proportional, method.
Details
Formula: H(t | z) = H0(t) exp(beta z); H(t | z2) / H(t | z1)
= exp(beta (z2 - z1)).
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 13.6.
Examples
Ghosalcoxmodel()
#> $estimate
#> [1] 2.013753
#>
#> $cum_hazards
#> [1] 1.000000 2.013753
#>
#> $proportional
#> [1] TRUE
#>
#> $method
#> [1] "Cox with BP baseline (GvdV 2017 sec. 13.6)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
