Simulate Correlated Progression-Free Survival and Overall Survival Using a Gumbel Copula1 months ago
Model | $$\Pr(X > x, Y > y) | $$\Pr(P > t) | \Pr(X > t, Y > t) | \exp\left[-\left{(\lambda_X^\theta + \lambda_Y^\theta)t^\theta\right}^{1/\theta}\right] | Choosing the Copula Parameter | $$\tau(P,Y) | $$\tau(P,Y)-\tau(X,Y) | Example | Practical Guidance | Appendix: Kendall's Tau for Observed PFS and OS | $$S_{X,Y}(x,y) | \Pr(X>x, Y>y) | $$\Pr(A>a, B>b) | $$S_{P,Y}(Y,Y) | $$E | $$L_R(s) | \frac{1}{\theta}\int_0^\infty e^{-(1+s)r}(r+\theta-1),dr | $$\int_c^1L_R\left{\left(\frac{1-w}{d}\right)^{1/\theta}\right}dw | $$\frac{d}{dt}\left(\frac{t^\theta}{1+t}\right) | $$d\left[\frac{t^\theta}{1+t}\right]_0^1 | c\frac | 4E{S_{P,Y}(P,Y)}-1 | \frac | 1-\frac{1}{\theta}\left(\frac{\lambda_X^\theta}{\lambda_P^\theta}\right)
TrialSimulator 1.19.1Han Zhang simulatePfsAndOsGumbel.Rmd