surv_data_dc.RdGenerate a sample of time to event dataset with, dependent right censoring based on one of the Archimedean copulas the given Kendall's tau, sample size n and covariates matrix Z.
surv_data_dc(n, a, Z, lambda, betas, phis, cons7, cons9, tau, copula, distr.ev, distr.ce)
| n | the sample size, or the number of the subjects in a sample. |
|---|---|
| a | the shape parameter of baseline hazard for the event time \(T\). |
| Z | the covariate matrix with dimension of \(n\) by \(p\), where \(p\) is the number of covariates. |
| lambda | the scale parameter of baseline hazard for event time \(T\). |
| betas | the regression coefficient vector of proportional hazard model for the event time \(T\) with dimenion of \(p\) by \(1\). |
| phis | the regression coefficient vector of proportional hazard model for dependent censoring time \(C\) with dimenion of \(p\) by \(1\). |
| cons7 | the parameter of baseline hazard for the dependent censoring time \(C\) if assuming an exponential distribution. |
| cons9 | the upper limit parameter of uniform distribution for the independent censoring time \(A\), i.e. \(A\)~U(0, cons9). |
| tau | the Kendall's correlation coefficient between \(T\) and \(C\). |
| copula | the Archemedean copula that captures the dependence between \(T\) and \(C\), a characteristc value, i.e. 'independent', 'clayton', 'gumbel' or 'frank'. |
| distr.ev | the distribution of the event time, a characteristc value, i.e. 'weibull' or 'log logit'. |
| distr.ce | the distribution of the dependent censoring time, a characteristc value, i.e. 'exponential' or 'weibull'. |
A sample of time to event dataset under dependent right censoring, which includes observed time \(X\), event indicator \(\delta\) and dependent censoring indicator \(\eta\).
surv_data_dc allows to generate a survival dataset under dependent right censoring, at sample size n, based on one of the Archimedean copula,
Kendall's tau, and covariates matrix Z with dimension of \(n\) by \(p\). For example, at p=2, we have Z=cbind(Z1, Z2),
where Z1 is treatment generated by distribution of bernoulli(0.5), i.e. 1 represents treatment group and 0 represents control group; Z2 is the age
generated by distribution of U(-10, 10).
The generated dataset includes three varaibles, which are \(X_i\), \(\delta_i\) and \(\eta_i\), i.e. \(X_i=min(T_i, C_i, A_i)\), \(\delta_i=I(X_i=T_i)\) and \(\eta_i=I(X_i=C_i)\), for \(i=1,\ldots,n\). 'T' represents the event time, whose hazard function is $$h_T(x)=h_{0T}(x)exp(Z^{\top}\beta)$$, where the baseline hazard can take weibull form, i.e. \(h_{0T}(x) = ax^{a-1} / \lambda^a\), or log logistic form, i.e. $$ h_{0T}(x) = \frac{ \frac{ 1 }{ a exp( \lambda ) } ( \frac{ x }{ exp( \lambda ) } )^{1/a -1 } }{ 1 + ( \frac{ x }{ exp( \lambda ) } )^{1/a} } $$. 'C' represents the dependent censoring time, whose hazard function is \( h_{C}(x) = h_{0C}(x)exp( Z^{\top}\phi) \), where the baseline hazard can take exponential form, i.e. \(h_{0C}(x)=cons7\), or weibull form, i.e. \(h_{0C}(x) = ax^{a-1} / \lambda^a\).'A' represents the administrative or independent censoring time, where A~U(0, cons9).
Xu J, Ma J, Connors MH, Brodaty H. (2018). "Proportional hazard model estimation under dependent censoring using copulas and penalized likelihood". Statistics in Medicine 37, 2238–2251.
Jing Xu, Jun Ma, Thomas Fung
##-- Copula types copula3 <- 'frank' ##-- Marginal distribution for T, C, and A a <- 2 lambda <- 2 cons7 <- 0.2 cons9 <- 10 tau <- 0.8 betas <- c(-0.5, 0.1) phis <- c(0.3, 0.2) distr.ev <- 'weibull' distr.ce <- 'exponential' ##-- Sample size n <- 200 ##-- One sample Monte Carlo dataset cova <- cbind(rbinom(n, 1, 0.5), runif(n, min=-10, max=10)) surv <- surv_data_dc(n, a, cova, lambda, betas, phis, cons7, cons9, tau, copula3, distr.ev, distr.ce) n <- nrow(cova) p <- ncol(cova) ##-- event and dependent censoring proportions colSums(surv)[c(2,3)]/n#> del eta #> 0.480 0.325X <- surv[,1] # Observed time del<-surv[,2] # failure status eta<-surv[,3] # dependent censoring status