surv_tte {CompAREdesign}

Survival function for composite time-to-event endpoints

Description

It provides the survival function for time-to-event composite outcomes. The composite endpoint is assumed to be a time-to-event endpoint formed by a combination of two events (E1 and E2). The effect size is calculated on the basis of anticipated information on the composite components and the correlation between them. Marginal distributions are assumed weibull for both endpoints.

Usage

surv_tte(
  p0_e1,
  p0_e2,
  HR_e1,
  HR_e2,
  beta_e1 = 1,
  beta_e2 = 1,
  case,
  copula = "Frank",
  rho = 0.3,
  rho_type = "Spearman",
  followup_time = 1,
  plot_res = TRUE,
  plot_store = FALSE
)

Arguments

p0_e1

numeric parameter between 0 and 1, expected proportion of observed events for the endpoint E1

p0_e2

numeric parameter between 0 and 1, expected proportion of observed events for the endpoint E2

HR_e1

numeric parameter between 0 and 1, expected cause specific hazard Ratio the endpoint E1

HR_e2

numeric parameter between 0 and 1, expected cause specific hazard Ratio the endpoint E2

beta_e1

numeric positive parameter, shape parameter (\beta_1) for a Weibull distribution for the endpoint E1 in the control group. See details for more info.

beta_e2

numeric positive parameter, shape parameter (\beta_2) for a Weibull distribution for the endpoint E2 in the control group. See details for more info.

case

integer parameter in {1,2,3,4}: (1) none of the endpoints is death; (2) endpoint 2 is death; (3) endpoint 1 is death; (4) both endpoints are death by different causes.

copula

character indicating the copula to be used: "Frank" (default), "Gumbel" or "Clayton". See details for more info.

rho

numeric parameter between -1 and 1, Spearman's correlation coefficient o Kendall Tau between the marginal distribution of the times to the two events E1 and E2. See details for more info.

rho_type

character indicating the type of correlation to be used: "Spearman" (default) or "Tau". See details for more info.

followup_time

numeric parameter indicating the maximum follow up time (in any unit). Default is 1.

plot_res

logical indicating if the survival curves should be displayed. The default is TRUE

plot_store

logical indicating if the plot of the survival curve for composite endpoint is stored for future customization. The default is FALSE

Details

Some parameters might be difficult to anticipate, especially the shape parameters of Weibull distributions and those referred to the relationship between the marginal distributions. For the shape parameters (beta_e1, beta_e2) of the Weibull distribution, we recommend to use \beta_j=0.5, \beta_j=1 or \beta_j=2 if a decreasing, constant or increasing rates over time are expected, respectively. For the correlation (rho) between both endpoints, generally a positive value is expected as it has no sense to design an study with two endpoints negatively correlated. We recommend to use \rho=0.1, \rho=0.3 or \rho=0.5 for weak, mild and moderate correlations, respectively. For the type of correlation (rho_type), although two different type of correlations are implemented, we recommend the use of the Spearman's correlation. In any case, if no information is available on these parameters, we recommend to use the default values provided by the function.

Value

For each group, if plot_res=TRUE, the function returns a plot of the survival functions for composite endpoint as well as the plots of the survival function for each component.