ARE_tte {CompAREdesign}

ARE method for composite time to event endpoints

Description

The composite endpoint is assumed to be a time to event endpoint formed by a combination of two events (E1 and E2). We assume that the endpoint 1 is more relevant for the clinical question than endpoint 2. This function calculates the ARE (Assymptotic Relative Efficiency) method for time to event endpoints. The method quantifies the differences in efficiency of using the composite or the relevant as primary endpoint to lead the trial and, moreover, provides a decision rule to choose the primary endpoint. If the ARE is larger than 1, the composite endpoint may be considered the best option as primary endpoint. Otherwise, the relevant endpoint is preferred.

Usage

ARE_tte(
  p0_e1,
  p0_e2,
  HR_e1,
  HR_e2,
  beta_e1 = 1,
  beta_e2 = 1,
  case,
  copula = "Frank",
  rho = 0.3,
  rho_type = "Spearman",
  subdivisions = 50,
  plot_res = FALSE,
  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.

subdivisions

integer parameter greater than or equal to 10. Number of points used to plot the ARE according to correlation. The default is 50. Ignored if plot_res=FALSE and plot_store=FALSE.

plot_res

logical indicating if the ARE according to the correlation should be displayed. The default is FALSE

plot_store

logical indicating if the plot of ARE according to the correlation 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

Returns the ARE value along with the fixed correlation. If the ARE value is larger than 1 then the composite endpoint is preferred over the relevant endpoint. Otherwise, the endpoint 1 is preferred as the primary endpoint of the study. In addition, if plot_store=TRUE an object of class ggplot with the ARE according to the correlation is stored in the output.

References

Gomez Melis, G. and Lagakos, S.W. (2013). Statistical considerations when using a composite endpoint for comparing treatment groups. Statistics in Medicine. Vol 32(5), pp. 719-738. https://doi.org/10.1002/sim.5547

Examples

# ARE for a specific study where the composite endpoint is recommended
ARE_tte(p0_e1=0.1, p0_e2=0.1, HR_e1=0.9, HR_e2=0.8, beta_e1 = 1, beta_e2 = 1, 
case=1, copula = "Frank", rho = 0.3, rho_type = "Spearman")
# ARE for a specific study where the composite endpoint is not recommended
ARE_tte(p0_e1=0.1, p0_e2=0.05, HR_e1=0.6, HR_e2=0.8, beta_e1 = 1, beta_e2 = 1, 
case=1, copula = "Frank", rho = 0.3, rho_type = "Spearman")