samplesize_tte {CompAREdesign}

Sample size for composite time to event endpoints

Description

This function calculates the required sample size for trials with a composite time to event endpoint as primary endpoint. The primary endpoint is assumed to be a composite time to event endpoint formed by a combination of two events (E1 and E2). The sample size is computed to evaluate differences between two groups based on the log rank test. The sample size is calculated on the basis of anticipated information on the composite components and the correlation between them.

Usage

samplesize_tte(
  p0_e1,
  p0_e2,
  HR_e1,
  HR_e2,
  beta_e1 = 1,
  beta_e2 = 1,
  case,
  copula = "Frank",
  rho = 0.3,
  rho_type = "Spearman",
  alpha = 0.05,
  power = 0.8,
  ss_formula = "schoenfeld",
  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.

alpha

numeric parameter. The probability of type I error. By default \alpha=0.05

power

numeric parameter. The power to detect the treatment effect. By default 1-\beta=0.80

ss_formula

character indicating the formula to be used for the sample size calculation on the single components: 'schoenfeld' (default) or 'freedman'

subdivisions

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

plot_res

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

plot_store

logical indicating if the plot of sample size 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.

The user can choose between the two most common formulae (Schoenfeld and Freedman) for the sample size calculation for the single components. Schoenfeld formula always be used for the composite endpoint.

Value

A list containing the following components:

ss_E1

Total sample size (both groups) for a trial using endpoint 1 as primary endpoint

ss_E2

Total sample size (both groups) for a trial using endpoint 2 as primary endpoint

ss_Ec

Total sample size (both groups) for a trial using composite endpoint as primary endpoint

In addition, if plot_store=TRUE an object of class ggplot with the sample size for composite endpoint according to correlation is stored in the list.

References

Friedman L.M., Furberg C.D., DeMets D.L. Fundamentals of Clinical Trials. 3rd ed. New York: Springer; 1998. Cortés Martínez, J., Geskus, R.B., Kim, K. et al. Using the geometric average hazard ratio in sample size calculation for time-to-event data with composite endpoints. BMC Med Res Methodol 21, 99 (2021). https://doi.org/10.1186/s12874-021-01286-x