plot_tte {CompAREdesign}

Plot graphics related to the composite endpoint.

Description

Plot the survival function and the HR for composite endpoint over time and the ARE (Assymptotic Relative Efficiency) and sample size size according to the correlation.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. #'

Usage

plot_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,
  alpha = 0.05,
  power = 0.8,
  ss_formula = "schoenfeld"
)

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.

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'

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

Four plots related to composite endpoint are returned:

S

Survival curve for the composite endpoint over time

HR

Hazard Ratio for the composite endpoint over time

ARE

ARE according to correlation (\rho)

SS

Sample size for the composite endpoint according to correlation (\rho)