powerCT.default0 {powerSurvEpi}

Power Calculation in the Analysis of Survival Data for Clinical Trials

Description

Power calculation for the Comparison of Survival Curves Between Two Groups under the Cox Proportional-Hazards Model for clinical trials.

Usage

powerCT.default0(k, 
		 m, 
		 RR, 
		 alpha = 0.05)

Arguments

k

numeric. ratio of participants in group E (experimental group) compared to group C (control group).

m

integer. expected total number of events over both groups.

RR

numeric. postulated hazard ratio.

alpha

numeric. type I error rate.

Details

This is an implementation of the power calculation method described in Section 14.12 (page 807) of Rosner (2006). The method was proposed by Freedman (1982).

Suppose we want to compare the survival curves between an experimental group (E) and a control group (C) in a clinical trial with a maximum follow-up of t years. The Cox proportional hazards regression model is assumed to have the form:

h(t|X_1)=h_0(t)\exp(\beta_1 X_1).

Let n_E be the number of participants in the E group and n_C be the number of participants in the C group. We wish to test the hypothesis H0: RR=1 versus H1: RR not equal to 1, where RR=\exp(\beta_1)=underlying hazard ratio for the E group versus the C group. Let RR be the postulated hazard ratio, \alpha be the significance level. Assume that the test is a two-sided test. If the ratio of participants in group E compared to group C = n_E/n_C=k, then the power of the test is

power=\Phi(\sqrt{k*m}*|RR-1|/(k*RR+1)-z_{1-\alpha/2}),

where z_{1-\alpha/2} is the 100 (1-\alpha/2)-th percentile of the standard normal distribution N(0, 1), \Phi is the cumulative distribution function (CDF) of N(0, 1).

Value

The power of the test.

Note

The power formula assumes that the central-limit theorem is valid and hence is appropriate for large samples.

References

Freedman, L.S. (1982). Tables of the number of patients required in clinical trials using the log-rank test. Statistics in Medicine. 1: 121-129

Rosner B. (2006). Fundamentals of Biostatistics. (6-th edition). Thomson Brooks/Cole.

See Also

powerCT.default, powerCT

Examples

  # Example 14.42 in Rosner B. Fundamentals of Biostatistics. 
  # (6-th edition). (2006) page 809
  powerCT.default0(k = 1, 
		   m = 171.9, 
		   RR = 0.7, 
		   alpha = 0.05)