ssizeCT.default: Sample Size Calculation in the Analysis of Survival Data for Clinical Trials

Description

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

Usage

ssizeCT.default(power, 
		k, 
		pE, 
		pC, 
		RR, 
		alpha = 0.05)

Arguments

power

numeric. power to detect the magnitude of the hazard ratio as small as that specified by RR.

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

numeric. probability of failure in group E (experimental group) over the maximum time period of the study (t years).

numeric. probability of failure in group C (control group) over the maximum time period of the study (t years).

numeric. postulated hazard ratio.

alpha

numeric. type I error rate.

Value

A two-element vector. The first element is $n_{E}$ and the second element is $n_{C}$ .

Details

This is an implementation of the sample size 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: $h (t | X_{1}) = h_{0} (t) \exp (β_{1} X_{1}) .$ 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 $H 0 : R R = 1$ versus $H 1 : R R$ not equal to 1, where $R R = \exp (β_{1}) =$ underlying hazard ratio for the $E$ group versus the $C$ group. Let $R R$ be the postulated hazard ratio, $α$ 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 number of participants needed in each group to achieve a power of $1 - β$ is $n_{E} = \frac{m k}{k p_{E} + p_{C}}, n_{C} = \frac{m}{k p_{E} + p_{C}}$ where $m = \frac{1}{k} {(\frac{k R R + 1}{R R - 1})}^{2} {(z_{1 - α / 2} + z_{1 - β})}^{2},$ and $z_{1 - α / 2}$ is the $100 (1 - α / 2)$ -th percentile of the standard normal distribution $N (0, 1)$ .

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.

Examples

Run this code

# NOT RUN {
  # Example 14.42 in Rosner B. Fundamentals of Biostatistics. 
  # (6-th edition). (2006) page 809
  ssizeCT.default(power = 0.8, 
		  k = 1, 
		  pE = 0.3707, 
		  pC = 0.4890, 
                  RR = 0.7, 
		  alpha = 0.05)
# }

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