lrSS: Sample size required to show difference in survival by log-rank test given prior information about Kaplan-Meier estimate

Description

No. of events required in a two-group trial (with one binary covariate) for a two-sided log-rank test to detect a given hazard ratio. This is calculated by: $$n= \frac{ ({Z_{\frac{\alpha}{2}}+Z_{\beta}) }^2}{ p(1-p) \log^2{HR} }$$ Where $Z$ refers to the corresponding Z-value from the standard normal distribution. This default calculation requires that the subjects be followed until all have experienced the event of interest (typically death). If this is not likely to be the case, then a more informed estimate may be generated by dividing $n$ by the overall probability of death occurring by the end of the study. This may be generated with prior information about $\hat{S}$ and median survival times (for the control group $B$; group $A$ is the experimental group). Given accrual time $a$ and follow-up time $f$, Simpsons rule can be used to give an estimate of the proportion of patients that will die in group $B$: $$d_B = 1-\frac{1}{6}[\hat{S}_B(f) + 4\hat{S}_B(f+0.5a) + \hat{S}_B(f+a)]$$ Given median survival time $t$, the proportion of patients expected to die in group $B$ is: $$d_B = [1 - \frac{ e^{ \frac{-0.69f}{t}} (1 - e^{ \frac{-0.69f}{t}})}{\frac{0.69a}{t}}]$$

Usage

lrSS(HR, alpha = 0.1, beta = 0.2, p = 0.5, Sp, tp, mtp, a, f)

Arguments

Hazard Ratio. Ratio of hazard with treatment to that without.

alpha

Significance level $\alpha$, two-tailed

beta

Power is $1-\beta$

Proportion of subjects allocated to one group. Needs to be in range $0-1$. Arbitrary - can be either of the two groups.

Prior Kaplan-Meier estimate of survival (given no intervention)

Prior times corresponding to survival estimates. There must be one time corresponding to each of: $f, 0.5*a+f, a+f$.

mtp

Median time, prior. (Prior median survival time).

Accrue. Time period for which subjects accrued.

Follow-up. Time period for which subjects followed-up.

Value

If any of Sp, tp, mtp a or f are missing, will return the number of subjects required (with no prior information). Otherwise, returns a list with the following values: [object Object],[object Object],[object Object]

source

Schoenfeld D, 1983. Sample-size formula for the proportional-hazards regression model. Biometrics. (39):499-503. http://www.jstor.org/stable/2531021{JSTOR}

Examples

Run this code

lrSS(HR=1.3, alpha=0.05)
data(btumors)
m1 <- mean(rep(btumors[,"ms"],btumors[,"n"]))
lrSS(HR=1.5, Sp=c(0.43, 0.2, 0.11), tp=c(1, 2, 3), mtp=m1, a=2, f=1)