ssize.stratify {powerSurvEpi} | R Documentation |
Sample size calculation for Survival Analysis with Binary Predictor and Exponential Survival Function
Description
Sample size calculation for survival analysis with binary predictor and exponential survival function.
Usage
ssize.stratify(
power,
timeUnit,
gVec,
PVec,
HR,
lambda0Vec,
alpha = 0.05,
verbose = TRUE)
Arguments
power |
numeric. Power of the test. |
timeUnit |
numeric. Total study length. |
gVec |
numeric. m by 1 vector. The s-th element is the proportion of the total sample size for the s-th stratum, where m is the number of strata. |
PVec |
numeric. m by 1 vector. The s-th element is the proportion of subjects in treatment group 1 for the s-th stratum, where m is the number of strata. |
HR |
numeric. Hazard ratio (Ratio of the hazard for treatment group 1 to the hazard for treatment group 0, i.e. reference group). |
lambda0Vec |
numeric. m by 1 vector. The s-th element is the hazard for treatment group 0 (i.e., reference group) in the s-th stratum. |
alpha |
numeric. Type I error rate. |
verbose |
Logical. Indicating if intermediate results will be output or not. |
Details
We assume (1) there is only one predictor and no covariates in the survival model
(exponential survival function); (2) there are m
strata; (3) the predictor x
is a binary variable indicating treatment group 1 (x=1
) or treatment group 0
(x=0
); (3) the treatment effect is constant over time (proportional hazards);
(4) the hazard ratio is the same in all strata, and (5) the data will be analyzed by
the stratified log rank test.
The sample size formula is Formula (1) on page 801 of Palta M and Amini SB (1985):
n=(Z_{\alpha}+Z_{\beta})^2/\mu^2
where \alpha
is the Type I error rate,
\beta
is the Type II error rate (power=1-\beta
),
Z_{\alpha}
is the 100(1-\alpha)
-th percentile of standard normal distribution, and
\mu=\log(\delta)\sqrt{ \sum_{s=1}^{m} g_s P_s (1 - P_s) V_s }
and
V_s=P_s\left[1-\frac{1}{\lambda_{1s}} \left\{
\exp\left[-\lambda_{1s}(T-1)\right]
-\exp(-\lambda_{1s}T)
\right\}
\right]
+(1-P_s)\left[
1-\frac{1}{\lambda_{0s}}
\left\{
\exp\left[-\lambda_{0s}(T-1)\right]
-\exp(-\lambda_{0s}T
\right\}
\right]
In the above formulas, m
is the number of strata,
T
is the total study length, \delta
is the hazard ratio,
g_s
is the proportion of the total sample size in stratum s
,
P_s
is the proportion of stratum s
, which is in treatment group 1,
and \lambda_{is}
is the hazard for the i
-th treatment group in
stratum s
.
Value
The sample size.
References
Palta M and Amini SB. (1985). Consideration of covariates and stratification in sample size determination for survival time studies. Journal of Chronic Diseases. 38(9):801-809.
See Also
Examples
# example on page 803 of Palta M and Amini SB. (1985).
n <- ssize.stratify(
power = 0.9,
timeUnit = 1.25,
gVec = c(0.5, 0.5),
PVec = c(0.5, 0.5),
HR = 1 / 1.91,
lambda0Vec = c(2.303, 1.139),
alpha = 0.05,
verbose = TRUE
)