| Title: | Design of Clinical Trials with Survival Endpoints Based on Binary Responses |
| Version: | 1.3 |
| Author: | Marta Bofill Roig [aut, cre], Guadalupe Gomez Melis [ctb], Yu Shen [ctb] |
| Maintainer: | Marta Bofill Roig <marta.bofillroig@meduniwien.ac.at> |
| Description: | Sample size and effect size calculations for survival endpoints based on mixture survival-by-response model. The methods implemented can be found in Bofill, Shen & Gómez (2021) <doi:10.48550/arXiv.2008.12887>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | false |
| Imports: | stats |
| RoxygenNote: | 7.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2021-03-30 08:32:40 UTC; marta.bofill |
| Repository: | CRAN |
| Date/Publication: | 2021-03-31 08:40:02 UTC |
Inside variance computation
Description
The following three functions are used to calculate the variance of th difference of two RMSTs. 'survw_integratef' is used for the integrations; 'inside_var' calculates the expression inside the integral; finally, 'var_f' computes the variance.
Usage
inside_var(t, ascale_r, ascale_nr, tau, bshape, ascale_cens, p)
Arguments
t |
time at which the survival distribution is evaluated |
ascale_r |
scale parameter for the Weibull distribution for responders |
ascale_nr |
scale parameter for the Weibull distribution for non-responders |
tau |
follow-up |
bshape |
shape parameter for the Weibull distribution |
ascale_cens |
distributional parameter for the exponential distribution for the censoring |
p |
event rate for the response |
Value
Variance computation
Author(s)
Marta Bofill Roig
Mean Weibull survival function
Description
The functions 'meanw_f' and 'medianw_f' calculate the mean and median for Weibull distributions, respectively.
Usage
meanw_f(ascale, bshape)
Arguments
ascale |
scale parameter for the Weibull distribution |
bshape |
shape parameter for the Weibull distribution |
Value
mean
Author(s)
Marta Bofill Roig
Median Weibull survival function
Description
The functions 'meanw_f' and 'medianw_f' calculate the mean and median for Weibull distributions, respectively.
Usage
medianw_f(ascale, bshape)
Arguments
ascale |
scale parameter for the Weibull distribution |
bshape |
shape parameter for the Weibull distribution |
Value
median
Author(s)
Marta Bofill Roig
The functions 'meanw_f' and 'medianw_f' calculate the mean and median for Weibull distributions, respectively.
Scale parameter computation
Description
returns the value of the scale parameter a given the survival (s) at time t
Usage
param_scale(s, t, shape = 1)
Arguments
s |
survival rate at time t |
t |
time at which the survival distribution is evaluated |
shape |
shape parameter for the Weibull distribution |
Value
Variance computation
Note
Weibull parametrization: S(x) = exp(- (x/a)^b)
Author(s)
Marta Bofill Roig
Restricted mean survival times Weibull distribution
Description
The function 'rmstw_f' computes the restricted mean survival times (RMST) according to the Weibull survival function.
Usage
rmstw_f(ascale, bshape, tau, low = 0)
Arguments
ascale |
scale parameter for the Weibull distribution |
bshape |
shape parameter for the Weibull distribution |
tau |
RMST evaluated from low to tau |
low |
RMST evaluated from low to tau |
Value
rmst
Author(s)
Marta Bofill Roig
Scale parameter computation
Description
returns the value of the scale parameter in the intervention group using Taylor series
Usage
scale1_taylorf(ascale0, Delta, tau)
Arguments
ascale0 |
scale parameter for the weibull distribution in the control group |
Delta |
RMST difference between groups |
tau |
end of follow-up |
Value
Variance computation
Note
Weibull parametrization: S(x) = exp(- (x/a)^b)
Author(s)
Marta Bofill Roig
Effect size calculation for mixture survival distributions
Description
The function 'survm_effectsize' calculates the effect size in terms of the difference of restricted mean survival times (RMST) according to the information on responders and non-responders.
Usage
survm_effectsize(
ascale0_r,
ascale0_nr,
delta_p,
p0,
bshape0 = 1,
bshape1 = 1,
ascale1_r,
ascale1_nr,
tau,
Delta_r = NULL,
Delta_0 = NULL,
Delta_nr = NULL,
anticipated_effects = FALSE
)
Arguments
ascale0_r |
scale parameter for the Weibull distribution in the control group for responders |
ascale0_nr |
scale parameter for the Weibull distribution in the control group for non-responders |
delta_p |
effect size for the response rate |
p0 |
event rate for the response |
bshape0 |
shape parameter for the Weibull distribution in the control group |
bshape1 |
shape parameter for the Weibull distribution in the intervention group |
ascale1_r |
scale parameter for the Weibull distribution in the intervention group for responders |
ascale1_nr |
scale parameter for the Weibull distribution in the intervention group for non-responders |
tau |
follow-up |
Delta_r |
RMST difference between intervention and control groups for responders |
Delta_0 |
RMST difference between responders and non-responders in the control group |
Delta_nr |
RMST difference between intervention and control groups for non-responders |
anticipated_effects |
Logical parameter. If it is TRUE then the effect size is computed based on previous information on the effect sizes on response rate and survival-by-responses (that is, based on Delta_r, Delta_0, Delta_nr); otherwise is based on the distributional parameters (ascale0_r, ascale0_nr, ascale1_r, ascale1_nr, bshape0, bshape1). |
Value
This function returns the overall mean survival improvement (RMST difference between groups) and it also includes the mean survival improvement that would be assumed for each responders and non-responders.
Author(s)
Marta Bofill Roig.
References
Design of phase III trials with long-term survival outcomes based on short-term binary results. Marta Bofill Roig, Yu Shen, Guadalupe Gomez Melis. arXiv:2008.12887
Examples
survm_effectsize(ascale0_r=8,ascale0_nr=5.6,ascale1_r=36,ascale1_nr=5.6,delta_p=0.2,p0=0.2,tau=5)
Sample size calculation for mixture survival distributions
Description
The function 'survm_samplesize' calculates the sample size according to the distributional parameters of the responders and non-responders.
Usage
survm_samplesize(
ascale0_r,
ascale0_nr,
ascale1_r,
ascale1_nr,
delta_p,
p0,
m0_r,
m0_nr,
diffm_r,
diffm_nr,
S0_r,
S0_nr,
diffS_r,
diffS_nr,
Delta_r,
Delta_nr,
ascale_cens,
tau,
bshape0 = 1,
bshape1 = 1,
all_ratio = 0.5,
alpha = 0.025,
beta = 0.2,
set_param = 0
)
Arguments
ascale0_r |
scale parameter for the Weibull distribution in the control group for responders |
ascale0_nr |
scale parameter for the Weibull distribution in the control group for non-responders |
ascale1_r |
scale parameter for the Weibull distribution in the intervention group for responders |
ascale1_nr |
scale parameter for the Weibull distribution in the intervention group for non-responders |
delta_p |
effect size for the response rate |
p0 |
event rate for the response |
m0_r |
survival mean for responders in the control group |
m0_nr |
survival mean for non-responders in the control group |
diffm_r |
difference in survival means between groups for responders |
diffm_nr |
difference in survival means between groups for responders |
S0_r |
tau-year survival rates for responders in the control group |
S0_nr |
tau-year survival rates for non-responders in the control group |
diffS_r |
difference in tau-year survival rates for responders |
diffS_nr |
difference in tau-year survival rates for non-responders |
Delta_r |
restricted mean survival times (RMST) difference between intervention and control groups for responders |
Delta_nr |
RMST difference between intervention and control groups for non-responders |
ascale_cens |
distributional parameter for the exponential distribution for the censoring |
tau |
follow-up |
bshape0 |
shape parameter for the Weibull distribution in the control group |
bshape1 |
shape parameter for the Weibull distribution in the intervention group |
all_ratio |
allocation ratio. The ratio of numbers of participants allocated in the control group. By default is assumed 1:1 (i.e., all_ratio=0.5) |
alpha |
type I error |
beta |
type II error |
set_param |
Set of parameters to be used for the responders/non-responders survival functions If the set of parameters is =1, then the sample size is computed using the survival means (m0_r,m0_nr,diffm _r,diffm_nr); if set_param=2, it is computed using the tau-year survival rates (S0_r,S0_nr,diffS_r,diffS_nr); if set_param=2, it is computed using the RMSTs and survival rates (Delta_r,Delta_nr,S0_r,S0_nr). If set_param=0, the computation is based on the distributional parameters (ascale0_r, ascale0_nr, ascale1_r, ascale1_nr). |
Value
This function returns the total sample size needed and the expected effect size for overall survival (RMST difference between groups).
Author(s)
Marta Bofill Roig.
References
Design of phase III trials with long-term survival outcomes based on short-term binary results. Marta Bofill Roig, Yu Shen, Guadalupe Gomez Melis. arXiv:2008.12887
Mixture survival function
Description
The function 'survmixture_f' computes the survival distribution as a mixture of responders and non-responders. The responders and non-responders distributions are assumed to be Weibull distributions.
Usage
survmixture_f(t, ascale_r, ascale_nr, bshape = 1, p)
Arguments
t |
time at which the survival distribution is evaluated |
ascale_r |
scale parameter for the Weibull distribution for responders |
ascale_nr |
scale parameter for the Weibull distribution for non-responders |
bshape |
shape parameter for the Weibull distribution |
p |
event rate for the response |
Value
This function returns the survival function evaluated at t based on a mixture model of responders and non-responders.
Author(s)
Marta Bofill Roig.
References
Design of phase III trials with long-term survival outcomes based on short-term binary results. Marta Bofill Roig, Yu Shen, Guadalupe Gomez Melis. arXiv:2008.12887
Examples
survmixture_f(t=0.2,ascale_r=8,ascale_nr=5.6,p=0.2)
Derivative Weibull survival function
Description
The function 'survw_derivf' computes the derivative of the survival distribution 'survw_f'.
Usage
survw_derivf(t, ascale, bshape = 1)
Arguments
t |
time |
ascale |
scale parameter for the Weibull distribution |
bshape |
shape parameter for the Weibull distribution |
Value
derivative
Author(s)
Marta Bofill Roig
Weibull survival function
Description
The function 'survw_f' computes the Weibull survival function.
Usage
survw_f(t, ascale, bshape)
Arguments
t |
time |
ascale |
scale parameter for the Weibull distribution |
bshape |
shape parameter for the Weibull distribution |
Value
survival function
Author(s)
Marta Bofill Roig
Integrate function
Description
the function 'survw_integratef' is used for the integrations
Usage
survw_integratef(t, tau, ascale, bshape)
Arguments
t |
time |
tau |
follow-up |
ascale |
scale parameter for the Weibull distribution |
bshape |
shape parameter for the Weibull distribution |
Value
Variance computation
Author(s)
Marta Bofill Roig
Variance computation
Description
The function 'var_f' computes the variance.
Usage
var_f(ascale_r, ascale_nr, tau, bshape, ascale_cens, p)
Arguments
ascale_r |
scale parameter for the Weibull distribution for responders |
ascale_nr |
scale parameter for the Weibull distribution for non-responders |
tau |
follow-up |
bshape |
shape parameter for the Weibull distribution |
ascale_cens |
distributional parameter for the exponential distribution for the censoring |
p |
event rate for the response |
Value
Variance computation
Author(s)
Marta Bofill Roig