historic_sim {BayesCTDesign}  R Documentation 
Two Arm Bayesian Clinical Trial Simulation with Historical Data
Description
historic_sim()
returns an S3 object of class bayes_ctd_array
, which
will contain simulation results for power, statistic estimation, bias,
variance, and mse as requested by user.
Usage
historic_sim(
trial_reps = 100,
outcome_type = "weibull",
subj_per_arm = c(50, 100, 150, 200, 250),
a0_vals = c(0, 0.33, 0.67, 1),
effect_vals = c(0.6, 1, 1.4),
rand_control_diff = c(0.8, 1, 1.2),
hist_control_data = NULL,
time_vec = NULL,
censor_value = NULL,
alpha = 0.05,
get_var = FALSE,
get_bias = FALSE,
get_mse = FALSE,
seedval = NULL,
quietly = TRUE
)
Arguments
trial_reps 
Number of trials to replicate within each combination of

outcome_type 
Outcome distribution. Must be equal to 
subj_per_arm 
A vector of sample sizes, all of which must be positive
integers. Default is 
a0_vals 
A vector of power prior parameters ranging from 0 to 1, where 0
implies no information from historical data should be used, and 1 implies all of
the information from historical data should be used. A value between 0 and 1
implies that a proportion of the information from historical data will be used.
Default is 
effect_vals 
A vector of effects that should be reasonable for the
outcome_type being studied, hazard ratios for Weibull, odds ratios for
Bernoulli, mean ratios for Poisson, etc.. When 
rand_control_diff 
For piecewise exponential and Weibull outcomes, this is
a vector of hazard ratios (randomized controls over historical controls)
representing differences between historical and randomized controls. For
lognormal and Poisson outcomes, this is a vector of mean ratios (randomized
controls over historical controls). For a Bernoulli outcome, this is a vector
of odds ratios (randomized controls over historical controls). For a Gaussian
outcome, this is a vector of mean differences (randomized minus historical
controls). Default is 
hist_control_data 
A dataset of historical data. Default is 
time_vec 
A vector of time values which are used to create time periods
within which the exponential hazard is constant. Only used for piecewise
exponential models. Default is 
censor_value 
A single value at which right censoring occurs when
simulating randomized subject outcomes. Used with survival outcomes.
Default is 
alpha 
A number ranging between 0 and 1 that defines the acceptable Type 1 error rate. Default is 0.05. 
get_var 
A TRUE/FALSE indicator of whether an array of variance
estimates will be returned. Default is 
get_bias 
A TRUE/FALSE indicator of whether an array of bias
estimates will be returned. Default is 
get_mse 
A TRUE/FALSE indicator of whether an array of MSE
estimates will be returned. Default is 
seedval 
A seed value for pseudorandom number generation. 
quietly 
A TRUE/FALSE indicator of whether notes are printed
to output about simulation progress as the simulation runs. If
running interactively in RStudio or running in the R console,

Details
The object bayes_ctd_array
has 6 elements: a list containing simulation
results (data
), copies of the 4 function arguments subj_per_arm
,
a0_vals
, effect_vals
, and rand_control_diff
, and finally
a objtype
value indicating that historic_sim()
was used. Each element of
data
is a fourdimensional array, where each dimension is determined by the
length of parameters subj_per_arm
, a0_vals
, effect_vals
, and
rand_control_diff
. The size of data
depends on which results are
requested by the user. At a minimum, at least one of subj_per_arm
,
a0_vals
, effect_vals
, or rand_control_diff
must contain at
least 2 values, while the other three must contain at least 1 value. The data
list will always contain two elements: an array of power results (power
) and
an array of estimation results (est
). In addition to power
and
est
, data may also contain elements var
, bias
, or mse
,
depending on the values of get_var
, get_bias
, and get_mse
. The
values returned in est
are in the form of hazard ratios, mean ratios, odds
ratios, or mean differences depending on the value of outcome_type
. For a
Gaussian outcome, the estimation results are differences in group means (experimental
group minus control group). For a logistic outcome, the estimation results are odds
ratios (experimental group over control group). For lognormal and Poisson outcomes,
the estimation results are mean ratios (experimental group over control group). For a
piecewise exponential or a Weibull outcome, the estimation results are hazard
ratios (experimental group over control group). The values returned in bias
,
var
, and mse
are on the scale of the values returned in
est
.
The object bayes_ctd_array
has two primary methods, print()
and
plot()
, for printing and plotting slices of the arrays contained in
bayes_ctd_array$data
.
As dimensions of the four dimensional array increases, the time required to complete the simulation will increase; however, it will be faster than a similar simulation based on repeated calls to MCMC routines to analyze each simulated trial.
The meaning of the estimation results, and the test used to generate power results, depends on the outcome used. In all cases, power is based on a twosided test involving a (1alpha)100% credible interval, where the interval is used to determine if the null hypothesis should be rejected (null value outside of the interval) or not rejected (null value inside the interval). For a Gaussian outcome, the 95% credible interval is an interval for the difference in group means (experimental group minus control group), and the test determines if 0 is in or outside of the interval. For a Bernoulli outcome, the 95% credible interval is an interval for the odds ratio (experimental group over control group), and the test determines if 1 is in or outside of the interval. For a lognormal or a Poisson outcome, the 95% credible interval is an interval for the mean ratio (experimental group over control group), and the test determines if 1 is in or outside of the interval. Finally, for a piecewise exponential or a Weibull outcome, the 95% credible interval is an interval for the hazard ratio (experimental group over control group), and the test determines if 1 is in or outside of the interval.
Please refer to the examples for illustration of package use.
Value
historic_sim()
returns an S3 object of class bayes_ctd_array
.
As noted in details, an object of class bayes_ctd_array
has 6 elements: a
list of simulation results (data
), copies of the 4 function arguments
subj_per_arm
, a0_vals
, effect_vals
, and
rand_control_diff
, and finally objtype
indicating that historic_sim()
was used. See details for a discussion about the contents of
data
. Results from the simulation contained in the bayes_ctd_array
object can be printed or plotted using the print()
and
plot()
methods. The results can also be accessed using basic list
element identification and array slicing. For example, to get the 4dimensional
array of power results from a simulation, one could use the code
bayes_ctd_array$data$power
, where bayes_ctd_array
is replaced
with the name of the variable containing the bayes_ctd_array
object. If
one wanted a table of power for sample size by a0, while holding effect equal to
the first considered value and control differences equal to the second considered
value, then the code is bayes_ctd_array$data$power[,,1,2]
, where
bayes_ctd_array
is replaced with the name of the variable containing the
bayes_ctd_array
object.
Examples
#Generate a sample of historical data for use in example.
set.seed(2250)
SampleHistData < genweibulldata(sample_size=60, scale1=2.82487,
hazard_ratio=0.6, common_shape=3,
censor_value=3)
histdata < subset(SampleHistData, subset=(treatment==0))
histdata$id < histdata$id+10000
#Run a Weibull simulation, using historic_sim().
#For meaningful results, trial_reps needs to be much larger than 2.
weibull_test < historic_sim(trial_reps = 2, outcome_type = "weibull",
subj_per_arm = c(50, 100, 150),
a0_vals = c(0, 0.50, 1),
effect_vals = c(0.6, 1),
rand_control_diff = c(0.8, 1),
hist_control_data = histdata, time_vec = NULL,
censor_value = 3, alpha = 0.05, get_var = TRUE,
get_bias = TRUE, get_mse = TRUE, seedval=123,
quietly=TRUE)
#Tabulate the simulation results for power.
test_table < print(x=weibull_test, measure="power",
tab_type="WXYZ", effect_val=0.6,
rand_control_diff_val=1.0)
print(test_table)
#Create a plot of the power simulation results.
plot(x=weibull_test, measure="power", tab_type="WXYZ",
smooth=FALSE, plot_out=TRUE, effect_val=0.6,
rand_control_diff_val=1.0)
#Create a plot of the estimated hazard ratio simulation results.
plot(x=weibull_test, measure="est", tab_type="WXYZ",
smooth=FALSE, plot_out=TRUE, effect_val=0.6,
rand_control_diff_val=1.0)
#Create a plot of the hazard ratio variance simulation results.
plot(x=weibull_test, measure="var", tab_type="WXYZ",
smooth=FALSE, plot_out=TRUE, effect_val=0.6,
rand_control_diff_val=1.0)
#Create a plot of the hazard ratio bias simulation results.
plot(x=weibull_test, measure="bias", tab_type="WXYZ",
smooth=FALSE, plot_out=TRUE, effect_val=0.6,
rand_control_diff_val=1.0)
#Create a plot of the hazard ratio mse simulation results.
plot(x=weibull_test, measure="mse", tab_type="WXYZ",
smooth=FALSE, plot_out=TRUE, effect_val=0.6,
rand_control_diff_val=1.0)
#Create other power plots using different values for tab_type
plot(x=weibull_test, measure="power", tab_type="XYWZ",
smooth=FALSE, plot_out=TRUE, subj_per_arm_val=150,
rand_control_diff_val=1.0)
plot(x=weibull_test, measure="power", tab_type="XZWY",
smooth=FALSE, plot_out=TRUE, subj_per_arm_val=150, effect_val=0.6)
plot(x=weibull_test, measure="power", tab_type="YZWX",
smooth=FALSE, plot_out=TRUE, subj_per_arm_val=150, a0_val=0.5)
plot(x=weibull_test, measure="power", tab_type="WYXZ",
smooth=FALSE, plot_out=TRUE, rand_control_diff_val=1, a0_val=0.5)
plot(x=weibull_test, measure="power", tab_type="WZXY",
smooth=FALSE, plot_out=TRUE, effect_val=0.6, a0_val=0.5)
#Run Poisson simulation, using historic_sim(), but set two design characteristic
# parameters to only 1 value.
#Note: historic_sim() can take a while to run.
#Generate a sample of historical poisson data for use in example.
set.seed(2250)
samplehistdata < genpoissondata(sample_size=60, mu1=1, mean_ratio=1.0)
histdata < subset(samplehistdata, subset=(treatment==0))
histdata$id < histdata$id+10000
#For meaningful results, trial_reps needs to be larger than 100.
poisson_test < historic_sim(trial_reps = 100, outcome_type = "poisson",
subj_per_arm = c(50, 75, 100, 125, 150, 175, 200, 225, 250),
a0_vals = c(1),
effect_vals = c(0.6),
rand_control_diff = c(0.6, 1, 1.6),
hist_control_data = histdata, time_vec = NULL,
censor_value = 3, alpha = 0.05, get_var = TRUE,
get_bias = TRUE, get_mse = TRUE, seedval=123,
quietly=TRUE)
#Tabulate the simulation results for power.
test_table < print(x=poisson_test, measure="power",
tab_type=NULL)
print(test_table)
#Create a plot of the power simulation results.
plot(x=poisson_test, measure="power", tab_type=NULL,
smooth=FALSE, plot_out=TRUE)
#At least one of subj_per_arm, a0_vals, effect_vals, or rand_control_diff
#must contain at least 2 values.
#Generate a sample of historical lognormal data for use in example.
set.seed(2250)
samplehistdata < genlognormaldata(sample_size=60, mu1=1.06, mean_ratio=0.6, common_sd=1.25,
censor_value=3)
histdata < subset(samplehistdata, subset=(treatment==0))
histdata$id < histdata$id+10000
#Run a Lognormal simulation, using historic_sim().
#For meaningful results, trial_reps needs to be larger than 100.
lognormal_test < historic_sim(trial_reps = 100, outcome_type = "lognormal",
subj_per_arm = c(25,50,75,100,125,150,175,200,225,250),
a0_vals = c(1.0),
effect_vals = c(0.6),
rand_control_diff = c(1.8),
hist_control_data = histdata, time_vec = NULL,
censor_value = 3, alpha = 0.05, get_var = TRUE,
get_bias = TRUE, get_mse = TRUE, seedval=123,
quietly=TRUE)
test_table < print(x=lognormal_test, measure="power",
tab_type=NULL)
print(test_table)
#Create a plot of the power simulation results.
plot(x=lognormal_test, measure="power", tab_type=NULL,
smooth=TRUE, plot_out=TRUE)