We offer various examples of data generation using the Simulation_Enroll function. Survival times are generated from an exponential distribution characterized by a hazard rate lambda, and the occurrence of events such as death, progression, and relapse is modelled using an independent binomial distribution with the rate event.
Patient enrollment is structured across multiple groups. Users of the function must define the duration of patient accrual, follow-up periods, and the maximum duration of the trial. The function allows for the specification of the number of groups, and the distribution of patients across these groups can be either uniform or varied. Below, we illustrate different scenarios utilizing this simulation function.
Consider a clinical trial structured to enroll 100 patients over a three-year period. Details of the patient enrollment are outlined below:
Within each group, the simulation parameters are set as follows:
lambda = 0.03: Survival times are simulated from an
exponential distribution using
rexp(n = 20, rate = 0.03).event = 0.1: Event occurrences are determined for each
patient based on a Bernoulli distribution
rbinom(n = 20, size = 1, prob = 0.1).censor = 0.9: It is assumed that the survival times for
90% of patients without an event are shorter than the maximum observed
survival time.The enrollment times for patients in each group are generated using a
uniform distribution that is between from the start of the enrollment
period to the start of the next group’s enrollment. For instance, the
enrollment times for the first group are simulated using
runif(n = 20, min = 0, max = 0.6). Since the start times
across groups are different and sequential, the maximum survival times
are adjusted accordingly; the first group’s survival times are capped at
5 years, while the second group’s are capped at 4.4 years.
data <- Simulate_Enroll(n = 100,
lambda = 0.03,
event = 0.1,
M = 1,
group = 5,
maxt = 5,
accrual = 3,
censor = 0.9,
followup = 2,
partition = "Even")
head(data)## Time Censor Enroll
## 1 0.003622395 1 0.38119674
## 2 0.931375698 1 0.02143771
## 3 3.341531660 0 0.16854679
## 4 5.000000000 0 0.45861611
## 5 5.000000000 0 0.08504683
## 6 5.000000000 0 0.49671817## Time Censor Enroll
## 95 2.600000 0 2.911322
## 96 2.600000 0 2.770435
## 97 2.600000 0 2.830726
## 98 2.600000 0 2.650107
## 99 2.545639 0 2.650065
## 100 1.908765 0 2.989230The first column Time indicates the survival times,
which are truncated at their respective maximum values. The second
column indicates the occurrence of events, with 1
representing an event occurrence and 0 indicating none. The
final column records the enrollment time points for each patient. The
data in the first two columns are utilized for survival analysis, while
the last column is intended for conducting group sequential interim
analysis.
In many trials, the patient enrollment can have different numbers of patients at different time points. The function can equally partition the enrollment period into 6 time intervals and allow different numbers of patients to enroll in the trial.
data <- Simulate_Enroll(n = c(30,20,20,15,10,5),
lambda = 0.05,
event = 0.2,
M = 1,
group = 6,
maxt = 4,
accrual = 3,
censor = 0.9,
followup = 1,
partition = "Uneven")
head(data)## Time Censor Enroll
## 1 0.5587254 1 0.2196622
## 2 0.8747189 1 0.4217051
## 3 4.0000000 1 0.3404610
## 4 4.0000000 1 0.1403269
## 5 4.0000000 1 0.2692308
## 6 4.0000000 1 0.2867221## Time Censor Enroll
## 95 1.8457387 0 2.417707
## 96 1.5000000 1 2.644800
## 97 1.5000000 0 2.934640
## 98 1.5000000 0 2.894264
## 99 1.5000000 0 2.890860
## 100 0.6652445 0 2.851738Consider a clinical trial recruiting different numbers of patients in different time intervals over a three-year period. Details of the patient enrollment are outlined below:
Within each group, the simulation parameters are set as follows:
lambda = 0.05: Survival times are simulated from an
exponential distribution using
rexp(n = 20, rate = 0.05).event = 0.2: Event occurrences are determined for each
patient based on a Bernoulli distribution
rbinom(n = 20, size = 1, prob = 0.2).censor = 0.9: It is assumed that the survival times for
90% of patients without an event are shorter than the maximum observed
survival time.The enrollment time points and maximum values in each group are generated in the same process as the example above.
The function can generate multiple survival outcomes based on the
same parameter settings. M stands for the number of streams
for MCMC. For example, we can set M = 4 to generate four
independent simulation outputs.
data <- Simulate_Enroll(n = c(30,20,20,15,10,5),
lambda = 0.05,
event = 0.2,
M = 4,
group = 6,
maxt = 4,
accrual = 3,
censor = 0.9,
followup = 1,
partition = "Uneven")
head(data[[1]])## Time Censor Enroll
## 1 0.1795778 1 0.459058912
## 2 0.7359768 1 0.107893938
## 3 1.5836122 1 0.004774509
## 4 2.3611913 1 0.245645842
## 5 3.6206806 1 0.473009109
## 6 3.6635945 1 0.233908861## Time Censor Enroll
## 1 0.5067142 1 0.38304947
## 2 2.7168873 1 0.05129808
## 3 3.1192227 1 0.18227654
## 4 4.0000000 1 0.33962788
## 5 4.0000000 1 0.36616630
## 6 4.0000000 1 0.08973113## Time Censor Enroll
## 1 0.4165583 1 0.1597006
## 2 2.4336370 1 0.0526736
## 3 3.5837114 1 0.3664232
## 4 4.0000000 1 0.1469325
## 5 4.0000000 1 0.4332290
## 6 4.0000000 1 0.3971429## Time Censor Enroll
## 1 0.2572423 1 0.16950544
## 2 3.2765855 1 0.04883483
## 3 3.3919331 1 0.46298125
## 4 4.0000000 1 0.06537026
## 5 4.0000000 1 0.04817034
## 6 4.0000000 1 0.15746224