Introduction
The purpose of this vignette is to explain the use of getClinicalTrials(), the core function of this package. getClinicalTrials() can be used to simulate a large number of clinical trials with endpoints progression-free survival (PFS) and overall survival (OS). The underlying model is a survival multistate model with an initial state, an intermediate progression state and an absorbing death state. The multistate model approach has the advantage of naturally accounting for the correlation between the PFS and OS endpoints (Meller, Beyersmann, and Rufibach 2019). OS is defined as the time to reach the absorbing state death and PFS is defined as the time to reach the absorbing state death or the intermediate state progression, whichever occurs first. Figure 1 shows the multistate model with the corresponding transition hazards. To get started quickly, we show a simple and quick example of a clinical trial simulation.
Simulation Specifications
getClinicalTrials() simulates trials with an arbitrary number of treatment arms. In general, the argument specifications were tried to be similar to the R-package Rpact (Wassmer and Pahlke 2021) in order to be more user-friendly. For illustration, we consider a trial with two arms. The number of patients per trial must be specified. In our example simulation there are 30 patients in the first treatment arm and 60 in the second treatment arm:
The transition parameters describing the transition hazards per treatment arm must be passed as a list to getClinicalTrials(). The class TransitionParameters contains the elements hazards, intervals, weibull_rates and family which allow to describe transition hazards leading to exponential, piecewise exponential or Weibull distributed survival times. There are some helper functions in the simIDM package to create the appropriate transition parameters for the desired distribution. - exponential_transition(): creates a list with class TransitionParameters containing hazards, time intervals and Weibull rates for exponential event times in an illness-death model. - piecewise_exponential(): creates a list with class TransitionParameters containing hazards, time intervals and Weibull rates for piecewise exponential event times in an illness-death model. - weibull_transition(): creates a list with class TransitionParameters containing hazards, time intervals and Weibull rates for Weibull distributed event times in an illness-death model.
In our example we consider constant hazard rates, i.e. exponential distributed event times.
The specification for random patient dropouts can be passed directly to getClinicalTrials(). A list with elements rate and time specifies the drop-out probability. Random censoring times are generated using the exponential distribution. dropout$rate specifies the drop-out probability per dropout$time time units. The dropout parameters can be specified either as one list that should be applied to all treatment groups or a separate list for each treatment group. If dropout$rate is equal to 0, then no censoring due to dropout is applied. In our example we expect that 10% of the patients drop-out within 12 months per treatment group (we take month as the time unit of our trial), thus we specify:
There are two time-scales that we need to consider when simulating multistate data. The individual time scale with start in the initial state at time 0 and the study time scale, which matches the individual time scale only if the study start time (e.g. randomization date) is the same time in calendar time for all patients. It can also be specified that patients enter the study in a staggered manner. Uniformly distributed random variables are used to generate staggered study entry times. There are two possibilities for the specification: Either, the length of the accrual period is specified, e.g. 12 month, in which case the staggered entry times are generated in each treatment group using random variables \(U ~Unif(0, 12)\). Or, it is specified how many patients are recruited per time unit in each treatment group. Thus, if 10 patients are recruited per month, then the staggered entry times are generated using random variables \(U ~Unif(0, 30/10)\). A list accrual with elements accrualParam and accrualValue is passed to getClinicalTrials() describing the accrual intensity. For accrualParam equal time, accrualValuedescribes the length of the accrual period. For accrualParam equal intensity, it describes the number of patients recruited per time unit. If accrualValue is equal to 0, all patients start at the same calender time in the initial state. The accrual parameters can be specified either as one list that should be applied to all treatment groups or a separate list for each treatment group.
