Data Model
Summary
Data models define the process of generating patient data in clinical trials.
Initialization
A data model can be initialized using the following command
It is highly recommended to use this command as it will simplify the process of specifying components of the data model, e.g., OutcomeDist
, Sample
, SampleSize
, Event
and Design
objects.
Components of a data model
Once the DataModel
object has been initialized, components of the data model can be specified by adding objects to the model using the ‘+’ operator as shown below.
OutcomeDist
object
Description
This object specifies the distribution of patient outcomes in a data model. An OutcomeDist
object is defined by two arguments:

outcome.dist
defines the outcome distribution. 
outcome.type
defines the outcome type (optional). There are two acceptable values of this argument:standard
(fixeddesign setting) andevent
(eventdriven design setting).
Several distributions that can be specified using the outcome.dist
argument are already implemented in the Mediana package. These distributions are listed below along with the required parameters to be included in the outcome.par
argument of the Sample
object:
UniformDist
: generate data following a univariate distribution. Required parameter:max
.NormalDist
: generate data following a normal distribution. Required parameters:mean
andsd
.BinomDist
: generate data following a binomial distribution. Required parameter:prop
.BetaDist
: generate data following a beta distribution. Required parameter:a
andb
.ExpoDist
: generate data following an exponential distribution. Required parameter:rate
.WeibullDist
: generate data following a weibull distribution. Required parameter:shape
andscale
.TruncatedExpoDist
: generate data following a truncated exponential distribution. Required parameter:rate
antrunc
.PoissonDist
: generate data following a Poisson distribution. Required parameter:lambda
.NegBinomDist
: generate data following a negative binomial distribution. Required parameters:dispersion
andmean
.MultinomialDist
: generate data following a multinomial distribution. Required parameters:prob
.MVNormalDist
: generate data following a multivariate normal distribution. Required parameters:par
andcorr
. For each generated endpoint, thepar
parameter must contain the required parametersmean
andsd
. Thecorr
parameter specifies the correlation matrix for the endpoints.MVBinomDist
: generate data following a multivariate binomial distribution. Required parameters:par
andcorr
. For each generated endpoint, thepar
parameter must contain the required parameterprop
. Thecorr
parameter specifies the correlation matrix for the endpoints.MVExpoDist
: generate data following a multivariate exponential distribution. Required parameters:par
andcorr
. For each generated endpoint, thepar
parameter must contain the required parameterrate
. Thecorr
parameter specifies the correlation matrix for the endpoints.MVExpoPFSOSDist
: generate data following a multivariate exponential distribution to generate PFS and OS endpoints. The PFS value is imputed to the OS value if the latter occurs earlier. Required parameters:par
andcorr
. For each generated endpoint, thepar
parameter must contain the required parameterrate
. Thecorr
parameter specifies the correlation matrix for the endpoints.MVMixedDist
: generate data following a multivariate mixed distribution. Required parameters:type
,par
andcorr
. Thetype
parameter assumes the following values:NormalDist
,BinomDist
andExpoDist
. For each generated endpoint, thepar
parameter must contain the required parameters according to the distribution type. Thecorr
parameter specifies the correlation matrix for the endpoints.
The outcome.type
argument defines the outcome’s type. This argument accepts only two values:

standard
: for fixed design setting. 
event
: for eventdriven design setting.
The outcome’s type must be defined for each endpoint in case of multivariate disribution, e.g. c("event","event")
in case of multivariate exponential distribution. The outcome.type
argument is essential to get censored events for timetoevent endpoints if the SampleSize
object is used to specify the number of patients to generate.
A single OutcomeDist
object can be added to a DataModel
object.
For more information about the OutcomeDist
object, see the documentation for OutcomeDist on the CRAN web site.
If a certain outcome distribution is not implemented in the Mediana package, the user can create a custom function and use it within the package (see Userdefined functions).
Example
Examples of OutcomeDist
objects:
Specify popular univariate distributions:
Specify a mixed multivariate distribution:
Sample
object
Description
This object specifies parameters of a sample (e.g., treatment arm in a trial) in a data model. Samples are defined as mutually exclusive groups of patients, for example, treatment arms. A Sample
object is defined by three arguments:

id
defines the sample’s unique ID (label). 
outcome.par
defines the parameters of the outcome distribution for the sample. 
sample.size
defines the sample’s size (optional).
The sample.size
argument is optional but must be used to define the sample size only if an unbalanced design is considered (i.e., the sample size varies across the samples). The sample size must be either defined in the Sample
object or in the SampleSize
object, but not in both.
Several Sample
objects can be added to a DataModel
object.
For more information about the Sample
object, see the documentation Sample on the CRAN web site.
Example
Examples of Sample
objects:
Specify two samples with a continuous endpoint following a normal distribution:
Specify two samples with a binary endpoint following a binomial distribution:
Specify two samples with a timetoevent (survival) endpoint following an exponential distribution:
Specify three samples with two primary endpoints that follow a binomial and a normal distribution, respectively:
SampleSize
object
Description
This object specifies the sample size in a balanced trial design (all samples will have the same sample size). A SampleSize
object is defined by one argument:
sample.size
specifies a list or vector of sample size(s).
A single SampleSize
object can be added to a DataModel
object.
For more information about the SampleSize
object, see the package’s documentation SampleSize.
Example
Examples of SampleSize
objects:
Several equivalent specifications of the SampleSize
object:
Event
object
Description
This object specifies the total number of events (total event count) among all samples in an eventdriven clinical trial. An Event
object is defined by two arguments:

n.events
defines a vector of the required event counts. 
rando.ratio
defines a vector of randomization ratios for eachSample
object defined in theDataModel
object.
A single Event
object can be added to a DataModel
object.
For more information about the Event
object, see the package’s documentation Event.
Example
Examples of Event
objects:
Specify the required number of events in a trial with a 2:1 randomization ratio (Treatment:Placebo):
Design
object
Description
This object specifies the design parameters used in eventdriven designs if the user is interested in modeling the enrollment (or accrual) and dropout (or loss to follow up) processes. A Design
object is defined by seven arguments:

enroll.period
defines the length of the enrollment period. 
enroll.dist
defines the enrollment distribution. 
enroll.dist.par
defines the parameters of the enrollment distribution (optional). 
followup.period
defines the length of the followup period for each patient in study designs with a fixed followup period, i.e., the length of time from the enrollment to planned discontinuation is constant across patients. The user must specify eitherfollowup.period
orstudy.duration
. 
study.duration
defines the total study duration in study designs with a variable followup period. The total study duration is defined as the length of time from the enrollment of the first patient to the discontinuation of the last patient. 
dropout.dist
defines the dropout distribution. 
dropout.dist.par
defines the parameters of the dropout distribution.
Several Design
objects can be added to a DataModel
object.
For more information about the Design
object, see the package’s documentation Design.
A convienient way to model nonuniform enrollment is to use a beta distribution (BetaDist
). If enroll.dist = "BetaDist"
, the enroll.dist.par
should contain the parameter of the beta distribution (a
and b
). These parameters must be derived according to the expected enrollment at a specific timepoint. For example, if half the patients are expected to be enrolled at 75% of the enrollment period, the beta distribution is a Beta(log(0.5)/log(0.75), 1)
. Generally, let q
be the proportion of enrolled patients at 100p
% of the enrollment period, the Beta distribution can be derived as follows:

If
q < p
, the Beta distribution isBeta(a,1)
witha = log(q) / log(p)

If
q > p
, the Beta distribution isBeta (1,b)
withb = log(1q) / log(1p)

Otherwise the Beta distribution is
Beta(1,1)
Example
Examples of Design
objects:
Specify parameters of the enrollment and dropout processes with a uniform enrollment distribution and exponential dropout distribution: