## 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 (fixed-design setting) and event (event-driven 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 and sd.
• BinomDist: generate data following a binomial distribution. Required parameter: prop.
• BetaDist: generate data following a beta distribution. Required parameter: a and b.
• ExpoDist: generate data following an exponential distribution. Required parameter: rate.
• WeibullDist: generate data following a weibull distribution. Required parameter: shape and scale.
• TruncatedExpoDist: generate data following a truncated exponential distribution. Required parameter: rate an trunc.
• PoissonDist: generate data following a Poisson distribution. Required parameter: lambda.
• NegBinomDist: generate data following a negative binomial distribution. Required parameters: dispersion and mean.
• MultinomialDist: generate data following a multinomial distribution. Required parameters: prob.
• MVNormalDist: generate data following a multivariate normal distribution. Required parameters: par and corr. For each generated endpoint, the par parameter must contain the required parameters mean and sd. The corr parameter specifies the correlation matrix for the endpoints.
• MVBinomDist: generate data following a multivariate binomial distribution. Required parameters: par and corr. For each generated endpoint, the par parameter must contain the required parameter prop. The corr parameter specifies the correlation matrix for the endpoints.
• MVExpoDist: generate data following a multivariate exponential distribution. Required parameters: par and corr. For each generated endpoint, the par parameter must contain the required parameter rate. The corr 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 and corr. For each generated endpoint, the par parameter must contain the required parameter rate. The corr parameter specifies the correlation matrix for the endpoints.
• MVMixedDist: generate data following a multivariate mixed distribution. Required parameters: type, par and corr. The type parameter assumes the following values: NormalDist, BinomDist and ExpoDist. For each generated endpoint, the par parameter must contain the required parameters according to the distribution type. The corr 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 event-driven 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 time-to-event 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 User-defined 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 time-to-event (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 event-driven 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 each Sample object defined in the DataModel 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 event-driven 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 follow-up period for each patient in study designs with a fixed follow-up period, i.e., the length of time from the enrollment to planned discontinuation is constant across patients. The user must specify either followup.period or study.duration.

• study.duration defines the total study duration in study designs with a variable follow-up 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 non-uniform 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 is Beta(a,1) with a = log(q) / log(p)

• If q > p, the Beta distribution is Beta (1,b) with b = log(1-q) / log(1-p)

• 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: