Case study 6

Summary

Case study 6 is an extension of Case study 2 where the objective of the sponsor is to compare several Multiple Testing Procedures (MTPs). The main difference is in the specification of the analysis model.

Define a Data Model

The same data model as in Case study 2 will be used in this case study. However, as shown in the table below, a new set of outcome parameters will be added in this case study (an optimistic set of parameters).

Outcome parameter	Treatment Arm	Mean	Standard deviation
Standard	Placebo	16	18
	Dose L	19.5	18
	Dose M	21	18
	Dose H	21	18
Optimistic	Placebo	16	18
	Dose L	20	18
	Dose M	21	18
	Dose H	22	18

# Standard
outcome1.placebo = parameters(mean = 16, sd = 18)
outcome1.dosel = parameters(mean = 19.5, sd = 18)
outcome1.dosem = parameters(mean = 21, sd = 18)
outcome1.doseh = parameters(mean = 21, sd = 18)

# Optimistic
outcome2.placebo = parameters(mean = 16, sd = 18)
outcome2.dosel = parameters(mean = 20, sd = 18)
outcome2.dosem = parameters(mean = 21, sd = 18)
outcome2.doseh = parameters(mean = 22, sd = 18)

# Data model
case.study6.data.model = DataModel() +
  OutcomeDist(outcome.dist = "NormalDist") +
  SampleSize(seq(220, 260, 20)) +
  Sample(id = "Placebo",
         outcome.par = parameters(outcome1.placebo, outcome2.placebo)) +
  Sample(id = "Dose L",
         outcome.par = parameters(outcome1.dosel, outcome2.dosel)) +
  Sample(id = "Dose M",
         outcome.par = parameters(outcome1.dosem, outcome2.dosem)) +
  Sample(id = "Dose H",
         outcome.par = parameters(outcome1.doseh, outcome2.doseh))

Define an Analysis Model

As in Case study 2, each dose-placebo comparison will be performed using a one-sided two-sample t-test (TTest method defined in each Test object). The same nomenclature will be used to define the hypotheses, i.e.:

H1: Null hypothesis of no difference between Dose L and placebo.
H2: Null hypothesis of no difference between Dose M and placebo.
H3: Null hypothesis of no difference between Dose H and placebo.

In this case study, as in Case study 2, the overall success criterion in the trial is formulated in terms of demonstrating a beneficial effect at any of the three doses, inducing an inflation of the overall Type I error rate. In this case study, the sponsor is interested in comparing several Multiple Testing Procedures, such as the weighted Bonferroni, Holm and Hochberg procedures. These MTPs are defined as below:

# Multiplicity adjustments
# No adjustment
mult.adj1 = MultAdjProc(proc = NA)

# Bonferroni adjustment (with unequal weights)
mult.adj2 = MultAdjProc(proc = "BonferroniAdj",
                        par = parameters(weight = c(1/4,1/4,1/2)))

# Holm adjustment (with unequal weights)
mult.adj3 = MultAdjProc(proc = "HolmAdj", 
                        par = parameters(weight = c(1/4,1/4,1/2)))

# Hochberg adjustment (with unequal weights)
mult.adj4 = MultAdjProc(proc = "HochbergAdj", 
                        par = parameters(weight = c(1/4,1/4,1/2)))

The mult.adj1 object, which specified that no adjustment will be used, is defined in order to observe the decrease in power induced by each MTPs.

It should be noted that for each weighted procedure, a higher weight is assigned to the test of Placebo vs Dose H (1/2), and the remaining weight is equally assigned to the two other tests (i.e. 1/4 for each test). These parameters are specified in the par argument of each MTP.

The analysis model is defined as follows:

# Analysis model
case.study6.analysis.model = AnalysisModel() +
  MultAdj(mult.adj1, mult.adj2, mult.adj3, mult.adj4) +
  Test(id = "Placebo vs Dose L",
       samples = samples("Placebo", "Dose L"),
       method = "TTest") +
  Test(id = "Placebo vs Dose M",
       samples = samples ("Placebo", "Dose M"),
       method = "TTest") +
  Test(id = "Placebo vs Dose H",
       samples = samples("Placebo", "Dose H"),
       method = "TTest")

For the sake of compactness, all MTPs are combined using a MultAdj object, but it is worth mentioning that each MTP could have been directly added to the AnalysisModel object using the + operator.

Define an Evaluation Model

As for the data model, the same evaluation model as in Case study 2 will be used in this case study. Refer to Case study 2 for more information.

# Evaluation model
case.study6.evaluation.model = EvaluationModel() +
  Criterion(id = "Marginal power",
            method = "MarginalPower",
            tests = tests("Placebo vs Dose L",
                          "Placebo vs Dose M",
                          "Placebo vs Dose H"),
            labels = c("Placebo vs Dose L",
                       "Placebo vs Dose M",
                       "Placebo vs Dose H"),
            par = parameters(alpha = 0.025)) +
  Criterion(id = "Disjunctive power",
            method = "DisjunctivePower",
            tests = tests("Placebo vs Dose L",
                          "Placebo vs Dose M",
                          "Placebo vs Dose H"),
            labels = "Disjunctive power",
            par = parameters(alpha = 0.025)) +
  Criterion(id = "Dose H and at least one dose",
            method = "case.study6.criterion",
            tests = tests("Placebo vs Dose L",
                          "Placebo vs Dose M",
                          "Placebo vs Dose H"),
            labels = "Dose H and at least one of the two other doses are significant",
            par = parameters(alpha = 0.025))

The last Criterion object specifies the custom criterion which computes the probability of a significant treatment effect at Dose H and a significant treatment difference at Dose L or Dose M.

Perform Clinical Scenario Evaluation

Using the data, analysis and evaluation models, simulation-based Clinical Scenario Evaluation is performed by calling the CSE function:

# Simulation Parameters
case.study6.sim.parameters =  SimParameters(n.sims = 1000, 
                                            proc.load = "full", 
                                            seed = 42938001)

# Perform clinical scenario evaluation
case.study6.results = CSE(case.study6.data.model,
                          case.study6.analysis.model,
                          case.study6.evaluation.model,
                          case.study6.sim.parameters)

Generate a Simulation Report

This case study will also illustrate the process of customizing a Word-based simulation report. This can be accomplished by defining custom sections and subsections to provide a structured summary of the complex set of simulation results.

Create a Customized Simulation Report

Define a Presentation Model

Several presentation models will be used produce customized simulation reports:

A report without subsections.
A report with subsections.
A report with combined sections.

First of all, a default PresentationModel object (case.study6.presentation.model.default) will be created. This object will include the common components of the report that are shared across the presentation models. The project information (Project object), sorting options in summary tables (Table object) and specification of custom labels (CustomLabel objects) are included in this object:

case.study6.presentation.model.default = PresentationModel() +
  Project(username = "[Mediana's User]",
          title = "Case study 6",
          description = "Clinical trial in patients with schizophrenia - Several MTPs") +
  Table(by = "sample.size") +
  CustomLabel(param = "sample.size", 
              label = paste0("N = ", seq(220, 260, 20))) +
  CustomLabel(param = "multiplicity.adjustment", 
              label = c("No adjustment", "Bonferroni adjustment", "Holm adjustment", "Hochberg adjustment"))

Report without subsections

The first simulation report will include a section for each outcome parameter set. To accomplish this, a Section object is added to the default PresentationModel object and the report is generated:

# Reporting 1 - Without subsections
case.study6.presentation.model1 = case.study6.presentation.model.default +
  Section(by = "outcome.parameter")

# Report Generation
GenerateReport(presentation.model = case.study6.presentation.model1,
               cse.results = case.study6.results,
               report.filename = "Case study 6 - Without subsections.docx")

Report with subsections

The second report will include a section for each outcome parameter set and, in addition, a subsection will be created for each multiplicity adjustment procedure. The Section and Subsection objects are added to the default PresentationModel object as shown below and the report is generated:

# Reporting 2 - With subsections
case.study6.presentation.model2 = case.study6.presentation.model.default +
  Section(by = "outcome.parameter") +
  Subsection(by = "multiplicity.adjustment") 

# Report Generation
GenerateReport(presentation.model = case.study6.presentation.model2,
               cse.results = case.study6.results,
               report.filename = "Case study 6 - With subsections.docx")

Report with combined sections

Finally, the third report will include a section for each combination of outcome parameter set and each multiplicity adjustment procedure. This is accomplished by adding a Section object to the default PresentationModel object and specifying the outcome parameter and multiplicity adjustment in the section’s by argument.

# Reporting 3 - Combined sections
case.study6.presentation.model3 = case.study6.presentation.model.default +
  Section(by = c("outcome.parameter", "multiplicity.adjustment"))

# Report Generation
GenerateReport(presentation.model = case.study6.presentation.model3,
               cse.results = case.study6.results,
               report.filename = "Case study 6 - Combined Sections.docx")

Download

Click on the icons below to download the R code used in this case study and report that summarizes the results of Clinical Scenario Evaluation:

Report without subsections

Report with subsections

Report with combined subsections