Efficacy Table Development for Clinical Study Reports

Introduction

Efficacy tables are among the most important statistical outputs in a Clinical Study Report (CSR). They transform the statistical analysis described in the Statistical Analysis Plan into a compact presentation of the evidence supporting the study's efficacy conclusions.

A good efficacy table is more than a formatted collection of numbers. Every number should have a defined endpoint, analysis population, treatment group, denominator, analysis method, and source in the underlying analysis datasets.

Where Efficacy Tables Fit in the CSR

A typical CSR contains several layers of efficacy evidence. The tables should tell a coherent statistical story from the primary endpoint through secondary and supportive analyses.

The Core Principle: Start With the SAP

The first step in efficacy-table development is not programming. It is understanding exactly what the SAP requires.

For each efficacy endpoint, identify:

• the endpoint definition;
• the analysis time point or assessment window;
• the analysis population;
• the statistical method;
• the treatment effect measure;
• the missing-data strategy;
• the handling of intercurrent events;
• the multiplicity strategy, if applicable;
• the confidence interval level;
• the rounding and presentation conventions.

The Efficacy Table Shell

Before results are available, statisticians commonly develop a table shell. The shell specifies the structure, labels, statistical summaries, footnotes, and treatment columns without inserting actual study results.

For example, a continuous primary endpoint might use the following structure:

Illustrative values only. Actual CSR values must be generated from the prespecified analysis datasets and statistical methods.

Step 1: Define the Analysis Population

The same efficacy endpoint can produce different results depending on the analysis population.

Common populations include:

• Intent-to-Treat (ITT) population: generally based on treatment assignment or randomization.
• Full Analysis Set (FAS): defined according to the protocol and SAP.
• Per-Protocol (PP) population: subjects satisfying prespecified protocol-adherence criteria.
• Safety population: generally used for safety analyses rather than primary efficacy analyses.

Step 2: Establish the Correct Denominator

Denominators are one of the most common sources of errors in clinical reporting.

For a binary endpoint, the observed response rate is:

where \(x\) is the number of responders and \(n\) is the number of patients included in the denominator.

For example, suppose 72 of 140 evaluable patients respond:

or:

If the table instead uses 150 randomized patients as the denominator, the reported rate becomes:

Both calculations are mathematically correct, but they answer different questions. The correct denominator is determined by the SAP-defined analysis.

Step 3: Determine the Endpoint Type

The structure of an efficacy table depends heavily on the statistical nature of the endpoint.

Continuous Efficacy Endpoints

For a continuous endpoint, the table may present baseline values, post-baseline values, and change from baseline.

The arithmetic change from baseline is:

A descriptive table might contain:

Arithmetic Mean vs. Least-Squares Mean

One of the most important distinctions in efficacy reporting is the difference between a descriptive arithmetic mean and a model-based least-squares mean.

The arithmetic sample mean is:

A least-squares mean, or model-adjusted mean, is instead derived from the prespecified statistical model.

Binary Efficacy Endpoints

For binary endpoints, the fundamental table structure is usually:

The observed response rate is:

and the treatment difference in response rates is:

For the illustrative values:

or approximately:

Confidence Intervals for Binary Endpoints

The confidence interval accompanying a responder analysis depends on the prespecified statistical method.

For a treatment difference:

the table should identify the confidence interval method when appropriate, particularly when an exact or adjusted method is used.

Time-to-Event Efficacy Endpoints

Time-to-event endpoints require a different table structure because not every patient necessarily experiences the event.

Typical information includes:

• number of patients;
• number of events;
• number censored;
• median time-to-event;
• confidence interval for the median;
• hazard ratio;
• confidence interval for the hazard ratio;
• p-value.

The hazard ratio is generally interpreted as a relative comparison of the instantaneous event rates under the specified model.

Repeated-Measures Efficacy Tables

Longitudinal efficacy endpoints often require tables containing multiple assessment visits.

Change From Baseline Tables

When the primary endpoint is change from baseline, the table should clearly distinguish the baseline value from the change being analyzed.

For each patient:

where \(Y_{i,0}\) is the baseline measurement and \(Y_{i,t}\) is the value at the specified post-baseline time point.

The treatment effect may then be represented as:

where \(\mu_T\) and \(\mu_C\) are the corresponding treatment-group estimands.

Responder Analyses

Responder analyses convert a continuous or ordinal endpoint into a binary clinical outcome.

For example, suppose a responder is defined as a reduction of at least 30 units from baseline.

The response definition must match the prespecified endpoint definition. Changing the threshold after reviewing results can introduce substantial bias.

Multiplicity and P-Value Presentation

A CSR efficacy table may contain many p-values. The presence of a p-value in a table does not automatically mean that the associated hypothesis was formally tested at the nominal significance level.

The table should distinguish among:

• confirmatory hypothesis tests;
• multiplicity-adjusted tests;
• nominal p-values;
• descriptive analyses;
• exploratory analyses.

If multiplicity adjustment is used, the table should clearly identify the adjusted testing procedure or indicate through a footnote how the reported p-values should be interpreted.

Missing Data and Unevaluable Patients

Missing data can affect both the numerator and denominator of efficacy analyses.

Potential reasons for missing efficacy assessments include:

• withdrawal;
• loss to follow-up;
• missed visits;
• treatment discontinuation;
• protocol deviations;
• technical failure of an assessment;
• death or another intercurrent event.

The treatment of missing data should follow the SAP-defined analysis method. For example, an analysis may use a model-based missing-data assumption rather than simply classifying every missing patient as a non-responder.

Estimands and Efficacy Tables

Modern clinical-trial analyses distinguish the treatment effect being estimated from the raw endpoint measurement.

An estimand generally specifies the key components of the treatment-effect question, including:

• the population;
• the treatment condition;
• the variable or endpoint;
• the handling of intercurrent events;
• the population-level summary measure.

This distinction matters because two analyses using the same endpoint can answer different scientific questions if they handle treatment discontinuation, rescue medication, death, or other intercurrent events differently.

Subgroup Efficacy Tables

Subgroup tables evaluate whether the treatment effect appears consistent across clinically relevant categories.

Table Titles and Footnotes

A strong table title should tell the reader what is being analyzed without requiring them to search elsewhere in the CSR.

A useful structure is:

Table X.X.X
Summary of Primary Efficacy Endpoint at Week 24
Full Analysis Set

Footnotes should clarify important details such as:

• analysis population;
• statistical model;
• covariates;
• confidence interval method;
• missing-data handling;
• multiplicity adjustment;
• rounding conventions;
• definitions of abbreviations.

Example: Complete Primary Efficacy Table

Consider a randomized Phase III study comparing an experimental treatment with placebo. The primary endpoint is change from baseline in a continuous score at Week 24.

An appropriate footnote might state:

LS = least squares; SD = standard deviation;
SE = standard error; CI = confidence interval.

LS means and treatment difference are based on the prespecified
analysis model. The model includes treatment and prespecified
baseline covariates. The 95% CI is two-sided.

Analysis population: Full Analysis Set.

How to Build the Table From the Analysis Dataset

The relationship between the clinical-trial datasets and the final CSR table should be traceable.

A simplified reporting chain is:

Table Programming Specifications

Before programming begins, the statistician should provide a sufficiently detailed table specification.

Independent QC of Efficacy Tables

A second programmer or statistician should independently verify the critical components of the table.

QC should include both statistical validation and presentation validation.

Numerical QC Example

Suppose a responder table reports:

The QC calculation for Drug A is:

For placebo:

The treatment difference is:

The QC process should verify not only the displayed percentage but also the underlying numerator and denominator.

Cross-Table Reconciliation

A particularly important CSR QC step is comparing related outputs.

For example, the number of randomized patients in an efficacy table should reconcile with the corresponding disposition and demographic tables when the same population is intended.

Common Efficacy Table Errors

1. Using the wrong analysis population. A table may accidentally use the safety population instead of the prespecified efficacy population.
2. Using the wrong denominator. Percentages may be calculated using randomized patients rather than the endpoint-specific denominator.
3. Confusing observed and model-based results. Arithmetic means and LS means should not be labeled interchangeably.
4. Reporting an incorrect time point. A Week 24 analysis should not accidentally use the closest available visit unless that is specified in the SAP.
5. Ignoring treatment discontinuation. Intercurrent events may materially change the interpretation of an efficacy analysis.
6. Using the wrong confidence interval. The confidence interval must correspond to the prespecified treatment-effect measure and method.
7. Overinterpreting subgroup results. Apparent differences between subgroup estimates do not necessarily establish treatment-effect heterogeneity.
8. Incorrect p-value adjustment. Multiplicity requirements must be reflected in the reported inferential results.
9. Rounding too early. Intermediate calculations should generally use full precision, with rounding performed for presentation.
10. Inconsistent footnotes. Table terminology must remain consistent with the SAP and other CSR outputs.

Rounding and Display Conventions

Rounding is part of table specification and should be standardized.

Statistical vs. Presentation QC

These are related but distinct activities.

From Table to CSR Narrative

The efficacy narrative should be derived from the validated table, not independently recreated from memory or preliminary outputs.

For example, if the primary efficacy table shows:

the CSR narrative should report the same estimate, confidence interval, and inferential result.

A Practical Efficacy Table Development Workflow

What Should Be Documented in the Table Specification?

A robust table specification should contain enough information for another qualified statistician or programmer to reproduce the output.

• table identifier and title;
• endpoint definition;
• analysis population;
• treatment variable;
• baseline definition;
• analysis visit or time point;
• statistical method;
• covariates;
• estimand and intercurrent-event strategy, where applicable;
• treatment-effect measure;
• confidence interval method;
• hypothesis-testing method;
• multiplicity adjustment;
• missing-data handling;
• rounding conventions;
• footnotes and abbreviations;
• program and dataset traceability.

Final Efficacy Table Checklist

Key Takeaways

Efficacy-table development is fundamentally an exercise in statistical translation and traceability.

The protocol defines what the trial is trying to establish. The SAP defines how the efficacy question will be analyzed. The analysis datasets provide the data required for the analysis. The statistical program converts those data into estimates and inferential results. The efficacy table then presents those results in a form that can be independently reviewed.

The most important principles are:

• Build from the SAP, not from the data.
• Make analysis populations explicit.
• Verify every denominator.
• Distinguish descriptive statistics from model-based estimates.
• Preserve the prespecified treatment-effect definition.
• Apply missing-data and intercurrent-event rules consistently.
• Handle multiplicity explicitly.
• Perform independent statistical and presentation QC.
• Reconcile tables, figures, listings, and CSR text.
• Maintain complete traceability from the final table back to the analysis data.

References

International Council for Harmonisation (ICH). ICH E3: Structure and Content of Clinical Study Reports.

International Council for Harmonisation (ICH). ICH E9: Statistical Principles for Clinical Trials.

International Council for Harmonisation (ICH). ICH E9(R1): Addendum on Estimands and Sensitivity Analysis in Clinical Trials.

International Council for Harmonisation (ICH). ICH E6(R3): Good Clinical Practice.

European Medicines Agency. Guideline on Missing Data in Confirmatory Clinical Trials.

U.S. Food and Drug Administration. Statistical Principles for Clinical Trials.