Clinical trials and other studies commonly assess the effectiveness of an intervention through the use of responder-based endpoints. These classify patients based on whether they meet a number of criteria which often involve continuous variables categorised as being above or below a threshold. The proportion of patients who are responders is estimated and, where relevant, compared between groups. An alternative method called the augmented binary method keeps the definition of the endpoint the same but utilises information contained within the continuous component to increase the power considerably (equivalent to increasing the sample size by > 30%). In this article we summarise the method and investigate the variety of clinical conditions that use endpoints to which it could be applied.

We reviewed a database of core outcome sets (COSs) that covered physiological and mortality trial endpoints recommended for collection in clinical trials of different disorders. We identified responder-based endpoints where the augmented binary method would be useful for increasing power.

Out of the 287 COSs reviewed, we identified 67 new clinical areas where endpoints were used that would be more efficiently analysed using the augmented binary method. Clinical areas that had particularly high numbers were rheumatology (11 clinical disorders identified), non-solid tumour oncology (10 identified), neurology (9 identified) and cardiovascular (8 identified).

The augmented binary method can potentially provide large benefits in a vast array of clinical areas. Further methodological development is needed to account for some types of endpoints.

In clinical trials gathering evidence about the effectiveness of a medical intervention, it is necessary to specify a primary endpoint. An endpoint should represent how patients respond after being given the treatment; it should be expected that the distribution of the endpoint will be more favourable if a treatment is effective than if it is ineffective. In many disorders it is difficult to specify just one endpoint, as an intervention may have a variety of effects that cannot be adequately measured through one measurement. For this reason, it is common in many conditions to combine multiple distinct endpoints (which we will refer to as components) into a composite endpoint.

Composite endpoints have been recommended when there is large variability in the disease manifestation, e.g. in complex multisystem diseases, allowing multiple equally relevant outcomes to be considered without the need to correct for multiplicity. They have also been advocated for rare diseases, where they might improve the power by increasing the number of events observed. On the other hand, composite endpoints have been criticised for making trial results more difficult to interpret [

One specific type of composite endpoint is a composite responder endpoint, which divides patients into responders and non-responders on the basis of the set of components. Some of these components may be binary (present or absent), and some may be continuous. In the case of continuous components, some dichotomisation is necessary, so that patients are responders only if the continuous component is above or below a specified threshold. In Table

Examples of responder endpoints used in different areas of medicine; italicised components denote continuous dichotomisations. To be a responder, all numbered components are required to be met

Clinical area | Endpoint | Components and definitions |
---|---|---|

Oncology | Tumour response | 2. No new tumour lesions |

Rheumatology | ACR20 | 3. 20% improvement in at least three of: 4. No rescue therapy given |

Type II diabetes | Diabetes remission |
3. No non-study pharmacological treatment given |

Responder endpoints are appealing, as they simplify several (potentially complex) pieces of information into one responder/non-responder variable. The proportion of patients who are responders serves as an easy-to-interpret measurement of the effectiveness of a treatment.

From a statistical point of view, however, this appealing simplicity comes at a non-appealing cost when one or more components are continuous. Dichotomising continuous variables loses information, a point which has been made several times (see, e.g. [

Assuming that avoiding dichotomisation is desirable, it is not obvious how this is possible when the responder endpoint consists of a mix of continuous and binary components. One method would be to use the approaches of Lachenbruch [

This motivates statistical methods that can be used to keep what is clinically relevant by inferring the proportion of patients who are responders, but also utilise information contained in continuous components to improve the efficiency. For the single-component responder, this idea dates back to the 1990s, in studies where Suissa and Blais [

In this paper (and its associated

The augmented binary method extends previous work focused on a single dichotomised continuous endpoint [

For simplicity we focus on the case of a composite responder endpoint that combines a dichotomised continuous component with a binary component. For example, response in solid tumour oncology consists of the sum of target lesion diameters shrinking by at least 30% from a baseline scan (dichotomised continuous) and no new tumour lesions appearing on a scan (binary). The traditional, binary analysis would work with the data on whether or not each patient is a responder or not. If a patient meets the criteria, he/she is a responder, otherwise not. If analysing a randomised controlled trial (RCT), then one might test for a difference between arms in the proportion of patients who are responders with an established method that gives an effect size, confidence interval and

A detailed description of how to fit the method is provided in the

Illustration of how (hypothetical) response information from patients is weighted by the two different methods. Non-responders consist of those in whom the continuous component is below 1 and those who do not respond according to another binary criterion. Underlying the augmented binary method is a joint model that is fitted to the continuous and binary data and yields fitted ‘response weights’ for each patient; these can then be compared between arms

The benefit of the method is primarily the increased power. By better using the available information, the proportion of patients who respond (and therefore any differences between arms in an RCT) can be estimated more precisely. In more statistical language, the variance of the estimate is lower, and the width of the confidence interval (CI) is narrower. Simulation studies presented by Wason and Seaman [

There are some additional benefits of the approach. First, due to the underlying model being fitted, it better allows for missing data on different components [

There are also drawbacks. First, it is undoubtedly more complex to apply the method compared with standard binary approaches. Some code is available (see the

Up to now, the method has been applied to datasets in solid tumour oncology [

We made use of the COMET (Core Outcome Measures in Effectiveness Trials) database (

We reviewed physiological and mortality trial outcomes (categorised according to [

This process allowed us to identify 39 clinical areas (additional to solid tumour oncology, rheumatoid arthritis and SLE) where the augmented binary method could be utilised to gain efficiency. An additional 28 clinical areas had used responder endpoints formed from a single categorised/dichotomised continuous variable. Table

Number of new clinical areas identified by classification; full list provided in

Classification | Number of conditions with suitable composite responder endpoints | Number of conditions with single-variable responder endpoints |
---|---|---|

Bleeding and transfusion | 2 | 1 |

Cancer | 6 | 4 |

Cardiovascular and circulation | 5 | 3 |

Dentistry and vision | 2 | 1 |

Gastroenterology | 3 | 1 |

Infectious diseases | 3 | 0 |

Lungs and airways | 0 | 2 |

Mental health and addiction | 3 | 1 |

Neurology | 2 | 7 |

Orthopaedics and trauma | 1 | 3 |

Renal and urology | 2 | 1 |

Rheumatology | 8 | 3 |

Unclassified | 2 | 1 |

Total | 39 | 28 |

If a condition had both composite and non-composite responder endpoints identified, they were only included in the composite column

^{a}Excludes solid tumour oncology (as the utility of the method had previously been highlighted there)

The clinical classifications for which the method appears most useful in terms of number of endpoints are rheumatology (11 found), non-solid tumour oncology (10 found), neurology (9 found) and cardiovascular (8 found).

We note that this review was not systematic and it represents a likely substantial underestimate of the number of clinical areas where suitable endpoints are used, as our review only covered clinical areas which were covered by a COS published by 2016. As an example, Table

In this paper we have highlighted and summarised previous statistical work on an efficient analysis approach called the augmented binary method, which can be used to improve analysis of composite responder outcomes. The method allows retention of clinically relevant endpoints whilst improving the power of analyses by an amount equivalent to a considerable increase in sample size. As well as describing previous work, we have conducted a review of new clinical areas for which the method could be used. We have also provided a worked example of fitting the model using publicly available R code in the

Through our review of core outcome sets, we have found numerous new disease areas where the augmented binary method could be applied to gain power. We acknowledge that many of the core outcome sets were developed before best practice guidance [

Although the results indicate the widespread utility of the method, there are several areas where further methodological research is required to fully realise the possible benefits.

There are several endpoints which are typically analysed using time-to-event methods. Many progression, remission and relapse endpoints are used, and the time until such a negative event occurs is the quantity of interest. Although the augmented binary method is well developed for composite responder outcomes that are analysed at a single timepoint or longitudinally, further work is needed to apply it to time-to-event outcomes.

In some cases, the composite responder outcomes are particularly complex, with more than two components and with response being defined as meeting some, but not all, of the criteria. Recent work in this area [

We have focused on how the method can improve the statistical power of trials. An alternative way to use this improved power would be to reduce the sample size needed for a target power level. A barrier to widespread use of the method in this way is sample size estimation. Methods for conducting sample size estimation for trials using responder endpoints analysed using latent variable models are developed in McMenamin et al. [

In this paper we have shown that responder composite outcomes are used as primary clinical trial endpoints in many diseases. Analysing data from these trials using the augmented binary approach would improve power equivalent to increasing the sample size by at least 35%. Further methods research is needed to improve time-to-event analyses using these outcomes as events.

MMM and JW are supported by funding from the Medical Research Council (MRC), grant code MC_UU_00002/6. JW is also supported by Cancer Research UK (C48553/A1811). None of the funding bodies had a role in the design of the study, analysis, interpretation of data or writing the manuscript.

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All authors contributed to the design of the manuscript and interpretation of the data. JW developed the first draft, and MMM and SD critically revised the manuscript and approved the final version. The corresponding author attests that all listed authors meet authorship criteria and that no others meeting the criteria have been omitted. The author(s) read and approved the final manuscript.

The datasets used are available from the authors of [

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Confidence interval

Core Outcome Measures in Effectiveness Trials

Core outcome set

Randomised controlled trial

Systemic lupus erythematosus

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