TL; DR

1. One of the most promising contributions of M&S to R&D is the identification of responders. This aspect approaches the field of personalized medicine.

2. Responders are patients who would die when receiving placebo but would have survived when receiving the experimental treatment. They can also be defined with the use of EM and Absolute Benefit.

One of the most promising contributions of M&S to R&D is the identification of responders. This aspect approaches the field of personalized medicine.

Definition of a responder

In the current medical terminology, response to a treatment is defined as a favorable course once a treatment has been given. Such a wording, however, implies a causal relationship between treatment and improvement in the outcome. Since the causal link can rarely be established, even in very severe disease, the word response (and responder for designing the patient) is somewhat misleading in such instance. Thus, we should find a better definition.

Let’s assume that the expected effect of the treatment of interest is to prevent a yes/no event, such as death. A responder is a patient, who would experience the event if not treated and who will not experience the event, if treated.

In Table 3, the definition is applied to a number of fictitious patients (N), who would have their condition progress once without and once with treatment. Among these N patients, “b” are responders. In the current and misleading doctor jargon, (b + d) are wrongly said responders. The current saying is correct only if c = 0. Quite a rare setting, difficult to prove![1] While this definition is easy to apply in an in silico controlled trial, it is impossible to use in a real life trial unless the event of interest is recurrent.
 

Table 3: definition of responders

Legend: (see text) among N patients, when untreated, (a + b) experience the event; with the treatment, only “b” does not experience the event. “b” are the responders to the treatment. 

In a two-arm parallel placebo controlled RCT with mortality as primary outcome, responders are patients who would die when receiving placebo (P) but would have survived when receiving the experimental treatment (T). This definition is however difficult to apply in real life, but for a different reason than above: How to predict that a given patient is a responder? This assumes the new treatment is superior to the control, at least for a few patients, or even a single one. The section below illustrates the issue.

As suggested above, the M&S approach can overcome this challenge since the same virtual patient can be simulated for each arm to receive the given treatment, allowing the definition illustrated in Figure 3 to apply. However, it applies only when the occurrence of the event can be simulated. In every other case, one should recourse to other, surrogate, definitions (see below).

Number of responders in a two-arm RCT

For a completed real two-arm RCT, fictitious numbers of event-free patients and patients having had the event are shown in Table 4. At baseline, the two patient groups are assumed to be comparable due to randomisation [2]. Although in reality, the concealed randomisation process is aimed at yielding two groups comparable on average, we will assume that all patients included in the trial are similar, ie. are exchangeable. The rate of events are Rc = a/Nc and Rt = b/Nt in the control and new treatment groups, respectively. The new treatment efficacy is measured by the Absolute Benefit, AB = Rc - Rt, or any other efficacy metric[3].

Table 4: responders in a RCT

Legend: summary data of a completed RCT 

If the new treatment is efficacious, the true Rc is greater than the true Rt.

In order to identify responders in this trial according to the definition of responders given above, we are obliged to assume all patients in the trial are identical. The number of responders in the treatment arm is given by (Rc - Rt)_∗Nt. Accordingly, they are among the ‘d’ patients in this arm without event. The other ‘d’ patients are those who would not have presented the event when not receiving the new treatment. The total number of responders in the trial, i.e. the number of responders in the new treatment arm plus the number of potential responders in the control arm, is (Rc - Rt)_∗( Nc + Nt).

This example shows that it is impossible to say accurately if a given patient, who did not experience the event, at the end of a trial or after a run of therapy, is a responder or not.

Other definitions of responders

Actually, there are other definitions of responders, depending on the objective. They are illustrated in Figure 7.

1. Absolute Benefit greater than a threshold value “s”. Each patient with a predicted AB > s is said responder. Such a definition is convenient when the treatment induces adverse events the burden of which is deemed to be at most equivalent to “s”.
2. Locate responders on a chart of the treatment effect model. This definition remains based on the prediction of the Absolute Benefit.

Figure 7: two other definitions of responders: 1) AB greater than a threshold value “s”: all patients, represented by dots, are below the dotted red line offset to the right of the bisector (vertical distance from the bisector = s); 2) graphical location: example, the dots that fall inside the ellipse (the “optimal responders” in this example).