What I was alluding was something akin to your Scenario #4 here. That is, a relentlessly progressive cancer whose natural history is well known and where tumor shrinkage is unheard of.
In such cases, suppose a substantial minority of patients in the treatment arm, say a third, have their tumors shrink greatly. No shrinkage occurs in the other two thirds. In the control arm, no shrinkage occurs in anyone.
In these cases, it is probably reasonable to speak of that third in the treatment arm as being “responders” in the sense that they exhibited an otherwise unheard of course after their treatment. It is also probably fair to say that the treatment caused a third of the patients in the treatment arm to respond, wherein causality is implied by the fact that nothing else is known to cause such shrinkage.
Now, in said trial, we may not necessarily know why these patients exhibited this incredible course after their treatment. We therefore wouldn’t be able to be pre-specify a subgroup analysis of any sort (as we would not know which patient characteristics could’ve possibly interacted with the treatment to cause this unusual response). But nevertheless we would probably be justified in thinking that there’s some hitherto undiscovered feature(s) in that third of patients that caused the treatment to elicit such an unusually dramatic shrinkage of the tumor burden.
Again, this is completely different to heart failure, where 5-point changes are completely within the range of what one would expect in the disease’s natural history. In such cases I agree with you that comparing the proportions of “responders” is not at all advisable.
Pavlos is a lot more qualified than I am to comment on your post, but I’m inclined to agree with this statement. In this particular context, the “change from baseline” (i.e., reduction in tumour burden) can be validly attributed, clinically, to causality at the level of the individual patient since such change would not be expected to occur in the absence of intervention. But, as Pavlos noted in post #13 above, such individual-level and within-arm assessments aren’t the main goal of RCTs, even in oncology, where individual causality is sometimes assessable:
Outside the context of diseases with natural histories compatible with scenarios #3-5 in post #28 above, I maintain that continuing use of the terms “response” and “responder” will cause mass causal confusion and perpetuate many bad statistical practices by inexpert clinicians.
Yes, agreed. I think the word “responder” carries an inherently causative undertone (and, in the context of a trial aiming to assess a given treatment, this “causative” effect will invariably be attributed to the treatment in question without due consideration).
One way of understanding disease is that it is due to failure of a control mechanism (usually many of them). These failures can be upward or downward displacements of metabolic variables (e.g. blood sugar) and physiological variables (e.g. BP) when the feedback is known as homeostasis. Damaged tissue (e.g. a wound) is corrected by feedback re-growth and unwanted tissue growth (e.g. infection or tumour) is removed by the immune system which is a feedback process. Mostly, these things happen imperceptibly. However in disease states, the ‘elasticity’ of a feedback mechanisms is reduced or overcome leading failure of homeostasis or tissue repair with unpleasant outcomes or death if the essential feedback mechanism fails completely and cannot be substituted. There are also social feedback mechanisms.
Figure 1 shows sigmoid curves that model of these processes and their response to treatment. For example, if there is a small tumour with some low malignancy score (e.g. a fictitious score below 25), the feed-back removal of abnormal tissue will be effective. The probability of death within some specified time would be very low. Therefore a treatment (e.g. with an odds ratio of 0.2 say) will create very little absolute risk reduction. If the tumour is bulky with a high malignancy score, then the feedback removal will be weak and the probability of death may be 0.99 without treatment. At this level, the odds ratio of 0.2 will also have very little effect on lowering absolute risk. However, there may be a ‘sweet mid-range’ where the feedback mechanism can be helped so that the treatment odds ratio will have a useful effect on risk reduction (e.g. at a score of 40, the risk of death is reduced from 0.7 to 0.3, an absolute risk reduction of 0.4)…
Patients in the very high and very low malignancy score ranges will be poor responders on average and those in the sweet mid-range will be good responders on average. These various ranges represent treatment heterogeneity. I suspect that disease severity is by far the most important cause of treatment heterogeneity in medicine. It will not be possible to identify the ‘individual responders’ or non-responders with certainty unless someone had a probability of 1 of dying on placebo from a RCT and survives on treatment (as pointed out by Erin). Thus if in a RCT, 0% survive on placebo and 50% survive on treatment then survival will have been caused by treatment with a probability of 1. However, if 1% survive on placebo, what is the probability that someone’s survival will have been caused by the treatment?
I will propose an answer to this question. If in some RCT, 0% survive on placebo and 60% survive on treatment, then 60-0 = 60% will have been caused to survive by treatment. Therefore, of the total 60% in the trial surviving on treatment, a total of 60% in the trial were due to treatment. Therefore, the probability that the survival of a patient on treatment in front of us was caused by the treatment is 60/60 = 1.0 as Erin suggests.
If in some other RCT, 30% survive on placebo and 60% survive on treatment, then 60-30 = 30% will have been caused to survive by treatment. Therefore, of the total 60% in the trial surviving on treatment, a total of 30% in the trial were due to treatment. Therefore, the probability that the survival of a patient on treatment in front of us was caused by the treatment is 30/60 = 0.5.
If in some other RCT, 1% survive on placebo and 60% survive on treatment, then 60-1 = 59% will have been caused to survive by treatment. Therefore, of the total 60% in the trial surviving on treatment, a total of 59% in the trial were due to treatment. Therefore, the probability that the survival of a patient on treatment in front of us was caused by the treatment is 59/60 = 0.98.
It is only when there is 0% survival on placebo that we can be sure that a patient is a responder. If the placebo response is >0%, then all we can do is estimate the probability that the patient was a responder. What do you think?
In the first paragraph, the risk ratio for death is 0.4/1 = 0.4. The relative risk ratio is 100(1-0.4) = 60%. The probability that treatment was the cause of survival when the patient survived is 0.6/0.6 = 1.
In the second paragraph the risk ratio for death is 0.4/0.7 = 0.57 and the relative risk ratio is 100(1-0.57) = 43%. The probability that treatment was the cause of survival when the patient survived is 0.3/0.6 = 0.5.
In the third paragraph the risk ratio for death is 0.4/0.99 = 0.404 and the relative risk ratio is 100(1-0.404) = 59.6%. The probability that treatment was the cause of survival when the patients survived is 0.59/0.6 = 0.983.
In other words, the RRR is the absolute risk reduction due to treatment of an adverse effect divided by its risk without treatment. However, the probability of treatment being the cause of avoiding the adverse event in someone who has avoided it is the absolute risk reduction divided by the probability of avoiding the adverse event on treatment.
