Dichotomization

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.

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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?

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