Apropos the debate about @BioconLimited's limited trial of its #Itoluzimab, this is a brief note (that might grow) about common misunderstandings of terms and concepts in the statistical theory that underpins clinical trials and indeed statistics in general
So here goes:
So here goes:
1. The p- value that is often quoted in papers and journal articles and in the case of #Itoluzimab even in press conferences. It is NOT the probability that the results arose by chance. That is almost a nonsense statement. The results observed are the results.
If the null hypothesis was true-that there was indeed no difference (in the wider population of patients) between #Itoluzimab and #standardcare, THEN the probability that we would have observed in our trial of 30 patients a difference this big or bigger - that is the p value.
2. A type 1 error is the probability that the trial's findings are wrong. The trials findings may well have been wrongly recorded transcribed or analysed, but again the findings assuming they have been checked and rechecked are fact. They cannot be wrong.
A Type 1 error is the mistake we make when we reject the Null hypothesis of No difference, when it (the null Hypothesis) is in fact the true state of affairs. It is our choice where we set our tolerance for the probability of making a Type 1 error. Conventionally, we set it @ .05
"The null hypothesis is not that the two groups in the trial will have equal outcomes". The null hypothesis applies to the Population of patients 'out there'. And we want to make a statement about the population based on what we observe in our study sample.
Think of it like taking a spoon of #kheer out of the large vessel to see if is sweet enough. The spoonful you tasted may well be insipid, but that is not the conclusion of the experiment. The conclusion is that there is not enough sugar in the main vessel.
3."This trial has proved that DrugX is superior to placebo". Such a statement may well often be made esp by the product's sponsor but semantically that is not what the trial did. The trial does not 'prove' anything.
To be pedantic but logical what we mean is that 'The trial provided sufficient evidence to allow us with (1-alpha)% level of confidence that the Null hypothesis can be rejected. The alpha is the probab of a type 1 error and setting it to 0.05 means a 95% level of confidence.
In a criminal trial innocence is assumed until a guilty verdict is handed down. The Guilty verdict means that the evidence allows us to reject the guys's claim of innocence. We haven't proven his guilt (except in rare cases). The small chance of miscarriage is the Type 1 error.
4. "Randomisation(R) is needed to have comparable groups". Again, yes. truly random allocation usually gives us reasonably alike group in the 2 or more arms of the trial but that is neither the primary purpose of R nor is balalnced and alike groups a test of successful R
The purpose of randomisation is ultimately to deal with conscious or unconscious bias that might creep into allocation by the treating clinician. We don't know what factors influence outcome so we cannot deliberately create 2 equal group. Randomisation deals with unknown biases
As Senn has argued the purpose of randomisation ito end up with randomly allocated group. errorstatistics.com/2020/04/20/s-s…
The real import of this for RCTs is that the clinicians role is to select patient for the trial - for the trial, not for the test drug - take consent and then follow the remote random allocation algorithm that should assign the patient to one or other group.
Ideally it is best for the treating clinician's conscience and peace of mind not to know the allocation. Hence the control group will oftenh receive a placebo in the same shape or form as the active drug. All open label trials introduce subconcious bias.
If I was a trial clinician I'd rather talk of study patients and general patients. Among the study patients I would not wish to know who was active drug treated and who was placebo treated.
If I think of any others I'll add to this thread. But clinical trial work is complex, challenging and difficult. It needs special training and the attitude of a scientist seeking the truth rather than a clinician seeking to help her patient.
