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While it's quiet I thought I'd share an update on the 90% probability question I have been discussing on the other channel. It is quite long so if you find figures upsetting look away now.
Hi Inan et al,
I see you are desperate for me to post some workings, on the "where did the 90% chance of getting a 70% ORR in the next cohort of SCIB1 patients come from?" question
As I said in my last post, "I have never disputed the number given by Scancell but all I’m saying is I can’t verify the figures from the data I have. That either means I’m missing data or I’m too stupid."
Anyway, it turns out I may have been a bit stupid or at least slow.
In order to calculate probability (or chance), you need a data set. The published 82% is a percentage or ratio. It is a single number and cannot be analysed - merely projected forward which BTW would be an error. We aren't talking the throw of a die - in this instance the chances are fixed. You have a one in six chance of getting a one (on a six-sided die) and it will always be 1 in 6 regardless of the size and material of the die (assuming no bias)
So I followed the link you kindly provided to the January 2024 Interim Results presentation, page 10.
Here it presents the tumour size change percentages for each of the 11 patients:
68,-24,-31,-48,-58,-59,-69,-78,-81,-88,-94
If I was forecasting the next point it would be -51 (the arithmetic MEAN). But because of the large fluctuations the standard deviation would be high. So I'd only be 90% certain that the next value (patient) would be somewhere between 4% (growth) and -106% shrinkage. Of course, a shrinkage of 106% isn't possible. An increase of over 100% is, but a decrease isn't. So in this case we have a skewed distribution not a normal distribution.
So at this point I stopped looking - until today when I decided to revisit.
I arranged the results into groups -
above 0
0 to -29
-30 to -49
-50 to -69
-70 to -89
-90 to -100
The number of patients in each group is 1,1,2,3,3,1 - this looks like a normal (but skewed) distribution.
But the target is an ORR of 70%. So we can just take the top 70% (8 patients) and analyse the shrinkage data and variances of those. In this case we get:
Average shrinkage: 63%
Standard deviation: 22.3
1.28 SDevs (=90% probability): 28.6
Lower limit at 90%: 34.4%
Upper limit at 90%: 91.6
So a 90% probability of shrinkage between 34% and 92% - all within the PR/CR range.
There is a 91% probability of shrinkage between 30% and 90%, again all responses.
So, as far a the numbers alone go, it can be shown using probability and statistics that there is a 91% chance that a 70% ORR response rate will be achieved in future SCIB1 patients.
The one caveat is the sample size is very small. This will improve as data is gathered (and published!)
What needs to be achieved is the scan data from 34 patients and a 30% + response rate in 27 patients.
At the end of April we were told that 27 patients had enrolled.
So my question to anyone who understands the timelines of the trial is : When could we reasonably expect the scan results from a minimum of 34 patients ?
It would help to clarify just how long we have to wait for the SCiB1 + CPI data and hopefully stop people from keep asking why we’ve not heard anything.
I wouldn't get out of bed to calculate significance levels of any sample less than 20. And nothing we do will affect the emerging data, so better have a nice walk and pray to whichever is your god.
"I wouldn't get out of bed to calculate significance levels of any sample less than 20"
The maths teel is there is a 90% chance, on existing published data, of a 70% or higher response rate in the full population. That's worth getting out of bed for.
Jackdaw,
I agree, it is a very small sample. For sales forecasting I always use at least 24 months in order to at least get some idea of seasonality.
It was Scancell that came up with 90% based on the same data set. I just wanted to show where it may have come from.
Still, a data set of 11 is still better than a data set of 2 as advocated by the idiot over on ADVFN!
Ruck - IMO it's not right to insult Inan here when you know that he can't reply.
Re. "It was Scancell that came up with 90% based on the same data set. I just wanted to show where it may have come from".
Very noble of you I'm sure, but for me, I accepted that Scancell might just have known what they were saying, in the first place.
Sorry TF, I didn't insult him as I deliberately omitted to name him. But you've done that now!
If you want to defend him, do so on ADVFN where we can all engage.
Good try Ruck, BUT, don't pretend that everyone, excepting the newest of the 'newbies', wouldn't be aware of whom you were referring to. Never mind.
As for engaging, I've already posted, "I accepted that Scancell might just have known what they were saying, in the first place." ATB
Quite so, tf.
It literally isn’t worth obsessing about, still less arguing over.
Probabilities are calculated because one can, but the only certainty is that more data points are needed.
That said, there seems every reason to expect them to deliver more or less to expectation.