Something for the Weekend?19 May 2024 10:16
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!)