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Re: Q test of significance of the trend of the data

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On Sun, 8 Jan 2023 10:48:46 -0000 (UTC), "David Jones"
<dajhawkxx@nowherel.com> wrote:

>Rich Ulrich wrote:
>
>> On Sun, 8 Jan 2023 04:36:55 -0000 (UTC), "David Jones"
>> <dajhawkxx@nowherel.com> wrote:
>> 
>> > Cosine wrote:
>> > 
>> >> Say we have five groups of subjects, and each receives different
>> >> concentrations of medicine, from low to high.
>> >> 
>> >> At the endpoint, we measure the diameters of the lesion of each
>> >> subject and calculate the mean diameter of each group.
>> >> 
>> >> We expect a monotone decrease trend of the mean diameters of the
>> >> groups. But how do we demonstrate the significance?
>> > 
>> > As part of the first step in significance testing, you need to have
>> > a null hypothesis as well as an alternative hypothesis. 
>> 
>> Or - you can have a situation where you want to provide a
>> precise assessment, where basic "significance" is assumed, and
>> readily established by any test. 
>> 
>> Having 5 concentrations, without a Zero comparison, implies
>> that the questions (hypotheses) concern whether the lowest
>> dose (concentration) has much effect, or if there is continued 
>> gain from increasing dose by each step. 
>> 
>> A overall test: 
>> Assuming that the doses here are judged (by the PI) to be 
>> (in the relevant sense) equal intervals, a simple correlation
>> will show that increasing dose matters.  This will be HIGHLY 
>> significant, you hope. 
>> 
>> (Also, the outcome should probably take into account the size 
>> of the original lesion. Log of the Pre/Post ratio might be natural, 
>> if lesions don't decrease to 0.)
>> 
>> If I had data like these, I would want to plot the Pre vs. Post
>> for the 5 doses, and figure out from the picture what there is
>> to describe.  A strong linear trend of efficicay across dose (log 
>> concentration) with tiny contributions from the nonlinear ANOVA
>> components would be the outcome most convenient to describe. 
>> 
>> 
>> >                     There are two
>> > obvious but distinct possibilities for one aspect of what might be
>> > going on: in one the null hypothesis has an unspecified but varying
>> > pattern, to be compared to a monotone pattern, while in the other
>> > the null hypothesis has constant value, to be compared with a
>> > monotone pattern.
>
>The OP has been very unclear, so there seems also to be at least one
>other possibility, where the null hypothesis is that there is a
>monotone pattern, with the alternative hypothesis (that which one is
>looking evidence might be happening) is that there is a change in
>direction of the pattern as the dosage increases (but possibly just one
>turning point).


Concerning alternative hypotheses:  The OP's example might have been
made up, but I've seen real instances where the PI did not consider,
What do I REALLY want to show?  Will my numbers be able to show it? 

Oh -'randomization' is necessary if one wants the easier conclusions
of a 'randomized trial' (compared to observational reports). If size 
of lesion varies a lot, it could be worth stratifying the 
randomization. 

"Monotonic increase in response" is not as interesting as the actual 
degree of improvement.  Or: Has someone argued that 'high' will be
bad?  

If there is special concern about the end-points, it could be 
worthwhile to use larger Ns at the ends.  (Is a no-dose condition
non-informative? or well-known as having No-change?) 

Also, 'statistical power' is the reason that two-group studies are
by far the most common. Trying to reach a firm conclusion about
whether every two groups (dose) differ, out of five groups, when 
the dose-differences are small ... would require a larger N than 
anyone ordinarily justifies. 

-- 
Rich Ulrich 

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Q test of significance of the trend of the data Cosine <asecant@gmail.com> - 2023-01-06 03:14 -0800
  Re: Q test of significance of the trend of the data "David Jones" <dajhawk18xx@@nowhere.com> - 2023-01-06 14:17 +0000
    Re: Q test of significance of the trend of the data Rich Ulrich <rich.ulrich@comcast.net> - 2023-01-06 17:11 -0500
      Re: Q test of significance of the trend of the data Cosine <asecant@gmail.com> - 2023-01-07 17:48 -0800
        Re: Q test of significance of the trend of the data "David Jones" <dajhawkxx@nowherel.com> - 2023-01-08 04:36 +0000
          Re: Q test of significance of the trend of the data Rich Ulrich <rich.ulrich@comcast.net> - 2023-01-08 01:36 -0500
            Re: Q test of significance of the trend of the data "David Jones" <dajhawkxx@nowherel.com> - 2023-01-08 10:48 +0000
              Re: Q test of significance of the trend of the data Rich Ulrich <rich.ulrich@comcast.net> - 2023-01-10 00:45 -0500

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