1. ## Frequency analysis

Hello.

I have a problem with my analysis.

I got 2 groups which take drug (Group 1 (50 people) takes real medicine and Group 2 (40 people) takes placebo) and a specific measurement is concluded at the beginning and in the end of the course, thus I got 2 variables which correspond to "start"= beginning and "finish" = end. These 2 variables are binary (1 = yes, 0 = no).

Now, my task is to conclude a statistical analysis regarding these 2 groups and answer a question: "Is the drug effective?". From what I understood, the question can be rephrased as "Does the difference of positive percentage changes between group show statistical significance?"

By percentage change I mean situation like this:

Say group #1 has 50 people, our "start" variable has 28 "yes" and 22 "no", "finish" variable has 35 "yes" and 15 "no", so the percentage change is from 56% (28 out of 50) to 70% (35 "yes" out of 50) which is

In group #2 situation is different. Say, "start" has 20 "yes" out of 40, that is 50%, and "finish" has 25 "yes" out of 40 which is 62,5%, so the change is from 50% to 62,5%.

Now I'm stuck.
Doing a 2x2 frequency table feels weird for some reason. Percentages don't take into account group sizes so it feels rather skewed to operate with percentages as plain numbers. But otherwise I dont know what to do.

2. ## Re: Frequency analysis

Allocation to groups was not randomized, I suppose?
Changes can happen between yes and no either way, or only from no to yes?

With kind regards

K.

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Makina (05-20-2016)

4. ## Re: Frequency analysis

Not quite sure about "randomized" allocation to groups. What exactly do you mean? Sorry, I'm not great with these terms.
And yes, changes can go both ways.

5. ## Re: Frequency analysis

Not quite sure about "randomized" allocation to groups. What exactly do you mean? Sorry, I'm not great with these terms.
It is an extremely important concept for experimental research. If you perform clinical drug testing without being familiar with it, then I'd recommend that you do a little research about study designs.
And yes, changes can go both ways.
One possibility could be categorizing participants by "change from yes to no"/"change from no to yes"/"no change", and perform a group comparison for a 2x3 table, using Chi² test. Or, to leave out all those without a change, and to compare only the frequencies of yes->no and no->yes changes between groups (2x2 table with Chi² test).

For the interpretation of results, maybe the different base rates between groups will have to be taken into account.

With Kind regards

K.

6. ## The Following User Says Thank You to Karabiner For This Useful Post:

Makina (05-20-2016)

7. ## Re: Frequency analysis

Well, I might be bad at these terms when it comes to understanding English, but I do understand what randomization is. At least I hope so. Your assumption regarding allocation being not randomized kinda made me think if I actually knew what randomization was after all, because I thought it was a given that the allocation was randomized, that's why I replied in such a way.

Anyway
Each patient regardless of his parameters during screening visit was randomly allocated to his group in 1:1 proportion and in the end some got excluded so groups are unequal in numbers.

Now, unfortunatelly the actual study is abit more complicated than what I originally wrote. Here is the draft.

A patient is screened, then he is given 4 weeks to perform a particular test and then he fills a questionnaire after each test he performed, a questionnaire has that "YES" or "NO" which is then collected for further analysis - the "Start" variable.

Then 4 weeks later he comes for the second visit and there he's given a drug (or placebo) and another questionnaire to fill. He has to use the drug just before the test every time. So he fills the questionnaire and after another 4 weeks he comes to the last visit to deliver the questionnaire and that's when his duties as a study subject end. This is how data for "Finish" is acquired.

The amount of tests a subject can perform is not set, he can do as many as he wants (more than 4 though, but the upper limit is not there, so there were cases with up to 13 tests)

For example, Subject #1 did 5 tests at "Start" and 7 tests at "finish", Subject #2 did 4 tests at "Start" and 14 tests at "finish". Then, Subject #1 contributed with 3 "Yes" and 2 "No" (he did 5 tests - he filled the questionnaire with 5 evaluations respectively) to "Start" variable and then 6 "Yes" and 1 "No" to finish variable. Same for Subject #2. Etc

So, what I originally wrote was a cumulative of "Yes" and "No" answers for every Subject in respective groups, that's why I don't think that it's possible to put either of your approaches in practice since 1 person concluded more than 1 test.

I hope my English isn't to bad and I got my point through.

8. ## Re: Frequency analysis

Each patient regardless of his parameters during screening visit was randomly allocated to his group in 1:1 proportion and in the end some got excluded so groups are unequal in numbers.
Usually one cannot leave droputs completely out of the analysis.
I hope my English isn't to bad and I got my point through.
It was perfectly understandable, thank you. The crucial element (primary clinical endpoint)/outcome is missing, AFAICS.

But what do you want to achieve here? If you perform a clinical study with human beings, then you have to plan your analysis beforehand. Otherweise it's unethical and unprofessional. And if you do not have enough knowledge to do the analysis without help (after all, the design looks quite complicated), then you'd rather find some expert in real life rather than consulting a web Forum, IMHO. So, I'm afraid and hope you will forgive me that I do not like the idea to design a plan of analysis here and will abstain from further discussing the issue.

With kind regards

K.

9. ## Re: Frequency analysis

Dropouts weren't left out completely, of course. These subjects were included in safety analysis.

Regarding efficacy endpoint, it was concluded that the endpoint was "the change in the percentage of "YES" (out of all "YES" and "NO" combined) between "Start" and "Finish" "

Now then, since we have drug and placebo, I assume that I have to somehow compare the changes to prove efficacy.

Gonna quote myself - in my original post:

"
Say group #1 has 50 people, our "start" variable has 28 "yes" and 22 "no", "finish" variable has 35 "yes" and 15 "no", so the percentage change is from 56% (28 out of 50) to 70% (35 "yes" out of 50)

In group #2 situation is different. Say, "start" has 20 "yes" out of 40, that is 50%, and "finish" has 25 "yes" out of 40 which is 62,5%, so the change is from 50% to 62,5%.
"

So I'd try to compare the increase from 56% to 70% to the increase from 50% to 62,5%. And as I mentioned already, making a 2x2 table off these feels wrong, that's why I made the thread.

From what I understood, the endpoint doesn't specify comparison between 2 groups as in the dynamics in changes or anything. I could maybe compare "Finish" results and "Start" results separately with a 2x2 Chi-square and in this case I'd be able to prove efficacy if my "Start" results were equal ( p > 0,05) but the finish results were different (p < 0,05). This way I'd be able to say that the changes were, respectively, different and the difference would be (I guess?) statistically significant.
Would this work?

PS: real life experts are hard to find in my case, unfortunatelly. Regarding the "design plan for analysis" - I only really asked about the possible approach towards the data I have. I honestly do not know the method, that would be able to compare something like changes of percentages in different groups, thats why I asked. I also don't think that any info regarding my study was actually necessary to answer my question. Its either the method exists or I have to do roundabouts and try to get to the conclusion this way.

Thanks for the input nonetheless, it is very much appreciated.

10. ## Re: Frequency analysis

An update:

I've come to a conclusion that best way to compare these 2 groups would be to use 95% confidence intervals of the differences in proportions. With help of this tool it was easy to calculate and come to conclusions. As in, if intervals do not intersect, then the changes in groups are different and the difference is statistically significant.

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