Hello everybody and thank you in advance.
I would like to ask you about a power analysis problem starting from an example.
I have two medical devices (A and B) that finds lymphnodes.
My experiment consists in using the two medical devices on the same subjects.
The goal of the experiment is to demonstrate that device A finds 20% more lymphnodes than device B.
From a previous study I know that device A on about 60 subjects (of the same population, obviously) identifies 85 lymph nodes.
I wonder if it is possible to consider lymphnodes count as a Poisson (or negative binomial) variable, and to consider the single subject as a unit of time. In this way I would find myself constructing the sample size considering a Poisson regression coefficient of 1.2 as the effect size.
What do you think? Could it be a correct strategy?
Thanks again.
Hello Gianfranco,
The challenge is to identify an analytic approach which recognizes that the two screeners are used on cases which are not independent. One simple framework for this would be McNemar's test (which compares frequencies of cases which disagree between the two methods, e.g., A+/B- vs. A-/B+). This is a simple chi-square goodness-of-fit test, comparing the two cells for equality. Power analysis is pretty simple here (2 cells, 1 df, magnitude of effect = phi = sqrt(chi-square/N)).
There are other approaches, of course, but this one works with count/frequency data taken from two observations of the same set of cases.
A completely different approach would be to declare, a priori, some "noteworthy" (e.g., non-ignorable) difference in sensitivity, specificity (or both) that would cause decision-makers to declare one screener to be superior to another, then compare the resultant values for the two methods you wish to evaluate.
Good luck with your work.
The cutoff points of LNs are determined using X-tile and are randomly categorized into training and validation sets by the sample size ratio 1:1. The clinicopathologic characteristics should be analyzed and survival prognostic factors identified, whereas the survival prediction accuracy must also be compared by C-index during the different independent prognostic factors. Age, T stage, LNs are independent prognostic factors in lymph node-negative patients. If theses are closely associated with clinicopathologic features, then it may improve the prognostic prediction accuracy in node-negative patients.
I'd model the distribution with a negative binomial model (Poisson is usually too restrictive, and usually the V(X) > E(X) in biological data; the explanation here is the Poisson assumed equal rates in all subjects, what is clearly not a very sensible assumption. The neg.binom allows these rates to vary between subjects).
Here is an R function to calculate the sample size:
http://finzi.psych.upenn.edu/R/library/MKmisc/html/power.nb.test.html
David Morse thank you very much for your answer.
The problem here, is that I don't have trials with an outcome negative/positive (absence or presence of Lymphnodes). I only count them when the device sees them. I don't have a 2x2 table where I can perform a McNemar test.
And it's also impossible to calculate a sensitivity.
Anyway...thanks! It was very kind of you!
Obviously thanks to Pradeep Paraman . Unfortunately I don't have all the informations you cite. i only know the things I wrote in my question!
Dear Jochen Wilhelm . Thanks for your answer. Even though I don't have a real exposure time, do you think I can use Poisson (or Neg-Binomial)? That is I only look at the same patients and count lymphonodes with two different devices. There is no negative or positive: only count.
As if i were observing a certain number (the sample size i am looking for) of strawberry fields and counting how many overall blackbirds I see whatching with two different binoculars (I want to demonstrate that a binocular sees 20% more than the other). What's the exposure time???
Anyway...really really thanks.
For descriptive studies, the sample size can be reversely calculated via one sample tests formula (e.g. one sample t test for mean or for proportion). The different point of this general formula is the method of SE calculation (here is Poisson, ...).
However, I had previously a problem with Poisson!
https://www.researchgate.net/post/Why_Poisson_95_CI_does_not_match_with_area_under_the_function
And also I have a question. Why is Poisson SE the -sqrt- of lambda/n? Because lambda is variance (not SD).
Can negative binomial be used for more than 2 groups of outcome?
The above discussion puts me to ask some additional questions about the setteing of the problem. To the best of my understanding of the till-now stated description, I see the model as follows, when formulated in terms of balls in a box, observerved by two observers:
MODEL 1.
There is an unknown number - say n balls in the box.
Observer no.1 during one session recognizes each of the ball with probability p1 \in (0,1) as a Bernoulli
Observer no.2 during one session recognizes each of the special kind with probability p2 \in (0,1).
If the observations were treated as independent Bernoulli trials, then the results, say N1 and N2, are independent of the binomial distributions B(n,p1) and B(n,p2), respectively, if the number n is GIVEN.
MODEL 2.
In case of unknown n, it makes sense to consider it as a random variable with some reasonable distribution. This way however is usually unacceptable due to lack of well established info about such numbers (e.g. like for red cells in the blood). Therefore I would propose
MODEL 3.
The results N1 and N2 are independent Poisson variables with parameters Lambda1 and Lambda2, respectively. Since the subject of estimation is the ratio Lambda1/Lambda2, the MLE equals then N1/N2.
Looks simple, but it is not, since it is impossible to infere from this any fully justified test for the hypothesis that the ratio of Lambdas i say greater than 1.2, unless we apply some tricks. E.g. by replacing the value of Lambda2 by N2. Obviously this makes the test biased and of less power.
That's all I would like to suggest as a basis for further discussion.
Thanks in advance, Joachim
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