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I am working to design a phase I study with the goal being to determine whether a drug reduces the recurrence rate of a given disease.  The subjects will be those known to be recurring approximately 1-2 times per month before being treated.  I am not sure how to test for a change in recurrence rate in such a situation.  I had considered using the after treatment recurrence time minus the mean historical recurrence time as the basis for a one-sample t-test.  Unfortunately, Monte Carlo simulations show that this approach is conservative.  Does anyone have suggestions for testing in this situation?  Or perhaps, suggestions for alternative ways to think about designing the study?


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Robert Podolsky
Georgia Health Sciences University
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What you describe is a Phase 2 one group study. How many patients are you looking at? Why do you call it Phase 1?

In general, with 25-30 patients and diff = post-pre (however defined) you should do OK  with a  ~ 1SD or bigger alternative.  

To "prove" anything (the word makes me shiver) you will need a phase 3 trial with a control group.


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Borko Jovanovic
Associate Professor
Northwestern Univ-Feinberg School of Medicine
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Phase 1 vs 2... should have caught as I was typing.

The problem with post-pre is that the current design is to use each patient's health record for that patient's historical recurrence times and follow each patient with only 1 treatment with the drug.  We will then have, in effect, one post-drug recurrence time.  I can average the recurrence times from the pre-drug treatment, and then calculate post-pre.  The problem is that the difference post-pre, while normally distributed for each patient, will have a different variance for each patient, assuming that each patient's differ in their recurrence times pre-treatment.  In other words, the pre is calculated as a mean with the number of observations used to calculate the mean differing between subjects.  Thus the variance in pre will be subject-specific.  When I do Monte Carlo simulations of what I have proposed with a t-test, the test ends up being a little conservative.  For alpha=0.05, the observed type 1 error rate was 0.545.   Hopefully, this clarifies my problem.

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Robert Podolsky
Georgia Health Sciences University
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Original Message:
Sent: 11-06-2012 13:14
From: Borko Jovanovic
Subject: Change in recurrence rate?

What you describe is a Phase 2 one group study. How many patients are you looking at? Why do you call it Phase 1?

In general, with 25-30 patients and diff = post-pre (however defined) you should do OK  with a  ~ 1SD or bigger alternative.  

To "prove" anything (the word makes me shiver) you will need a phase 3 trial with a control group.


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Borko Jovanovic
Associate Professor
Northwestern Univ-Feinberg School of Medicine
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Hi Robert,

Is your design looking at the time to the first recurrence only? You could use all the recurrences. By using time to recurrence and re-starting the patient after each recurrence and waiting for the next one, etc., you will make use of all of your data. Each patient may have multiple intervals. An interval that doesn't end in a recurrence (e.g., your observation period ends and cuts off some people before a recurrence) would be censored. You need to use a survival analysis method that takes account of correlated time-to-event intervals. 

Alternatively, you could use a Poisson model, and the outcome is the count of recurrences during a defined period--one period before treatment, and one period after treatment (they do not have to be the same duration.) Your effect measure would be relative risk (the ratio of recurrence rates:(rate after)/(rate before). 

If you get good data on number of recurrences but can't get the dates of recurrences accurately, i would go with the Poisson method.

This is hand-wavey and you will need to formalize it, but this is my initial thought on what I would do.

Best wishes,

Nayak



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Nayak Polissar
Principal Statistician
The Mountain-Whisper-Light Statistics
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Thank you for the feedback!

The current design is to use each patient's health record for that patient's historical recurrence times and follow each patient with only 1 treatment with the drug.  We will then have, in effect, one post-drug recurrence time. 

I do like the idea of using survival analyses.  I'm not sure how to handle the challenge of each subject's multiple times to event being correlated, with a a single time-to-event following the treatment.  Do you have a more specific suggestion or a paper to read?

The problem with the Poisson model is that the recurrence rates are relatively high to begin (once to twice per month), so we expect to quickly observe the recurrence time following drug treatment.  As such, I don't expect to have recurrence rates and only recurrence times. 

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Robert Podolsky
Georgia Health Sciences University
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Original Message:
Sent: 11-06-2012 13:51
From: Nayak Polissar
Subject: Change in recurrence rate?

Hi Robert,

Is your design looking at the time to the first recurrence only? You could use all the recurrences. By using time to recurrence and re-starting the patient after each recurrence and waiting for the next one, etc., you will make use of all of your data. Each patient may have multiple intervals. An interval that doesn't end in a recurrence (e.g., your observation period ends and cuts off some people before a recurrence) would be censored. You need to use a survival analysis method that takes account of correlated time-to-event intervals. 

Alternatively, you could use a Poisson model, and the outcome is the count of recurrences during a defined period--one period before treatment, and one period after treatment (they do not have to be the same duration.) Your effect measure would be relative risk (the ratio of recurrence rates:(rate after)/(rate before). 

If you get good data on number of recurrences but can't get the dates of recurrences accurately, i would go with the Poisson method.

This is hand-wavey and you will need to formalize it, but this is my initial thought on what I would do.

Best wishes,

Nayak



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Nayak Polissar
Principal Statistician
The Mountain-Whisper-Light Statistics
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Robert,
Andersen and Gill (1982) wrote a good paper on this, although I suppose much more has been written since.  I just found the paper at http://hydra.usc.edu/pm599/2006%20notes%20etc/andersen%20and%20gill82.pdf.  This is also called a frailty process or frailty modeling.  You might find more under that. 

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Brian Johnson
Biostatistician
Essentia Institute of Rural Health
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Original Message:
Sent: 11-06-2012 17:34
From: Robert Podolsky
Subject: Change in recurrence rate?

Thank you for the feedback!

The current design is to use each patient's health record for that patient's historical recurrence times and follow each patient with only 1 treatment with the drug.  We will then have, in effect, one post-drug recurrence time. 

I do like the idea of using survival analyses.  I'm not sure how to handle the challenge of each subject's multiple times to event being correlated, with a a single time-to-event following the treatment.  Do you have a more specific suggestion or a paper to read?

The problem with the Poisson model is that the recurrence rates are relatively high to begin (once to twice per month), so we expect to quickly observe the recurrence time following drug treatment.  As such, I don't expect to have recurrence rates and only recurrence times. 

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Robert Podolsky
Georgia Health Sciences University
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Consider a run-in period, 1-2 months long, to assess the pre-treatment recurrence rate for each patient. Then the change from Baseline can be computed for each patient. It isn't clear if this was done. Then consider episodes per month.
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David Bristol
Statistical Consulting Services
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For recurrence rate analysis, one of the most powerful tests to distinguish between I.I.D. interarrival times (renewal process) and a monotonic trend (increasing or decreasing) is the nonparametric reverse arrangement test (RAT) originally devised by Kendall in 1938 and further developed by Mann (1945). I describe the test on pages 482 to 486 in my book Applied Reliability, 3rd.ed., by Tobias and Trindade, CRC Press (2012). If you have several subjects, you can combine the results from the separate tests using a procedure from Fisher (1954), also described in my book from pages 486 to 488. Although the method is applied to the analysis of data from repairable systems, the recurrence of tumors is another area of application.

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David Trindade
Fellow
Bloom Energy
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Original Message:
Sent: 11-06-2012 11:56
From: Robert Podolsky
Subject: Change in recurrence rate?

I am working to design a phase I study with the goal being to determine whether a drug reduces the recurrence rate of a given disease.  The subjects will be those known to be recurring approximately 1-2 times per month before being treated.  I am not sure how to test for a change in recurrence rate in such a situation.  I had considered using the after treatment recurrence time minus the mean historical recurrence time as the basis for a one-sample t-test.  Unfortunately, Monte Carlo simulations show that this approach is conservative.  Does anyone have suggestions for testing in this situation?  Or perhaps, suggestions for alternative ways to think about designing the study?


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Robert Podolsky
Georgia Health Sciences University
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