Sunday, July 06, 2008

Comparing treatment difference in slopes

In regulatory setting, can we showing the treatment difference by comparing the slopes between two treatment groups?
In a COPD study (e.g., a two arm, parallel group with primary efficacy variable measured at baseline and every 6 months thereafter), one can fit the random coefficient model and compare the treatment difference between two slopes. Also we can compare the treatment difference in terms of change from baseline to the endpoint (the last measure).
To test the difference in slopes, we would need to test whether or not the treatment*time interaction term is statistically significant. The assumption is that at the beginning of the trial, the intercept for both groups are the same - both groups started at the time level. Then if the treatment can slow the disease progression, the treatment group should show a smaller slope comparing with the placebo group.
If all patients are followed up to the end of the study, if the slopes are different, the endpoint (change from baseline) analysis should also be statistically different. However, with a smaller sample size, the results could be inconsistent by using slope comparison approach vs. endpoint analysis approach. For a given study, the decision has to be made which approach is considered as the primary endpoint. Why don't we analyze the data using both approaches? then we have to deal with the adjustment for multiplicity issue.
I used to make a comment and say "some regulatory authorities such as FDA recommend the simpler endpoint analysis"; then I was asked to provide the references to suport my statement. I did quite extensive search, but I could not find any real relevant reference. However, by reviewing 'statistical reviews' in the BLA and NDA in US, it is very rare to see any product approval based on the comparison of the slopes. Many product approvals are based on the comparison of 'change from baseline'.
So this is really a regulatory question. Every indication has their accepted endpoints so tradition takes precedence. According to my colleague, there is a movement in the Alzheimer's arena to look at differences in slopes, but this is basedon trying to claim disease modification. If this is the case, we may also apply this to the COPD area since for certain type of COPD, we can claim the disease modification by showing the differences in slopes.been used in COPD before?
On the other hand, It seems that that the slope model (random coefficient model) may be preferred in academic setting, but endpoint approach - change from baseline (with last value carried forward) may be more practical in the industry setting.
From statistical point of view, the slope approach makes a lot of sense, however, we need to be cautioned about some potential issues: 1. In some endpoint measure, there may be some type of plateau. If you reach that plateau prior to the end of the study there will be a loss of power comparing slopes as compared to some comparison of just the endpoint results or some type of general repeated measures assessment of the average treatment difference.2. If the slope comparison is used as the primary efficacy measure, the # of measurements per year on the primary efficacy variable is relevant. One may think that the more frequent measures will increase the power to show the treatmetn difference in slopes. The question arise when designing the study: are you choose a shorter trial with more frequent measures? or are you choose a longer trial with less frequent measures?

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