Dear, Leah, if you are interested if the average of a single biomarker in effect of treatment remained the same, then, yes, 40 paired t-tests is plausible. If you also want to make sure that this average increased (or decreased), you can carefully consider 'one-tailed' variant of the t-test. You are right, that t-test is best suited for normally distributed values of biomarker, but if you decide to do any transformation on any of the biomarkers, please transform both, 'baseline' AND '8-weeks-later', results.

Regarding the suggestion of two sample K-S test, I strongly advice against it, because it has poor statistical efficiency and, moreover, is not suited for the 'paired' assumption. Yes, it's non-parametric, but the correct alternative in 'paired' case would be 'Wilcoxon signed-rank test'.

Regarding logistic regression, unless you have at least 200 patients in your sample (5x40) and amounts of positive and negative outcomes are similar, then pooling all biomarkers makes sense. Regression on 'baseline' to find which biomarkers are best predictors is interesting, but I'd naively start by doing regression on '8-weeks-later' data, just to see which of them are best indicators of the success. :D I just hope you will not get tempted to pool 'baseline' with '8-weeks-later' data, just to boost sample size. Anyway, you are very welcome to construct the best regression, by using only a subset of your biomarkers, just make sure that this regression has best (minimal) AIC / BIC score.

Finally, what about control group? If you did not consider one already, you could do this at the same time next year, just in case some biomarkers are influenced by the time of the year. =). If it's not true, then appropriate (ages and gender not too different from your patients) sample of target population could do the trick. In case of a control group, your problem boils down to a quasi-experimental technique in econometrics known as 'Difference in differences' (DID). The basic premise of DID is to examine the effect of some sort of treatment by comparing the treatment group after treatment both to the treatment group before treatment AND to some other control group. Naively, you might consider simply looking at the treatment group before and after treatment to try to deduce the effect of the treatment. However, a lot of other things were surely going on at exactly the same time as the treatment. DID uses a control group to subtract out other changes at the same time, assuming that these other changes were identical between the treatment and control groups.

Dear Leah, doing tests is confirmatory, not exploratory. You should clarify if you want to see *how* useful the biomarkers are (also: which are more and which are less useful) or you can test *if* the observed associations between biomarker(s) and response is sufficiently unlikely when in fact biomarker(s) and response are not associated.

You are right here: you should analyze the correlation of the biomarkers first. If some of them are strongly correlated then you have at least two options: select one of them (based on biological reasoning) or combine them into a single "surrogate marker" (e.g. using the mean of the values or of the standardized values). You can also use principal component analysis (PCA) to find good independent marker combinations (take the first 1 to 3 principal components as surrogate markers).

A generalized linear model with binomial error model (what essentially *is* a logistic regression) to express the response (treatment success yes/no) depending on the predictors you have (the biomarker or surrogate marker values). The model calculated log odds ratios that quantify the influence of the predictors on the response. I think this is what you want. If you are comparing a "treatment group" against a "control group", you have to include the interaction of "treatment" and "time" in the model. This is what Evaldas called a "difference in difference analysis". The size of the interaction quantifies the difference in odds ratios (1) between treated and controls (what actually is the interesting thing).

Edit: (1) I meant the difference in *log* odds ratios; this equals the ratio of odds ratios.

Dear Leah

Please tell me more about:

how do you name a treatment success?

What are the nature of your 40 biomarkers (I mean the types of variables)?

I assume that you have a number of cases for your study. You treat them with something. Before and after treatment you measure 40 variables. How do you say that this treatment was successful on a case? or how do you say that it was not successful?

Mohsen

Hi Leah

A quick thought. If you're conducting 40 paired t-tests (or other bivariate analyses) against the same set of dependent variables, I'm sure you'reusing the FDR or other Bonferroni-based techniques to adjust the target p-values for multiple comparisons.

Best wishes,

Howard

Hi Leah,

One thing you can try is the n-way ANOVA (N-way analysis of variance). You can try different models, such as a 'linear' model which computes only the p-values for the null hypotheses on the 40 biomarkers' main effects; a 'interactive' model which computes the p-values for null hypotheses on the 40 biomarkers' main effects and the (40 choose 2) two-factor interactions, or a 'full' model which computes the p-values for null hypotheses on the 40 biomarkers' main effects and interactions at all levels. N-way ANOVA has been well implemented in MATLAB: http://www.mathworks.com/help/toolbox/stats/anovan.html#brx09p_-50

Hope this helps.

Wen

Hi Leah,

so! baseline -8weeks treatment -post treatment. First of all you should know or better you should expect the trend on biomarkers you are using (why you chose all of them?). Biomarkers are "commonly" related eachother (eg: CK-LDH or PPAR alpha, gamma, ecc.... what ever it is). I'm expecting to see all of them grouped (4-8) on positive and negative trend! but this is import for your research purpose? if yes you just need to highligth this phenomena!! if you need an overview of your study results, is enough an excel file and perform paired t test (one tail), that's It. Sorry for my english! I'm not native in uk! This is my first impression

Hi Leah, Paired t test with two tail probability adjusting by Bonferroni correction factor is applicable, if data are large enough. otherwise, Wilcoxon sign rank tests with two tail probability.

Rajvir, it's a misconception that Wilcoxon (rank) tests are just substitutes for t-tests. They test different things, and what they test depends on the shapes of the distributions. For instance, a location shift (difference in medians) is tested only if the distributions are equal in all(!) characteristics except the location. I also think that the question if one likes to "test" the mean or the median should be aswered following scientific reasoning and not following the availability of tools.

In case of pure exploratory data analysis, you can use data clustering techniques to find biomarkers that are correlated. One handy technique is principle component analysis. Once you get som clusters of correlated biomarkers, you can start building hypotheses from a scientific point of view (reviewing your pathways etc...). Next, confirm your hypotheses by statistical modeling and probability testings (finding significancies, cfr. what other have said).

Last point: significany only points out the effect can be distinguished form "background noise, analytical error...". It doesn't point out to what extend the effect impacts your treatment. Make sure to evaluate significant effects in perspective of the level of impact on the treatment.