What statistical test to use to compare effectiveness of drugs used to fight a diseaseSo let's say that I want to collect some data on a sample of people who has the same type of disease.One group will take a drug AAnother one will take drug BThird type will take both of them.I want to perform a statistical test to see whether taking both of the drugs simultaneously results in getting back to health quicker.Can anyone tell me what test would I use and what hypothesis would I state? Assumptions that I would make?I need to plan a research project (Without actually doing it)

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What statistical test to use to compare effectiveness of drugs used to fight a diseaseSo let&#039;s say that I want to collect some data on a sample of people who has the same type of disease.One group will take a drug AAnother one will take drug BThird type will take both of them.I want to perform a statistical test to see whether taking both of the drugs simultaneously results in getting back to health quicker.Can anyone tell me what test would I use and what hypothesis would I state? Assumptions that I would make?I need to plan a research project (Without actually doing it)

zupa1z · Accepted Answer

First, you need some value to measure for each patient that expresses his/her progress toward recovery. Lower level of a liver enzyme, low count of bacterium or virus in blood, days for temperature return to normal, etc. Call such a measured value Y.Model. The standard design that best matches the description of your study is a one-factor analysis of variance (ANOVA) with three levels of the factor, A, B, AB. One hopes it would be ethical from a medical point of view to assign, say N=60 patients at random, so that there are n=20 subjects in each of g=3 groups (with N=ng).The model for such an ANOVA design is      Y          i      j        =  μ  +      α    i    +      e          i      j        ,where   i  =  1  ,  2  ,  3  ;    j  −  1  ,  …  ,  10 and       e          i      j                          ∼                    i        i        d                  N    o    r    m    (  0  ,  σ  )  .Assumptions. Assumptions of the model are that the subjects are randomly selected, data are normal, and the population SD σ is the same in each group.Hypotheses. The null hypothesis is       H    0    :      α    1    =      α    2    =      α    3   and the alternative is       H    a    :      α    i   not all equal.You can look up the ANOVA table, formulas, and F-test in a statistic text or online. There are also help pages online for doing ANOVA computations in various kinds of statistical software.Power. In planning such an experiment, you might try to do a preliminary power computation. That requires guessing the numerical value of σ, perhaps based on prior experience with recovery from this disease using drugs A and B. Also, you would need to have an idea how much difference in Y-values would be of interest. Then you could find out whether n=20 subjects per group gives a realistic chance of detecting a difference of the desired size if it is really present.Contrast. Also you might want to look at a &#039;contrast&#039; of the form                     α        A            +              α        B              2    −      α          A      B        . That focuses on the specific goal to see whether the combination of A and B together gives better results than one drug by itself. [A &#039;contrast&#039; is a linear combination of &#039;effects&#039; αi of the form       c    1        α    1    +      c    2        α    2    +      c    3        α    3    , such that       ∑    i        c    i    =  0. In my example,       c    1    =      c    2    =  .5 and       c    3    =  −  1.A text on basic experimental design will include information about power computations and testing (pre-planned) contrasts. You can also find such information online, but stick to pages from authoritative sources--NIST, class notes at reputable universities, and Wikipedia pages that seem to be in final form. (Any idiot can pose as an expert on experimental design, and several do.)

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