It’s OK if the answer will be Dunnett’s test.
Multiple comparisons lead to alpha inflation (increase in type I error rate) so correction is required. Many-to-one comparisons are comparisons of many treated samples with a single control group.
1. Standard case. For example, groups of patients treated with drugs A, D, C, D, E plus control (untreated) group. This is the case where groups are independent, and results in the group A do not affects results in the group B, and no other links can be found. Dunnett’s test can be useful.
2. Another case is survival curves. The x-axis represents days (or other units of time) and the y-axis represents survival rates. Similarly, we can put curves for groups A,B,C, … , control. However, it is an absurd to perform multiple testing because of an enormous amount of pairs (for example, group A and group C in the 4th day). Notably, the compared samples are not independent because the number of survived patients (or rats, etc.) within a given group can not be greater in a later day than in an earlier day. It can be either equal to it or less than it. Kaplan-Meier estimator is used to compare the groups here.
3. My question is about another case. Serial dilutions (for example, 2-fold dilutions) of an inhibitor of a biological process lead to arrays of monotonically decreasing concentrations of this compound. The higher concentration, the more pronounced effect, and the exact function describing this dependence does not matter. Theoretically, the number of diluted samples is not limited. Samples are not independent, too. The higher concentration of an inhibitor must lead to a more pronounced effect (compare to survival curves). I want to compare the measured effect for each treated sample, i.e. corresponding to each specific concentration, with the untreated group.
1) Is there alpha inflation and the multiple comparisons problem? Remembering that the number of dilutions can be infinite, false discoveries are guaranteed? Intuitively no.
2) What should I do to compare all groups (treated with many concentrations of the compound) with a single control group?
Of course, I can compare compound A and compound B by calculating IC50 or AUC values. But I want to calculate p-values for all samples to find out if they are significant and to estimate minimal active concentration of a specific compound.
Rothman // Epidemiology, 1(1), 1990 suggests that corrections are not required. Personally I:
1) agree with the concept of multiple comparison problem (false discovery rate),
2) do not consider type II error as less problematic than type I error,
3) tend not to agree that “planned comparisons” are the reason not to perform correction. See a somewhat expressive but deep article Frane // Journal of Research Practice 11(1), 2015.
All answers and opinions will be appreciated.
#multiplecomparisons #Dunnett #statistics
A way to compare many samples treated with decreasing concentrations of a compound with a single control group is to use a standard curve. A standard curve is a graph that plots the concentration of a known substance against the response of an analytical instrument. You can use this curve to determine the concentration of an unknown sample by measuring its response and comparing it to the standard curve.
To compare many samples treated with decreasing concentrations of a compound with a single control group, you can use an ANOVA or two t-tests. The ANOVA is used to avoid type-1 errors when there are three groups or more. However, if you are only interested in differences between the treatment groups and the control group, then two t-tests might be the best way to go.
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