Tc2

P[D,]

qi

q2

i

4 shows the error relationship for the decision that signal 1 was detected (Di) or signal 2 was detected (D2). In customary frequentist statistical practice, a is chosen to be fixed at 0.05, and a fixed sample size (n) is estimated to attain a power = 1 - p for some specified value in the interval (0.75,0.95).The reality in biomedical science is that the power is fudged to get a sample size that the scientist can afford. It should really be set at some conventional value like a, so that experiments are comparable and have the same probability of missing the signal. Everything in hypothesis testing is focused on controlling a and letting p float. Unless a biomarker whose characteristics are fully understood is being used to prove efficacy in a phase III trial, this is probably not the best way to evaluate the biomarker. Table 4 looks very similar to Table 1 but includes only the q/s.

Table 5 is the proper setup for evaluating the information. This is a Bayesian-like framework because is requires the prior probability for each hypothesis. If it is assumed that n1 = n2 = 0.5, then Tables 4 and 5 are equivalent, a state of ignorance in many cases. However, most biologists are not ignorant about the underlying system; a bad guess for these probabilities would probably be better for evaluating biomarkers than assuming equality because it can be very misleading to assume that the maximum information is transmitted if, in fact, it is not (see Tables 2 and 3). Much money can be wasted when numbers are misused.

Diagnostic tests (biomarkers) are usually evaluated in terms of true positives (TPs), true negatives (TNs), false positives (FPs), and false negatives (FNs). Table 6 is a typical setup for this evaluation. Again these are just the qt/s obtained by counting in most cases. The concepts of biomarker sensitivity and specificity are as follows [5]:

TABLE 6 Outcomes for a Binary-Decision Diagnostic Test

Signal

Decision

Total

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