Potency index (or Efficacy) : calculation and examples

• Potency index is the (control)/(treated) ratio. It was estimated for each agent in each study, by calculating the ratio of mean value (e.g., tumor number) in control rats divided by mean value in treated rats. Thus, potency tells the times-fold reduction in ACF or tumor endpoint, due to the agent. According to my friend Pierre-Louis Toutain, a great pharmacologist, "my" potency should be called "Efficacy" (see his figure on Potency & Efficacy). ! caution ! See "Inaccurate potency" at the bottom of this page.
• ACF example: In the 2000 Wargovich's study, a mean number of 193 aberrant crypt foci (ACF) was observed per control rat, and of 28 ACF was observed per rat given sulindac sulfide: the potency of sulindac sulfide to reduce the ACF number was calculated as 193/28 = 6.89
• Tumor example: In the 2000 Corpet's study, the incidence of tumors (confirmed by histology) was 22/27 in the control group, and 2/21 in the group of rats given polyethylene glycol (PEG): the potency of PEG to reduce the tumor incidence was calculated as (22/27)/(2/21) = 8.55
• Min mouse example: In the 1997 Pierre's study, a mean number of 52.4 polyps was observed in the gut of control mice (small + large bowel, 50.3 + 2.1 polyps). The number was 47.4 (46.7 + 0.7) in mice given a diet with 5.8% fructo-oligosaccharide. The potency of fructo-oligosaccharide to reduce the polyp number was calculated as 52.4/47.4 = 1.11 (in this case, potency in the colon would have been better, see colon data). When colon (or small intestinal) data are not known, potency is calculated with available data. Promoting agents show potencies smaller than 1.
• Relative risk When incidence is concerned, potency is the inverse of the relative risk (e.g., a potency of 8.55 corresponds to a relative risk of 1/8.55= 0.12)
• Percent reduction: To help the reader, some endpoints were also reported as percent inhibition afforded by the agent. Percent inhibition is equal to (100 - 100/potency). For instance, a potency of 8.55 is equivalent to (100- 100/8.55) = 88.3% inhibition.
• Division by zero: When no tumor was seen in the control group, potency calculation was arbitrarily based on 0.5 tumors in the control group. A similar triks is used in Chi-square test when a cell contains zero.
• Inaccurate potency: Potency cannot be accurately estimated when the number of tumor-bearing rats is too small in the control group. For instance, if only one tumor bearing rat is found in the control group, and 0 in the treated group, it would not be accurate to assume that the treatment suppresses 100% tumors! To acknowledge this imprecision, studies with less than eight tumor-bearing control rats (or less than 8 ACF per control rats) are thus tagged with a !.
  This ! tag is placed after the name of the agent in the first column, and near the incidence raw data in the tumor table.