Good statistical practice in pharmacology. Problem 1

Abstract

Background and purpose: This paper is intended to assist pharmacologists in making the most of statistical analysis and in avoiding common errors that can lead to false conclusions.

Approach: A scenario is presented where a pathway inhibitor increased blood pressure responses to an agonist by about one third. The fictional experimenter concludes that the inhibitor enhanced the responses to the agonist, but has not applied any statistical analysis. Questions are asked of the reader, and a discussion of the author's answers is presented.

Results: The agonist responses have unequal standard errors, as often seen in data like these concentration-response curves with responses expressed as change from baseline. The uneven variability (heteroscedasticity) violates an assumption of conventional parametric statistical analyses, but can be corrected by data transformation. Expressing the data as absolute blood pressure and then transforming it to log blood pressure eliminated the heteroscedasticity, but made evident an effect of the inhibitor on baseline blood pressure.

Conclusions and implications: Statistical analysis is a sensible precaution against mistakes, but cannot protect against all erroneous conclusions. In this scenario, the inhibitor reduced the blood pressure and increased responses to the agonist. However, it is likely that the latter effect was a consequence of the former and thus no conclusion can be safely drawn about any direct interaction between the agonist and the pathway inhibitor from this experiment. Where results are awkward to interpret because of confounding factors such as an altered baseline, statistical analysis may not be very useful in supporting a safe conclusion.

Figure 1

Blood pressure responses to an α-adrenoceptor agonist in untreated rats (control) or in rats pretreated with an intracellular pathway inhibitor (test). Each rat was randomly assigned to either treatment or control (n=8 per group) and the agonist doses were applied in ascending sequence.

Figure 2

Variability of standard error of the mean (s.e.m.) with responses expressed as percentage of the baseline (left panel), blood pressure (centre panel) and log blood pressure (right panel). The logarithmic transformation removes the tight correlation between the size of the response and the variability in the response measurement.

Figure 3

Data from Figure 1 re-expressed as raw blood pressure (left) and as log blood pressure (right). Note that these illustrations of the data allow the baseline blood pressure to be displayed. Compare the patterns of effect with that in Figure 1.