Why does Prism report the standard error for logEC50, but not for the EC50 itself, when it fits dose-response curves?

Last modified January 1, 2009

See this long answer, or read on for a shorter answer.

If, as is typical, your doses are equally spaced on a LOG scale, then the uncertainty of the IC50 (or EC50) is symmetrical on a LOG scale. In this case, the SE of logEC50 is a measure of uncertainty. That single value expresses uncertainty in both directions. Consider this example: the logEC50 is -6 with a SE of 1. If you go up one SE, then you are at -5 (10 uM). If you go down one SE, you are at -7 (0.1 uM). Therefore, on a concentration scale, one SE down is a distance of 0.9 uM; one SE up is a distance of 9 uM.

If you compute the antilog of 1, which is 10, you certainly cannot say that the SE of the EC50 is 10 Molar! Rather than being a plus/minus error value, this value (the antilog of the SE of the logEC50) is It is a times/divided by error value. To get an equivalent to the logEC50 plus or minus one  of the logEC50, find the lower limit by dividing the EC50 by 10 (for this example where the SE of the logEC50 is 1) and the upper limit by multiplying by 10.

If you want to see the results on a concentration scale, you need to look at a range of numbers, not a single number. The SE of logEC50 can be used to compute a confidence interval, and the two confidence limits can then be transformed to antilogs. The confidence interval for concentration is then asymmetrical on a concentration scale. This makes sense, as the uncertainty really isn't the same in each direction.

Prism 7 can report asymmetrical confidence intervals for parameters fit by nonlinear regression. You can ask it to compute this kind of CI for the IC50 or EC50 and the result will be sensible (and very asymmetrical).

The bottom line: If the doses are equally spaced on a log scale, the SE only makes sense on a log scale. Trying to express the uncertainty as a single number on a concentration scale doesn't make sense, as your experimental design generated errors that are not symmetrical on that scale.

Is your goal really to find the ratio of two EC50 values? If so, Prism can fit that ratio directly.

If you really want to fit the EC50 and its SE, even knowing it probably is not a great way to express the uncertainty,  this page explains how to do so

Keywords: ED50 IC50 logED50 logIC50 SE EC50 SE IC50

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