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This equation extends the previous equation, but allows for a variable slope. This equation is also called a four-parameter logistic equation.

Bottom is the Y value at the bottom plateau.

Top is the Y value at the top plateau.

LogEC50 is the X value when the response is halfway between Bottom and Top. With different kinds of variables, this variable is sometimes called ED50 (effective dose, 50%), or IC50 (inhibitory concentration, 50%, used when the curve goes downhill).

HillSlope describes the steepness of the curve. This variable is called the Hill slope, the slope factor, or the Hill coefficient. If it is positive, the curve increases as X increases. If it is negative, the curve decreases as X increases. A standard sigmoid dose-response curve (previous equation) has a Hill Slope of 1.0. When HillSlope is less than 1.0, the curve is more shallow. When HillSlope is greater than 1.0, the curve is steeper. The Hill slope has no units.


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