Hi...I am not aware of any, but have not really looked. It is also worth mentioning that if you use a) dose or b) a measure of average drug exposure (e.g. average concentration at steady state (Css)) or c) use actual/predicted concentrations over time to drive the pharmacodynamic response, then Hill cannot be simultaneously equal to 1 under all three. Hence if you set it to 1 using dose, then you are implicitly setting it to something different to 1 based on concentrations. In short, do not fix it!! Estimate it, just like we would an ED50 (or EC50). cheers Al
Great video. I was wondering when you discussed the problems of the richards model you discussed the difficulty of getting enough data even with the emax. I was wondering, is there a rule of thumb for the number of observations for the Emax? Also, is there some seminal paper about Emax or dose response in experimental context? I am in economics so I might not be up there in that particular area... I already have some paper on dose ranging with Emax... Anyways very useful! Thanks!
Delighted you thought the video was OK. Alas there is no rule of thumb for the number of observations, as it is always a combination of the size of the residual error variance (our noise), the design (i.e. what doses you picked), and the precision you want (wide or narrow uncertainty in the final estimated dose response). You can pick the doses in an optimal way (see L4 lecture), based on what you want to optimise. Maths wise, we 'know' the asymptotic behaviour of the variance-covariance matrix is the inverse of the expected Fisher Information Matrix. If you want the formulae, just email me at the address in the video. If maths is not your strong point, just simulate your design and estimate it (say 20-1000 times). You can then play with different designs (doses and observations per dose) to see how they do relative to your metric(s) of interest. As a rule of thumb, D optimal designs for this model are 4 point designs, at doses that yield 0%, 26%, 74% and 100% of the response (although we must replace the 100% dose with our highest dose). Good luck.
Hi, this is the same three-parameter Hill model wich are cited on Toxcast EPA project?
I expect so, but just compare the two equations to be sure.
This is interesting. Are there any published papers treating the issue of the fixed Hill coefficient?
Hi...I am not aware of any, but have not really looked. It is also worth mentioning that if you use a) dose or b) a measure of average drug exposure (e.g. average concentration at steady state (Css)) or c) use actual/predicted concentrations over time to drive the pharmacodynamic response, then Hill cannot be simultaneously equal to 1 under all three. Hence if you set it to 1 using dose, then you are implicitly setting it to something different to 1 based on concentrations. In short, do not fix it!! Estimate it, just like we would an ED50 (or EC50). cheers Al
Great video. I was wondering when you discussed the problems of the richards model you discussed the difficulty of getting enough data even with the emax. I was wondering, is there a rule of thumb for the number of observations for the Emax? Also, is there some seminal paper about Emax or dose response in experimental context? I am in economics so I might not be up there in that particular area... I already have some paper on dose ranging with Emax... Anyways very useful! Thanks!
Delighted you thought the video was OK. Alas there is no rule of thumb for the number of observations, as it is always a combination of the size of the residual error variance (our noise), the design (i.e. what doses you picked), and the precision you want (wide or narrow uncertainty in the final estimated dose response). You can pick the doses in an optimal way (see L4 lecture), based on what you want to optimise. Maths wise, we 'know' the asymptotic behaviour of the variance-covariance matrix is the inverse of the expected Fisher Information Matrix. If you want the formulae, just email me at the address in the video. If maths is not your strong point, just simulate your design and estimate it (say 20-1000 times). You can then play with different designs (doses and observations per dose) to see how they do relative to your metric(s) of interest. As a rule of thumb, D optimal designs for this model are 4 point designs, at doses that yield 0%, 26%, 74% and 100% of the response (although we must replace the 100% dose with our highest dose). Good luck.
Hey mate, thanks for the video. What software are you using?
Hi Ken...this was done using SAS 9.4