You are here: Home / Exposures / Lockwood, Ewy, Hermann, Holford, 2006 / Application of clinical trial simulation to compare proof-of-concept study designs for drugs with a slow onset of effect; an example in Alzheimer's disease

Model Mathematics

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Component: environment

Component: population_pharmacodynamics_model

S = S0 + alpha time + ADAS_Cog_p + PD_CeA + epsilon

Component: placebo_response_model

ADAS_Cog_p = \frac{beta_P Keq_p}{Keq_p - Kel_p} (ⅇ^{(- Kel_p) time} - (ⅇ^{(- Keq_p) time})) Keq_p = \frac{\ln 2}{t_half_eq_p} Kel_p = \frac{\ln 2}{t_half_el_p}

Component: pharmacokinetic_model

CL = 2268.0 ⅇ^{(- 0.0135) (age - 40)} smk

Component: drop_out_model

Sv = ⅇ^{(- 0.00145) time}

Component: drug_response_model

PD_CeA = beta_a CeA

Component: drug_clearance

\frac{d}{d time} (CC) = \frac{k_ab A_in - (CL CC + CL_ic (CC - PC))}{Vc} \frac{d}{d time} (PC) = \frac{CL_ic (CC - PC)}{Vp} \frac{d}{d time} (A_in) = (- 115.44) A_in

Source: Derived from workspace Lockwood, Ewy, Hermann, Holford, 2006 at changeset 5781efa9e2dd.

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Application of clinical trial simulation to compare proof-of-concept study designs for drugs with a slow onset of effect; an example in Alzheimer's disease