Monday, 29 August 2011

The Quick-Kill™ Model

The Quick-Kill™ model assumes drug discovery is a stochastic process.  The simplest form assumes drug discovery to be a binomial process with probability of discovery p such that the expected number of failures before the first success has a geometric distribution with a mean of 1/p

The following discussion considers the simplest case where the development process is divided into two phases.  However, the Quick-Kill™ model can be extended easily to include multiple decision points, multiple therapeutic targets, a range of time and development costs, and first-to-market considerations.  In the discussion, the probability of success is 0.10.  However, this can be changed to reflect differences in probabilities from one therapeutic area to another.  The model has been tested assuming estimated lifetime values of a compound that is first to market as $400m compared to $100m for compounds that are second to the market place.   If a successful compound is missed as a result of poorer decision making the strategy incurs development costs associated with the rejection of that compound but we see no return on that investment.  The model is robust to these assumptions.
The Quick-Kill™ Model

If the costs of killing a drug candidate are $Ckill and the development cost for a successful product is $Csuccess  then the expected costs for each successful market launch are

E(Cost) = (1/p) Ckill + Csuccess .

Similarly, if the time to kill a compound is tkill and the development time for a successful drug is tsuccess and discovery is a binomial process then the expected time to first marketing authorisation approval,

EMAA = (1/p) tkill + tsuccess

This latter finding means that the EMAA is a function not just of the development time for successful compounds but the amount of time unsuccessful compounds spend in the development pipeline.  Depending upon the discovery rate p the development time for unsuccessful compounds can have a significant impact on the EMAA.   This gives rise to the development speed paradox in which strategies directed at increasing development speed and reducing the development time for successful compounds can actually increase the EMAA through their impact on the time taken to kill a compound tkill.

False Negatives

We can extend this model to incorporate the quality of decision making by considering, in particular, pfn, the probability of a false negative, where a compound is killed even though it is active.

 EMAA = (p (1-pfn) )-1 tkill + tsuccess

Furthermore we can compare the efficiency of different screening strategies by considering the number of compounds discovered per screening year. 

If the number of NCEs to be screened is N, the time taken to reach the critical decision point is t, the proportion of “good” compounds is p and the probability of a false negative is pfn then if we ignore the development costs following the critical decision points, the number of “good” compounds discovered per screening year is given by:

g = Np(1-pfn)/Nt

Assuming pfn = 0 for the traditional approach, we can equate gtraditional and gQuick-Kill and solve to give the maximum tolerable false negative rate pfn for the Quick-Kill™ strategy:

pfn = 1 – (t Quick-Kill /t traditional )

For example, if t Quick-Kill = 1 year and t traditional = 2 years then the maximum tolerable false negative rate for the Quick-Kill™ strategy is 50%. 

© Dennis Lendrem, 2011

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