3. Statistics Test results on a drug such as (1) with17 variants (No. of compounds, n, = 17 ) differing only in X are tabulated with the values of physical descriptors such as logP, (logP) 2, , E S obtained from tables. Cmpd NoXActivitylog P(logP) 2  E S 1F Me : 17OMe (1) What goes into the QSAR equation? logP, (logP) 2, , E S and constant? (P=5) The biological data (Activity), C 0 log P only? (No. of variables, P, = 2, incl const) log P and (logP) 2 ? (P = 3) Whichever gives the best result! How do we chose? +10

3. Statistics F 4,12 = 10.9 (Why 4,12? Number of descriptors=4; P - n = 12) correlation coefficient, r, = 0.96 Equation explains 92% of the biological data (r 2 = 0.92 = 0.96  0.96; r 2 > 0.95 fortuitous Is n high enough? Usually need at least 5 compounds per variable. Here we have n=17 - should ideally be 25. If we let P=17, r would equal 1 & we would get a perfect fit, but it would be meaningless What does F mean? Generally, the higher F the better. Whether a given number, like 10.9 is good/bad (high/low) depends on the subscripts. F gives a probability that the whole equation is not random. For a good equation the probability may be say 0.01 or 1% ie. 99% chance equ. Good. These values are given by statistical programs 3.1. What comes out of the QSAR? standard deviation, s, = how well is the data predicted (i.e. what is the error?)

3.2. Statistics: comparing equations Equation (5) has a low r E S coefficient also low r - suggests term in E S not significant E S is a steric term that says how large a group is Much better (logP) 2 coefficient is small but term is significant because (logP) 2 big

3.3 Statistics: t-test Used to check significance of individual terms/coefficients t for all terms in equations (5)-(7) is ____ _____ ____ ____ If t is low (<~2) term is not significant If t is high (>~2) term is significant Probability that term is not random is usually printed by stats. programs. F is similar but applies to whole equation rather than individual terms 10 t 5 =.02/.02=1; t6=4.98/.99=5.03, t 7,1 =3.4/.1=34; t 7,2 =9.4/.01=940

3.4. Statistics summary Use the following to decide whether a QSAR is good or not: r or preferably r 2 is it near 1.0? sis it small? t is it > 2? F is it high enough? value of whole term is it significant? nis it high enough? 10

2.4. Some limitations of QSAR (1) ,  only valid for substituted benzenes - need to consider diverse structures For new groups: ,  not available in tables Difficult to deal with inactive compounds (what is activity?) or crude biological data (that may be expressed +, ++, etc) Need to synthesise at least 5 compounds per descriptor Descriptors , , etc are often related to each other so increase in activity due to increase in  may actually be due to increase in size Does not address conformation of drug Only gives optimum values of ,  etc, not structure of new drug. Compounds must be described similarly even if structures are very different (using log P instead of  can get round the problem - but then log P has to be measured (but  does not as it is found in tables) Can prevent researchers looking at a new series of compounds Often have to use response from a single concentration rather than concentration to achieve set effect - therefore loss of accuracy A single QSAR only addresses one property - may need to consider solubility, stability, absorption, metabolism, transport, safety… QSAR only valid if all compounds in series operate by a common mechanism. This is often not valid. Requires accurate data on weakly active compounds