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"*+    ! # &()$ .,- 10'/o2$TQS=%rV $2$#t,j0 58 V 2$#:/s#-.2$lL>_yc-'_$$$b$Ԛ'~KۤDW$q 0AA 333@dg4fdfdx: 0ppp@  <4!d!d@ 0t<4BdBd@ 0tg4ddddx: 0p pʚ;ʚ;<4dddd@U 0@r0___PPT10 2___PPT9/ 0?l, XDose-response screening of enzyme inhibitorsO = >  0g Assumptions  XMeasures of inhibitory potencyYHTight binding inhibitors : [E] K iR%ZProblem: Negative Ki from IC50V   [,Solution: Do not use four-parameter logistic-- \,Fitting model for enzyme inhibition: Summary--U  ]$Problem: Occasional "outlier" points%%c$Solution: Robust regression ("IRLS")%%^$Robust fit: Practical considerations%%_3Robust fit: Constant weighting of negative controls44:k-Robust fit: Limiting the number of "outliers"..a.Robust fit: Productivity and objectivity gains//bRobust fit: SummaryV  W3What is the "true" value of an inhibition constant?44-e%Formal standard errors are too narrow&&/f+Symmetrical confidence intervals are better,,*d0Nonsymmetrical confidence intervals are the best11<l$Confidence intervals (C.I.): Summary%%7j  5i-Toward "best-practice" in secondary screening../C=>@ABC DEFGHJKL+M.N2O3P6R8S;T=U   0` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> <4(    6 P  T Click to edit Master title style! !  0   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0 ``  X*  0 `   l*(    0( `   `* H  0޽h ? ̙33 Default Design 0 @4 (  4 4 N@y@y .  { p* a00aa 4 N{@y@y 3 .  r* a00aad 4 c $ ?  4 4 N{@y@y 9 f  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  4 T@y@y r   p* a00aa 4 T8@y@y r3   r* a00aaH 4 0ηo~ ? ̙3380___PPT10.aX 0\x(  \ \ Nc{e{e     p* AAA \ N\{{e{e %    r* AAA  \ Tr{e{e    p* AAA \ TL{{e{e %   r* AAAH \ 0ηo~ ? ̙3380___PPT10.  0 A 9   (  XB  0D  X  0A?`m(  6̂{  @Advanced Methods in Dose-Response Screening of Enzyme InhibitorsfA33333$S  <{P  1. Fitting model: Four-parameter logistic (IC50) vs. Morrison equation (K i*) 2. Robust regression: Implementing outlier exclusion in practice 3. Confidence intervals: What should we store in activity databases?  ++ 1  <{ f 9TOPICS:XB  0Dv  <{ j jAcknowledgements: Craig Hill & Jim Janc Celera Genomics, Department of Enzymology and HTSPk 3) 3 3# 3,;X  <Ч{  >Petr Kuzmi , Ph.D. BioKin, Ltd.^      ,    <{ ]Society for Biomolecular Screening 10th Annual Conference, Orlando, FL, September 11-15, 2004^^ 3XB  0D0H  0޽h ? ̙33  P 0   `PZ (  Pr P S 4`   XB P 0D`X P 0A?`m P << S  3c P <0p 1 We need a portable measure of inhibitory potency. Failing portability, at least we need to rank compounds correctly. For correct ranking, we need both precision and accuracy. No measurement is perfectly accurate: confidence intervals. Few experiments are designed ideally and executed flawlessly.2 K: 33*B P < d  ? Reminder: ^B  P 6DjJ  P <(M  ? PRECISION 3x  P <A ??O =  x P <A ??O @ .=   P <@ u >ACCURACY 3x P <A ??O n=   P < LPRECISION & ACCURACY3H P 0޽h ? ̙33$ A 0 pd(   r  S ܂`   XB  0D`X  0A?`m   <P2  01. Inhibition constant 2. Apparent K i 3. IC50T1%    <  hDepends on [S] [E]2 ^B   6DjJP^B   6DjJ ^B   6DjJ    < ,   NO YES YESX    < t ,   NO NO YESX   <X0 4  OK i0 -  <0  K i* = K i (1 + [S]/KM)    C  < l 0 g@  IC50 = K i (1 + [S]/KM) + [E]/2    ^B  6DjJ    <V  _Example: Competitive inhibitor$   <D  ~INTRINSIC MEASURE OF POTENCY: * 33  <@` W%DEPENDENCE ON EXPERIMENTAL CONDITIONS&& X  03f ^  <4%0   :[E] K i: IC50 K i*       </f0 z |DG = -RT log K iP3 333x  < 2 x :[E] K i: IC50 K i*       <tB` @  K"CLASSICAL" INHIBITORS:   <(F X  O"TIGHT BINDING" INHIBITORS: H  0޽h ? ̙33& B 0  f( "  r  S `   XB  0D`X  0A?`m  <  W!HOW PREVALENT IS "TIGHT BINDING"?"" 3  <x0N* E ... NOT SHOWN x  <A b??P& b  <l  r: A typical data set: Completely inactive: Tight binding:;;3  <䕉 l ~ 10,000 compounds ~ 1,100 ~ 4000!   ^  63fjJ*0  <@: X Data courtesy of Celera Genomics!! 3H  0޽h ? ̙33X C 0 ( "  r  S `   XB  0D`X  0A?`mx   <A j????C j  <ĉ4  UFIT TO FOUR-PARAMETER LOGISTIC:  3  <ɉfp` J K i* = IC50 - [E] / 2t     <щ@: X Data courtesy of Celera Genomics!! 3H  0޽h ? ̙33  D 0  M( "  r  S `   XB  0D`X  0A?`mx  <A i????C i  <  X"FIT TO MODIFIED MORRISON EQUATION:## 3   < O0 WeP. Kuzmic et al. (2000) Anal. Biochem. 281, 62-67. P. Kuzmic et al. (2000) Anal. Biochem. 286, 45-50.f           ,+   <@: X Data courtesy of Celera Genomics!! 3H  0޽h ? ̙33" E 0  b( "  r  S '`   XB  0D`X  0A?`mM   <PP"   Apparent inhibition constant K i* is preferred over IC50 Modified Morrison equation is preferred over four-parameter logistic Optionally, adjust the enzyme concentration in fitting K i*    K   ,:K>   <ae V  EMEASURE OF INHIBITORY POTENCY MATHEMATICAL MODEL METHODOLOGYFF3, x   <A l?f?@P  lH  0޽h ? ̙33P= 0  ( "  XB  0D  X  0A?`m  <P  1. Fitting model: Four-parameter logistic (IC50) vs. Morrison equation (K i*) 2. Robust regression: Implementing outlier exclusion in practice 3. Confidence intervals: What should we store in activity databases? ++ 1  <`f4 9TOPICS:XB   0DH  0޽h ? ̙33 F 0 ia(  r  S ̌`   XB  0D`X  0A?`mx  <A {????` {  <,ό GLEAST-SQUARES FIT 3L  <ӌ d 2P. Kuzmic et al. (2004) Meth. Enzymol. 383, 66-81.^3       ,H  0޽h ? ̙33 L 0 ph0(  0r 0 S `   XB 0 0D`X 0 0A?`mx  0 <A |????` |  0 <D NHUBER'S "MINIMAX" METHOD 3L  0 < d 2P. Kuzmic et al. (2004) Meth. Enzymol. 383, 66-81.^3       ,H 0 0޽h ? ̙33, G 0 l( c r  S $+`   XB  0D`X  0A?`m  <0-s T"The devil is in the details." 32  <2P0&  p Treat negative controls in a special way (unit weight). Allow only a certain maximum number of "outliers".qq96H  0޽h ? ̙331 H 0 q( "  r  S O`   XB  0D`X  0A?`m  <@P S  3x  <A }????C }  <LUm JNEGATIVE CONTROL WELLS ([I] = 0) ARE EXCLUDED FROM ROBUST WEIGHTING SCHEMEKK 3  <Z@: X Data courtesy of Celera Genomics!! 3H  0޽h ? ̙339 T 0 xy(  K xr x S X{`   XB x 0D`X x 0A?`m x <|} S  3x x <A ????  x <g @I.R.L.S.: AT MOST ONE HALF OF DATA POINTS WITH NON-UNIT WEIGHTS ,A 39 3 x <8@: X Data courtesy of Celera Genomics!! 3H x 0޽h ? ̙33% J 0   e(   r   S $`   XB   0D`X   0A?`m   <Ĭ S  3   <찑 t>A CASE STUDY "BEFORE AND AFTER" IMPLEMENTING ROBUST REGRESSION?? 3x   <A ??     <@: X Data courtesy of Celera Genomics!! 3H   0޽h ? ̙33 K 0 ~v0(( i@ (r ( S tڑ`   XB ( 0D`X ( 0A?`m ( <0 S  3 ( <<p i  i Tested on 10,000+ dose response curves Huber's "Minimax method" proved most effective Modifications for inhibitor screening: a. Handling of negative controls b. Prevent too many outliers Increase in scientific objectivity & productivity &$xH ( 0޽h ? ̙33`> 0 @( "  XB  0D  X  0A?`m  <LP  /1. Fitting model: Four-parameter logistic (IC50) vs. Morrison equation (K i*) 2. Robust regression: Implementing outlier exclusion in practice 3. Confidence intervals: What should we store in activity databases?++ 1  <`f4 9TOPICS:XB  0DH  0޽h ? ̙33 @ 0 zrP  (  r  S $:`   XB  0D`X  0A?`mx   <A ???    <|<4  e/AVERAGE & STANDARD DEVIATION FROM 43 REPLICATES00 3   <@A  U @Average:     < E,@ N d Std. Dev.:    <LI,7~ b0.9 mM@  <. 7 c13.7 mM@X  0   <pS a  n#76 : Ki = 11.5 mM@     <U@: X Data courtesy of Celera Genomics!! 3H  0޽h ? ̙33y N 0 )!` @( .... @r @ S `   XB @ 0D`X @ 0A?`m @ <䍖 DEXPERIMENT #76 X  @ 0A ? X @ 0A?` : @ <p )D K i* = (11.5 1.2) mM ^ @ 6  P ^ @ 6 p P0  @ <L` 4 KFormal standard error36 @ <  .INTERVAL DOES NOT INCLUDE "TRUE" VALUE 13.7 mM/  3 3 3 3 3 3 3 @ <@@: X Data courtesy of Celera Genomics!! 3H @ 0޽h ? ̙33 O 0 p HE(   Hr H S $˖`   XB H 0D`X H 0A?`mX H 0A ? X H 0A?` F H <8p HD K i* = (8.6 ... 14.4) mM ^  H 6     H <ٖ` 4 Y#Symmetrical 95% confidence interval$$3  H <Hޖ  *INTERVAL DOES INCLUDE "TRUE" VALUE 13.7 mM\+  3 3 3 3 3  H <t@: X Data courtesy of Celera Genomics!! 3 H < DEXPERIMENT #76 H H 0޽h ? ̙33 M 0 zr8 (  8r 8 S `   XB 8 0D`X 8 0A?`mx 8 <A ???  8 < b  _NONSYMMETRICAL 99% C.I.,33y 8 <  L0 _Watts, D.G. (1994) Meth. Enzymol. 240, 23-36. Bates & Watts (1988) Nonlinear Regression, p. 207^`  "    ,@ 8 <@: X Data courtesy of Celera Genomics!! 3H 8 0޽h ? ̙33 U 0 X(  r  S f`   XB  0D`X  0A?`m  <h S  3  <mp  Report two numbers for each compound: high and low end of the C.I. If two C.I.'s overlap, the two inhibitory activities are indistinguishable. Thus, many compounds can end up with identical rank!M)H  0޽h ? ̙33S 0 h>(  hXB h 0D  X h 0A?`m9 h <LP  !1. Fitting model: Four-parameter logistic (IC50) vs. Morrison equation (K i*) 2. Robust regression: Implementing outlier exclusion in practice 3. Confidence intervals: What should we store in activity databases? Conclusions: Toward a "best-practice" standard in secondary screeningn"++  9 1 h <h`f4 9TOPICS:XB h 0DH h 0޽h ? ̙339 R 0  `y( x `r ` S xÛ`   XB ` 0D`X ` 0A?`m ` <Л S  3  ` <֛  3 Measure Ki*, not IC50 (dependence on experimental conditions). Use a mechanism-based model (Morrison equation), not the four-parameter logistic equation (no physical meaning). Employ robust regression techniques, but very carefully. Report a high/low range (confidence interval) for every Ki*.  4 JP-"  >@v;@ ` <;  a+DOSE-RESPONSE STUDIES OF ENZYME INHIBITORS ,, 3XB  ` 0D` ` H ` 0޽h ? ̙33H 0 P( @Y@ X  C 4     S &49 f   JPoints to make: Thank organizers. Thank Craig and Jim. Go over topics.4@:@ < H  0ηo~ ? ̙33U 0  P( 4@ ^  S 4     c $䚌49 f   FPoints to make: It's important to talk about "robust regression", because various commercial software packages have incorporated it recently. You could really shoot yourself in the foot with "robust fit", if you are not very careful.>@@  H  0ηo~ ? ̙33>V 0 (  ^  S 4     c $h$49 f   Points to make: Final topic. Again, this has to do with "Science-101": No quantitative result reported in any branch of experimental science is meaningful at all, without being accompanied by some measure of uncertainty. @@       H  0ηo~ ? ̙33 W 0   2 (  ^  S 4     c $xb49 f   (Points to make: Can we ever get a "true" value of inhibition constant? No, we cannot. "True" values in nature are forever obscured from us. But we can get arbitrarily close, under certain statistical assumptions. For example, we can determine the same Kiapp many different times, from many independently measured dose-response curves, and then take an average from many replicates. Then the "uncertainty" of the completely super-set of experiments would be (say) something like the standard deviation. In this case, we 43 replicated dose-response curves. Let's call 13.7 mM the "true" value of Kiapp. But there is a problem, with Experiment #76: 11.5 mM does not fall within (13.7 0.9) mM! What, if anything, can we do to get at least close to the "true" value from a single dose-response curve, rather from 43 or 100 or 200 of them?<@>@   X     !       4 %  2    < ,SH  0ηo~ ? ̙33 X 0   0 (  ^  S 4      c $,O49 f   & Points to make: Ki is the best, but laborious to get (need to vary both [S] and [I]). Kiapp is the next best. It "costs" as much as getting IC50 (vary [I] only), but is more informative than IC50 (does not depend on [E]). Of these three, IC50 is the least appropriate measure of potency, because... ... for tight binding inhibitors, IC50 shifts with [E]! That means, with a new protocol, a new staff person who changes [E] for some reason, in a different lab, etc., everyone will be getting a different IC50 for the same tight binding inhibitor (e.g., staurosporine) under otherwise identical conditions! Remember, "tight binding" has nothing to do with any particular value of Ki (picomolar, nanomolar, etc.). "Tight binding" is not a property of an inhibitor, but rather a characteristic of experimental conditions: whenever [E] is numerically close to Ki. For example, an inhibitor with Ki = 1 mM is "tight binding" when [E] = 500 nM (this could happen, if your substrate is really slow).@@    F     4   1   .   ^       Q  M           #    ' *   >Y v /H  0ηo~ ? ̙33nY 0 .&(  ^  S 4      c $49 f   Points to make: How prevalent is tight binding? For how many compounds is IC50 really meaningless? This is a histogram of Kiapp for 10,000+ compounds. Two groups of compounds, centered at about 200 mM and 6 mM, respectively. About 400 (or 4%, or one in 25) are "tight binding", so for one compound out of 25, the IC50 has no meaning. @E@ @   .     H  \     }H  0ηo~ ? ̙33LZ 0  (  ^  S 4     s *ډ 49 f   Points to make: Can't fix the problem by the "nave" method: 1. Measure IC50 as usual (four-parameter logistic) 2. Subtract [E]/2 from resulting IC50. PROBLEM! The Kiapp is negative, which is a nonsensical result. We never know exactly what the enzyme concentration really is, so that's why the above "nave" method fails. __________________________ If there is time: Physical meaning of parameters in the four-parameter logistic equation: The Hill exponent (nHill = 1.4 in this case) has not physical meaning at all for a tight binding inhibitor. We do know independently that this compound is very "clean" mechanistically, with exactly 1:1 stoichiometry, a pure competitive inhibitor. The value nHill = 1.4 simply means that the original Hill equation (transformed into the "four parameters logistic") was derived under the assumption that no tight binding occurs! In other words, the basic assumptions of the four-parameter logistic equation are violated. It should not be used for tight binding..@@ A   J        <  t  ^           >%+H  0ηo~ ? ̙33[ 0 (  tP ^  S 4     c $*49 f   fPoints to make: Here is how to fix the problem: - forget about IC50's completely - forget about the four-parameter logistic equation (4PLE) Instead of 4PLE, use a modification of the Morrison equation (paper #1 above). This will get you the Kiapp directly (it is, of course, positive). As a bonus, you may learn what your enzyme concentration really was. The conditions under which this simultaneous determination of [E] and Kiapp is possible are described in paper #2 above. In this case, the enzyme appears about 65% active (4.5 nM actual concentration, as opposed to 7.0 nM nominal concentration). ^@U@ 7   w  +       0  T         i  $   ,H  0ηo~ ? ̙33c\ 0 #(  ^  S 4     c $l49 f   EPoints to make: Summarize: Let's stop talking about IC50's completely, and move to apparent inhibition constants (Kiapp) as the most basic measure of inhibitory potency. For (in this case) 95% of compounds, IC50 and Kiapp are the same number, but for the 5% of "tight binders", they are not. I call this the "modified Morrison" equation, because the original equation (Williams & Morrison, 1979) does not have background rate term (Vb). Not knowing [E] exactly is not a problem, because of an interesting "circular logic" situation: - If you can't determine [E] from the data, it does not matter, because under those circumstances [E] does not affect Kiapp ("classical" or weak binding). - If [E] is in fact important in the sense that it could affect your Kiapp ("tight binding") then you can determine it from the data. @4@@ *   ;     \                     -    2        ucdyH<H  0ηo~ ? ̙33] 0 og0(  ^  S 4   a  c $49 f   QPoints to make: This is the reason why we worry about "robust regression": an occasional defective dose-response curve. The point with blue dashed line is the most highly outlying (greatest distance from the solid red curve). However, throwing this point out as an "outlier" would be nave, because it really isn't (see next slide). @@@ L    T  H  0ηo~ ? ̙33^ 0 nfP (   ^   S 4   `   c $;49 f   tPoints to make: You could shoot yourself in the foot terribly: "robust regression" is attractive but treacherous. d@c@   X  H   0ηo~ ? ̙33_ 0 ]U`(  ^  S 4   O  c $b49 f   IPoints to make: The first kind of problem: negative control rejected as an 'outlier'. This is, in part, because the data set is "not nice": the first nonzero concentration of inhibitor already produced more than 50% inhibition. Regardless, in an automated setting, we do want and need to have a way of dealing with such "not nice" data sets. A purely empirical fix: if and when your negative control gets rejected as an "outlier", then (depending on the exact shape of the curve, not necessarily every time) reject the results of IRLS and revert to Ordinary Least Squares (OLS). d@8@  *   HH  0ηo~ ? ̙33a 0 $(  $^ $ S 4   { $ c $49 f   KPoints to make: Given that "robust fit" (IRLS) is so tricky to implement correctly, is it worth the hassle? Yes it is, for two reasons: PRODUCTIVITY: The scientists doing secondary screening stop trying to "improve" the look of their dose-response curves, by (at least temporarily) manually deleting this data point or that. The percentage or data re-submissions went down 10 times. OBJECTIVITY: Before "robust fit" was implemented at Celera, when "Fred" looked at a somewhat irregular dose-response curve, he wanted to remove data point #3 as an outlier. But when "Judy" looked at the same data, she thought that data points #5 was really an outlier. Those issues have completely disappeared. Now everyone is happy with how the machine is 'cherry picking' data points for exclusion: manual exclusion of data points went down to zero.@;@   2  s  0  ,  H $ 0ηo~ ? ̙33+b 0 ,{( @ ,^ , S 4    , s * 49 f   kPoints to make: Summarize Robust fit (IRLS) is good, but one must be extremely careful and do a lot of testing. Overall, this initial work is worth it, because the productivity and objectivity does go up. ~@@ -  6  ?  H , 0ηo~ ? ̙33c 0 c[@4(  4^ 4 S 4   U 4 c $49 f   %Points to make: The "right thing" to do, in general, is not to use least-squares regression. Instead, let the machine decide, by using "robust regression", which point (if any) is an outlier. Don't try to guess outliers and "fix up" your dose-response curves by hand! There are many flavors of "robust regression", a.k.a. "iteratively reweighted least squares", a.k.a. "IRLS". Here, I have chosen Huber's flavor ("Minimax"). The technical details, including some comments on the choice of the tuning constant are in the Methods article cited.@@ + #   u      H 4 0ηo~ ? ̙33Qd 0  <( | <^ < S 4    < c $%49 f   }Points to make: The best measure of uncertainty is the (in general) nonsymmetrical confidence interval, computed by the method of Bates & Watts (references). Blue symbols: upper limits of the nonsymmetrical 99% (as opposed to 95%) confidence intervals. Red symbols: lower limits of the nonsymmetrical 99% (as opposed to 95%) confidence intervals. Importantly, the lowest of the high-end limits and the highest of the low-end limits do enclose the "true" value! This means that if we only had any one of these 43 dose response curves, then (regardless of the "best-fit" value of Kiapp) the nonsymmetrical 99% confidence interval would in fact always include the "true" value. Thus, we managed to "boot strap" ourselves: we can in fact get close to the "true" value of Kiapp from just a single dose-response curve: all we need to do is report the nonsymmetrical 99% confidence interval. @k@ 7  %   %     ;     +          !  O         y      6    ,HrH < 0ηo~ ? ̙33"e 0 Dr( dSp= D^ D S 4    D c $$49 f   hPoints to make: First attempt, not successful: let's look at the "formal standard error" reported. It does not work: the interval (11.5 1.2) mM does not include the "true" value 13.7 mM. Is there anything better? Yes, there is. v@@ |   M  H D 0ηo~ ? ̙33df 0 $L(  L^ L S 4    L c $49 f   Points to make: That "something better" is the (symmetrical) 95% confidence interval also reported by the software. Now, the interval (8.6 ... 14.4) mM does encompass the "true" value, 13.7 mM. Unfortunately, these symmetrical confidence intervals do not work in every case, although they do work for most "nice looking" data. Is there something even better? Yes, there is. @k@ e g  %  g  H L 0ηo~ ? ̙33g 0 T?(  T^ T S 4    T s * 49 f   /Points to make: (possibly skip this slide) Why is everyone getting a different IC50 for (say) staurosporine against the same enzyme? This isn't right. There should be uniformity/portability. Even if you don't believe that complete portability is possible, at least we want to rank compounds correctly within the given screening campaign. So that's where the need for very high accuracy really arises. In "Science-101" we were taught that no measurement is perfectly precise, so why aren't we reporting our experimental errors for Ki / IC50? The statement "My Ki is 5 nM..." is completely meaningless, without adding "... with the confidence interval between 4 and 7 nM." We need to deal with less-then-perfect data (hence, robust regression). ,@@@*      %              ` H T 0ηo~ ? ̙33 i 0 @ 8 d(  d^ d S 4   2 d c $l49 f   Points to make: In the case of in vitro assays using purified enzymes, let's all stop using the IC50 as the most basic measure of inhibitory potency: let's use Kiapp instead. To get the Kiapp, we don't need to do any more work. Use the same data, but type a different fitting equation into whatever software you are using. Robust regression is good, but let's be extremely wary of what various commercial packages report: we must always check final "robust weights"! Let's make room in corporate databases not just for "Kiapp", but also for "Kiapp - LOW" and "Kiapp - HIGH" estimates. Then let's use those estimates for rank ordering that allows for multiple inhibitors of the same rank. Possible objection #1: "But we've been measuring IC50's since the 1940's!" Answer: "The industry is slow to change, but business as usual is no longer an option." - Kenneth Kaitlin (Tufts Center), SBS-10 opening session Possible objetion #2: "Why should I worry about 5% of 'tight binders', they are not that useful anyway." Answer: "We must be absolutely exact practitioners of our craft. We have to be perfect." - Carol Homon (Boehringer-Ingelheim), SBS-10 opening sessionD@@     $   =            !  M                 V  G   # % )   9   ?  L 11   H d 0ηo~ ? ̙33Fj 0 l(  l^ l S 4    l s *x 49 f   Points to make: In the last several years, SBS managed to put forward a standard for physical layout of microplates: Perhaps it is time to begin talking about standardizing how we report basic basic measures of inhibitory potency. ~@@    1   H l 0ηo~ ? ̙33k 0 p|c(  52 |^ | S 4    | s *h 49 f   SPoints to make: The second kind of problem: almost every point is an 'outlier'. You must watch, very carefully, what weights (as in Iteratively Reweighted Least Squares) your software is reporting! If only a minority of data points are given less than unit weight (100%), forget about IRLS completely and go back to OLS. There are many more things that can go wrong with "robust fit" (IRLS), these are just two examples out of many.@@  #   1   H | 0ηo~ ? ̙33/l 0 (  ^  S 4     c $49 f   uePoints to make: "Science-101": a quantitative result without some type of confidence band reported for it is completely meaningless. Therefore, we need to report not only the "best fit" value of Kiapp, but two additional values: the low / high ends of the appropriate confidence interval. The existence of confidence intervals has consequences for ranking: "Strict rank-ordering" (without multiple compounds sharing the same rank) is really impossible. 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