{ From user ktluser, Model Dose_response_estima at 14. Aprta 2008 14:23 ~~ } Softwareversion 4.1.0 { System Variables with non-default values: } Samplesize := 5000 Typechecking := 1 Checking := 1 Saveoptions := 2 Savevalues := 0 Allwarnings := 0 Model Dose_response_estima Title: Dose-response estimator Author: ktluser Date: 9. Aprta 2008 6:59 Saveauthor: ktluser Savedate: 14. Aprta 2008 14:23 Defaultsize: 48,24 Diagstate: 1,24,58,668,377,17 Windstate: 2,102,90,476,224 Fontstyle: Arial, 15 Fileinfo: 0,Model Dose_response_estima,2,2,0,0,C:\Documents and Settin~~ gs\ktluser\My Documents\Jouni\Tee\0407_RiskCourse_Cypros\Dose-respons~~ e estimator.ANA Module One_hit_model Title: One-hit model Author: ktluser Date: 10. Aprta 2008 14:36 Defaultsize: 48,24 Nodelocation: 536,32,1 Nodesize: 48,24 Diagstate: 1,49,329,550,300,17 Text Te1 Description: One-hit model Nodelocation: 96,48,-1 Nodesize: 48,24 Variable Number1 Title: Number Definition: Table(Dose1)(~ 50,50,48,47) Nodelocation: 96,104,1 Nodesize: 48,24 Nodecolor: 65535,52427,65534 Variable Cases1 Title: Cases Definition: Table(Dose1)(~ 1,0,4,12) Nodelocation: 96,160,1 Nodesize: 48,24 Nodecolor: 65535,52427,65534 Index Dose1 Title: Dose Definition: [0,10,30,100] Nodelocation: 232,112,1 Nodesize: 48,12 {!40000|Att_previndexvalue: [0,10,30,100]} Variable Dose_response1 Title: Dose-response Definition: 1-exp(-Q2-Q3*Dose1) Nodelocation: 232,80,1 Nodesize: 48,24 Valuestate: 2,462,14,698,218,0,MIDM Reformval: [Q3,Dose1] {!40000|Att_resultslicestate: [Q0,5,Dose,1,Q1,1]} Variable Q2 Title: q0 Definition: var rows:= 9;~ var median:= 0.02;~ var interval:= 0.003;~ sequence(median-(rows+1)/2*interval, median+(rows+1)/2*interval, inte~~ rval) Nodelocation: 352,80,1 Nodesize: 48,24 Windstate: 2,7,417,300,224 Nodecolor: 52425,39321,65535 {!40000|Att_previndexvalue: [0.6,0.7,0.8,0.9,1,1.1,1.2,1.3,1.4]} Variable Q3 Title: q1 Definition: var rows:= 11;~ var median:= 0.0024;~ var interval:= 0.0003;~ sequence(median-(rows+1)/2*interval, median+(rows+1)/2*interval, inte~~ rval) Nodelocation: 352,136,1 Nodesize: 48,24 Windstate: 2,317,418,262,224 Valuestate: 2,616,49,416,303,0,MIDM Nodecolor: 52425,39321,65535 {!40000|Att_previndexvalue: [0.75]} Variable Likelihood1 Title: Likelihood Definition: var a:= (Factorial(Number1)/(factorial(Cases1)*factorial(N~~ umber1-Cases1)))*Dose_response1^Cases1*(1-Dose_response1)^(Number1-Ca~~ ses1);~ product(a,Dose1);~ Nodelocation: 232,160,1 Nodesize: 48,24 Valuestate: 2,474,19,713,243,0,MIDM Reformval: [Q3,Q2] {!40000|Att_resultslicestate: [Dose,1,Q0,1,Q1,1]} Objective A_2log1 Title: -2log(likelihood) Definition: var a:=ln(Likelihood1);~ max(max(a,Q2),Q3)-a Nodelocation: 232,224,1 Nodesize: 48,24 Valuestate: 2,572,302,626,337,0,MIDM Reformval: [Q2,Q3] Close One_hit_model Variable Ed50_quantiles Title: ED50 quantiles Units: mg/kg/d Description: Quantiles for the ED50 parameter. This can be used to pro~~ duce the distribution for ED50 that is not corrected for scaling unce~~ rtainty. Definition: Table(Quantile)(~ 10,12,15,35,50,100,150,200,220) Nodelocation: 80,64,1 Nodesize: 48,24 Defnstate: 2,24,198,416,303,0,MIDM Valuestate: 2,213,87,416,303,0,MIDM Nodecolor: 65535,52427,65534 Index Quantile Title: Quantile Definition: [0.01,0.025,0.05,0.25,0.5,0.75,0.95,0.975,0.99] Nodelocation: 80,96,1 Nodesize: 48,12 Windstate: 2,147,155,476,224 {!40000|Att_previndexvalue: [0.01,0.025,0.05,0.25,0.5,0.75,0.95,0.975,~~ 0.99]} Chance Scaling_factor_uncer Title: Scaling factor uncertainty AFa Description: Uncertainty about the proper scaling from the laboratory ~~ animals used in the study to humans. Definition: Lognormal( 1, 3 ) Nodelocation: 200,72,1 Nodesize: 48,40 Windstate: 2,102,90,476,224 Valuestate: 2,88,43,610,358,1,PDFP Nodecolor: 65535,52427,65534 Chance Dr_slope_sigma_h Title: DR slope sigma h Units: 1/ln(mg/kg/d) Description: There is human heterogeneity within the population. The s~~ igma h describes the geometrical standard deviation of this variabili~~ ty distribution, described as the individual probability of observing~~ the disease. Definition: Triangular( 2.1, 3.5, 4.9 ) Nodelocation: 328,72,1 Nodesize: 48,24 Valuestate: 2,361,38,416,303,1,PDFP Nodecolor: 65535,52427,65534 Index Risk_level Title: Risk level Description: This is the acceptable risk level. Definition: [0.5,0.2,0.1,0.05,0.01,1m,100u,10u,1u] Nodelocation: 328,176,1 Nodesize: 48,12 Valuestate: 2,778,72,416,303,0,MIDM Variable Dose_risk Title: Dose|risk Description: This gives the estimate of the dose that causes an indivi~~ dual risk at the risk level. Definition: Ed50_modelled/Af_h Nodelocation: 216,216,1 Nodesize: 48,24 Windstate: 2,249,216,476,224 Valuestate: 2,858,230,415,333,0,MIDM Graphsetup: {!40000|Att_graphvaluerange Dose_risk:1,,,,1}~ {!40000|Att_contlinestyle Graph_cdf_valdim:1} Reformval: [Risk_level,Risk_level,Undefined,Undefined,1] Chance Ed50_modelled Title: ED50 modelled Description: ED50 corrected for scaling uncertainty. Definition: cumdist(quantile,Ed50_quantiles,quantile)/Scaling_factor_u~~ ncer Nodelocation: 136,152,1 Nodesize: 48,24 Windstate: 2,116,147,476,224 Valuestate: 2,50,45,706,375,1,CDFP Graphsetup: {!40000|Att_graphvaluerange Ed50_modelled:1,,0,,,,,0,1000}~~ ~ {!40000|Att_contlinestyle Graph_pdf_valdim:6}~ Diststeps:2 Module Weibull1 Title: Weibull Author: ktluser Date: 11. Aprta 2008 23:57 Defaultsize: 48,24 Nodelocation: 536,80,1 Nodesize: 48,24 Diagstate: 1,642,116,609,492,17 Variable N Title: Number Description: Number of individuals in a dose group Definition: Table(Study_dose)(~ 50,50,48,47) Nodelocation: 56,72,1 Nodesize: 48,24 Nodecolor: 65535,52427,65534 Variable K Title: Cases Description: Number of cases in each study group Definition: Table(Study_dose)(~ 1,0,4,12) Nodelocation: 56,128,1 Nodesize: 48,24 Nodecolor: 65535,52427,65534 Index Study_dose Title: Study dose Description: Doses used in the study Definition: [0,10,30,100] Nodelocation: 176,80,1 Nodesize: 48,13 {!40000|Att_previndexvalue: [0,10,30,100]} Variable P Title: Dose-response Description: This is the dose-response function for the study doses, g~~ iven the parameters ED50 and v. Definition: 1-exp(-ln(2)*(Study_dose/Ed50)^V) Nodelocation: 176,48,1 Nodesize: 48,24 Valuestate: 2,462,14,698,218,0,MIDM Reformval: [V,Study_dose] {!40000|Att_resultslicestate: [Ed50,6,Study_dose,1,V,1]} Variable Ed50 Title: ED50 Description: Parameter ED50 in the Weibull function. NOTE! This parame~~ ter is the effective dose 50 only if the Gamma parameter=0. Definition: var rows:= 35;~ var median:= 380;~ var interval:= 15;~ sequence(median-(rows+1)/2*interval, median+(rows+1)/2*interval, inte~~ rval) Nodelocation: 296,48,1 Nodesize: 48,24 Windstate: 2,7,417,300,224 Nodecolor: 52425,39321,65535 {!40000|Att_previndexvalue: [0.6,0.7,0.8,0.9,1,1.1,1.2,1.3,1.4]} Variable V Title: v Description: Parameter v in the Weibull function Definition: var rows:= 20;~ var median:= 1.5;~ var interval:= 0.1;~ sequence(median-(rows+1)/2*interval, median+(rows+1)/2*interval, inte~~ rval) Nodelocation: 296,104,1 Nodesize: 48,24 Windstate: 2,317,418,262,224 Valuestate: 2,616,49,416,303,0,MIDM Nodecolor: 52425,39321,65535 {!40000|Att_previndexvalue: [0.75]} Variable Likelihood Title: Likelihood Description: Likelihood of the result given the parameter values. Definition: var a:= (Factorial(N)/(factorial(K)*factorial(N-K)))*P^K*~~ (1-P)^(N-K);~ a:= if study_dose=0 then 1 else a;~ a:= product(a,Study_dose);~ a Nodelocation: 176,128,1 Nodesize: 48,24 Valuestate: 2,474,19,794,270,0,MIDM Reformval: [V,Ed50] {!40000|Att_resultslicestate: [Study_dose,2,Ed50,1,V,1]} Variable A_2log Title: -2log(likelihood) Description: -2*log(likelihood) Definition: var a:=ln(likelihood);~ max(max(a,Ed50),V)-a Nodelocation: 176,192,1 Nodesize: 48,24 Valuestate: 2,489,308,770,337,0,MIDM Reformval: [Ed50,V] {!40000|Att_resultslicestate: [Study_dose,4,V,1,Ed50,1]} Variable Dr_data__mle_fit Title: DR data +MLE fit Description: The maximum likelihood estimate for the dose-response fun~~ ction, together with the original study data. Definition: var a:= argmax(-A_2log,Ed50);~ var b:= A_2log[Ed50=a];~ b:= argmax(-b,V);~ a:= a[V=b];~ a:=1-exp(-ln(2)*(Study_dose/a)^b);~ Index x:= ['Data','Fitted'];~ array(x,[K/N, a]) Nodelocation: 432,48,1 Nodesize: 48,24 Nodeinfo: 1,0,1,1,1,1,0,,0, Valuestate: 2,443,18,815,451,1,MIDM Reformval: [Study_dose,Sys_localindex('X')] {!40000|Att_resultslicestate: [Ed50,7,V,1,Sys_localindex('X'),1,Study_dose~~ ,1]} Text Te2 Description: Weibull model Nodelocation: 56,24,-1 Nodesize: 48,24 Variable Edx Title: EDx Description: Estimated dose that results in the given effect level (pr~~ obability of response). This is an analytical solution to the Weibull~~ . Definition: (-ln(1-risk_level)/ln(2))^(1/v)*ed50 Nodelocation: 296,256,1 Nodesize: 48,24 Valuestate: 2,77,36,662,550,0,MIDM Graphsetup: {!40000|Att_graphindexrange Risk_level:1,,,,1}~ {!40000|Att_contlinestyle Graph_primary_valdim:1} Reformval: [V,Ed50] {!40000|Att_resultslicestate: [Risk_level,5,Ed50,1,V,8]} Variable Khi2 Title: Khi2 Description: Chi squared with one degree of freedom. CHECK THE CALCULA~~ TIONS, THEY ARE PROBABLY WRONG. Definition: Cumnormalinv(quantile)^2/2 Nodelocation: 64,256,1 Nodesize: 48,24 Valuestate: 2,200,210,416,303,0,MIDM Variable Acceptable_values Title: Acceptable values Description: Gives 1 if the parameter values result in a likelihood th~~ at is within the given probability bounds. Definition: var a:= A_2log;~ a:= if a>Khi2 then 0 else 1 Nodelocation: 176,256,1 Nodesize: 48,24 Valuestate: 2,169,22,1088,613,0,MIDM Reformval: [V,Ed50] {!40000|Att_resultslicestate: [Quantile,1,Ed50,1,V,1]} Objective Ci_ed50_v Title: CI ED50,v Description: Confidence intervals for pairs of parameters ED50, v. The~~ confidence intervals are calculated based on the cloud of DR-functio~~ ns at the risk level set in the Reference level node. Note that the t~~ he probabilities are calculated for pairs [ed50, v], and thus the dis~~ tributions of the parameters are NOT independent. Definition: var a:= Edx[risk_level=Reference_level];~ a:= if acceptable_values=1 then a;~ var b:= if quantile < 0.5 then argmin(a,v) else argmax(a,v);~ var c:= if quantile < 0.5 then argmin(a[v=b],ed50) else argmax(a[v=b]~~ ,ed50);~ b:= b[ed50=c];~ index param:= ['ED50','v'];~ array(param,[c,b]) Nodelocation: 176,320,1 Nodesize: 48,24 Windstate: 2,102,90,476,224 Valuestate: 2,52,119,474,447,0,MIDM Reformval: [Sys_localindex('PARAM'),Quantile] {!40000|Att_resultslicestate: [Sys_localindex('PARAM'),1,Quantile,4,Re~~ ference_level,1]} Chance Dr_param_distributio Title: DR param distribution Description: A sample of dose-response function parameters that togeth~~ er produce a cloud of curves that fulfil the probability bounds deriv~~ ed in CI_ED50_v. Definition: var x:= 1;~ var a:= 0;~ while x