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# Class Note for ESRP 531 at WSU 10

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Date Created: 02/06/15

ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 September 14 2005 Lecture 6 DoseResponse I Overview of the Dose Response Relationship I Summary from Lecture 3 A In lecture 3 we discussed how the typical dose response relationship is derived from a normally distributed population response 1 The response could be any biochemical genetic physiological morphological behavioral etc observation that we wish 2 In the normal distribution we are interested first in the median numbers responding at a specific dose we are also concerned with the variation in individuals responding across the full regime of tested doses B We also discussed that examining the normal distribution as a percentage of population responding changes the bell shaped curve to a logistic or S shaped curve 1 By definition the median response on the logistic curve is called the LD50 if lethality is the toxicological endpoint or measured response and the dose is expressed on a body weight basis usually employing the units mgkg a If a concentration were used such as it would be if aquatic organisms were being tested than the median response would be the LC50 2 If a sublethal response is being measured or alternatively we are measuring a biochemical or physiological response we could express the median response as an effective dose or concentration ED50 or EC50 3 Note that we could examine any proportion or percentage of response a For example if we were interested in 95 of the population responding we would examine the dose response relationship to estimate the LC95 if a series of concentrations were being tested b Similarly we might be interested in just the dose that gives 10 response LD10 C In addition to expressing the magnitude of population response as a relationship to dose we could express the response in relationship to time 1 In this case we might use a fixed dose or concentration and determine the time it takes to kill or adversely affect 50 of the population LT50 See below V example 2 Time to Die II How the DoseResponse Relationship Is Measured and Mathematically Deduced A Organisms reared under standard uniform conditions to minimize inter individual variability are divided into separate groups and then either dosed with a series of increasing concentrations or doses of toxicant by feeding by topical or dermal application by exposure to vapors etc One group is not exposed to toxicant 1 Thus the dose or concentration the different groups are exposed to is considered the independent variable in the experiment We have control over the independent variable and know its value magnitude prior to the start of the experiment 2 At each dose level observations of mortality or any other biological response are made These observations are the dependent variables Their values are ESRP531 Lecture 6doc Page 1 of 12 ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 unknown at the beginning of the experiment but they are measured in response to the known independent Variables B The data which are now expressed as number of organisms tested per dose and the number responding are fed into a computer program that can calculate one of two basic statistical techniquesiprobit analysis or logit analysis logistical regression l The computer program will estimate the response at any percentage of population response C Be aware that the resulting LDSO or LCSO for example is just a statistical estimate of the median response of the population under the conditions of the experiment 1 The number generated is not a fixed solid characteristic of the toxicant 39s interaction with the population of test organisms a If the experiment was repeated again a different estimate of LDSO or LCSO would be calculated owing to the natural Variation in response from each group of individuals tested 2 Thus in reality if we kept on repeating the experiment we would be measuring a population ofpotential responses of some specific leVel of response a Thus to know the likelihood that we have captured in our measurements the true population response the computer program also calculates confidence limits about each LD or LC estimate b In probit analysis these confidence limits are called 95 fiducial limits FL Adverse Response 95 Fl 100 7 Probit Tr 50 0 Dose Log Dose Figure 1 Doserresponse function arithmetic plot to show sigmoidal nature of curve left side and probit transformation using logarithmic dose right side along with 95 fiducial limits ESRP531 Lecture 6doc Page 2 of 12 ESRP 531 C Fundamentals of Environmental Toxicology Fall 2005 The significance of a 95 fiducial limit If the experiment was conducted 100 times than the 95 FL is predicted to capture within its interval the true population response at the specified dose 95 times Thus there is a 5 probability that the true population response is outside of this interval Because the fiducial limits are narrower meaning less variation in response about the median response ie the LD50 toxicologists usually rely on this parameter for expressing comparative toxicity Thus at the lower and higher levels of response a lot more variability is seen and the estimates of toxicity are less reliable 1 One can compare the toxicity of a toxicant to two or more populations by looking for overlap between the LC50 or LD50 of the tested populations 2 Similarly one can compare the in uence on toxicity response of any independent variable for example temperature effect pH effect second chemical in a mixture etc One would conduct a dose response experiment statistically estimate the LD50 or LC50 and then observe whether overlap has occurred about the LDLC50 for each independent variable tested D The threshold for toxicity can be estimated by mathematically extrapolating the dose response function through the dose at which no response has occurred or been measurable This corresponding threshold dose is the NOAEL or NOAEC Often however the NOAEL or NOAEC is estimated by Visual observation of which dose in the testing regime caused no significant difference in response compared to the undoes group ie the control group 1 IIIUsing the DoseResponse Relationship to Deduce Genetic Variation in a Population and Track Changes over Time The Value of the Slope of the Curve A For any single compound the slope of the dose response line helps determine the margin of safety Figure 2 Shallow slope allows greater margin of safety in other words comparatively larger changes in dose result in small changes in response Figure 2BD The slope also tells something about the variability in the population Figure 2B D 1 2 ESRP531 Lecture 6doc a This variation is actually the variation in response largely stemming from genetic variation leading to phenotypic variation within a given population A steep slope indicates little variation in the population response A comparatively shallower slope indicates that the response is much more variable over a greater dose range Page 3 of 12 ESRP 531 Fundamentals of Envhonmental Toxicology Fall 2005 A 0 Memo Response Meolan Response 3 3 E E l s s o o E E 6 r 6 o o l g l g r l 2 l 2 l l r l Dose Dosage Concentratlon Dase Dosage Concentratlan 03 B 8 i E 501 e e e e e e 50 9 l u a l E l 0 l Log Dose Log Doso Flgure 2 Relauonshrp between slope and varrabrhty dlsmbuuon of response of one or more populatrons to a slngle ohernroal orresponse of a slngle populauon to two dr erentohernroals or response of two dlfferent speores to a ohernroal B Two dlfferent speores nnghtrespond to a ohernroal wth the same LD50LC50 but the Vanauon m susoeptrbrlrty rnay dlffer substantrally Flgure ZA B Altgmauvely the LDso39s may be substantrally dlfferenL m addrtron to the Vanablllty belng dlfferenLFlgure ZC D c Note thatthe slope can also be used to assess the occurrence of resrstanoe m a populatron Populatrons name to a toxroantare falrly homogeneous m response As a toxroant selects torresrstantrndwrduals the mnablllty m response rnoreases dlsmbuuon flattens out and as seleouon oontrnues rnostrndwrduals wlll eventually become resrstant establrshrng a new homogenous dlsLnbuLlon but exhlblung a substantrally hlgher LD50 Flgure 3 ESRP531 Lecture 5 doc Page4 of 12 ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 Nu m bars Respon Sdit l g Dose Dosage Concentration ponae S ng i u sow390 E Gum ulatiue Ft Log Dose Figure 3 Change in susceptibility after repeated selection for resistant individuals IV Example 1 Computer Program and Output for Estimating LC50 A The following data represents the input and output to determine the LC50 for an organophosphate insecticide on codling moth neonate larvae B Experimental Procedure 1 2 3 4 The data was transferred to an Excel spreadsheet and than imported in a ESRP531 Lecture 6doc Insecticide was pipetted on leaf disks of known surface area Neonate codling moth n25 were placed on replicate leaf disks per dose 24 h and 48 h dead larvae were counted statistical program called SAS Statistical Analysis System Page 5 of 12 ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 5 After the toxicity parameters were estimated and printed out the data for the probability of mortality was plotted in a graphing program A SAS Statistical Analysis System Program for Estimating the LC50 ofan Insecticide on Treated Leaf Surfaces Against Codling Moth Neonate Larvae INPUT FILE Data Guthion1 Input Dose N Dead ObserveddeadN datalines 00000 43 02 00099 42 13 00198 50 35 00296 36 28 00395 48 43 Proc Probit LOG10 OPTC INVERSECL Model DeadNDose run39 OUTPUT FILE Probit Procedure Data Set WORKGUTH ION1 Dependent VariableDEAD Dependent VariableN Number of Observations 5 Number of Events 121 Number of Trials 219 Number of Events In Control Group 2 Number of Trials In Control Group 43 Log Likelihood for NORMAL 1001627644 Probit Procedure Variable DF Estimate Std Err ChiSquare PrgtChi LabelNaIue INTERCPT 1 533581127 087014 3760266 00001 Intercept Log10DOS1 292578526 05153 3223771 00001 Slope C 1 004566056 00314 Lowerthreshold Probit Model in Terms of Tolerance Distribution MU SIGMA 182372 0341789 Probit Procedure Estimated Covariance Matrix for Tolerance Parameters MU SIGMA C ESRP531 Lecture 6doc Page 6 of 12 ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 MU 0002272 0001592 0000500 SIGMA 0001592 0003624 0000277 C 0000500 0000277 0000991 Probit Procedure Probit Analysis on Log10DOSE Probability Log10DOSE 95 Percent Fiducial Limits Lower Upper 001 261884 312633 236712 002 252567 298501 229688 003 246655 289546 225221 004 242208 282817 221853 005 238591 277349 219108 006 235512 272699 216768 007 232813 268625 214712 008 230396 264981 212867 009 228197 261670 211187 010 226174 258625 209638 015 217796 246053 203188 020 211138 236113 198008 025 205425 227640 193512 030 200295 220089 189415 035 195542 213161 185549 040 191031 206671 181798 045 186667 200498 178061 050 182372 194563 174245 055 178077 188814 170242 060 173713 183221 165926 065 169202 177764 161140 070 164449 172414 155697 075 159319 167091 149372 080 153606 161626 141867 085 146948 155699 132675 090 138570 148669 120682 091 136546 147019 117738 092 134348 145242 114524 093 131931 143303 110974 094 129232 141156 106992 095 126153 138725 102432 096 122535 135891 097054 097 118089 132432 090415 098 112177 127868 081557 099 102860 120732 067538 Probit Procedure Probit Analysis on DOSE Probability DOSE 95 Percent Fiducial Limits Lower Upper 001 000241 000075 000429 002 000298 000104 000505 003 000342 000127 000559 ESRP531 Lecture 6doc Page 7 of 12 ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 004 000378 000149 000605 005 000411 000168 000644 006 000441 000188 000680 007 000470 000206 000713 008 000497 000224 000744 009 000522 000242 000773 010 000547 000259 000801 015 000664 000346 000929 020 000774 000435 001047 025 000883 000529 001161 030 000993 000630 001276 035 001108 000739 001395 040 001229 000858 001521 045 001359 000989 001657 050 001501 001133 001809 055 001657 001294 001984 060 001832 001472 002192 065 002032 001669 002447 070 002267 001887 002774 075 002552 002133 003208 080 002910 002420 003814 085 003393 002773 004712 090 004114 003261 006211 091 004311 003387 006647 092 004534 003528 007157 093 004794 003689 007767 094 005101 003877 008513 095 005476 004100 009455 096 005952 004376 010702 097 006593 004739 012469 098 007555 005264 015291 099 009363 006204 021117 The first graph below Figure 4 represents the plotted results arithmetic data from the second table above for Guthion azinphos methyl insecticide 100 80 r 60 lt gt M rt I39 o a Ity 4O I I gt LCo LC 20 5 0015 5 0055 0 5 0001 001 01 1 Concentration on Leaf Surface ngcmz Figure 4 Concentration response function for neonate codling moth on leaf disks treated With Guthion insecticide ESRP531 Lecture 6doc Page 8 of 12 ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 The second graph below Figure 5 represents analysis of data for a bioassay with Intrepid methoxyfenozide Note that not only is methoxyfenozide less toxic to neonate codling moth larvae than azinphos methyl but the slope of the line is somewhat atter Methoxyfenozide has an entirely different pharmacodynamics action than azinphosmethyl Also the slope of the line suggests greater genetic variability in susceptibility to methoxyfenozide than to azinphos methyl n n I I I n I u n I I u I n I I I n I I n n I I n n I I n I I u 80 39 39 60 39 39 n Mortality 4O 39 20 39 e Lcsn Lcss 39 0077 1130 E 0 u 0001 001 01 1 10 Concentration on Leaf Surface pgcmz Figure 5 Concentration response function for neonate codling moth on leaf disks treated with methoxyfenozide V Example 2 Time to Die the LTSO time of exposure before 50 of population respond Apple trees were sprayed with Guthion insecticide on both sides or only on one side to test the hypothesis that sufficient spray moves through a canopy to be lethal to codling moth larvae The rationale for this experiment is that perhaps only one side of a tree needs to be sprayed and therefore growers can use less insecticide and save money After the trees were sprayed leaves were collected and neonate codling moth larvae were exposed for vaiious time intervals over 120 minutes Numbers of dead larvae were counted after specified time intervals 15 30 60 90 120 minutes Untreated leaves were also assayed The first step is to make a table of the data Note that there was mortality in the untreated controls at some time intervals so the mortality in the treatments had to be corrected for this natural background To correct for control mortality Abbott s formula is a commonly used function Abbott WS 1925 A method of computing the effectiveness of an insecticide J Econ Entomol 18 265 267 Corrected Mortality Treatment Mortality Control Mortality100 Control Mortality 100 ESRP531 Lecture 6doc Page 9 of 12 ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 Raw Data Entered Into an Excel Spreadsheet for Calculation of Mortality and Correction for Mortality in the Control Untreated Leaves Number Total CONGCted Treatment Time Dead Number Mortality Mortality Untreated 15 0 48 00 Untreated 30 0 50 00 Untreated 60 2 46 43 Untreated 90 19 46 413 Untreated 120 22 46 478 Both Sides 15 1 49 20 20 Both Sides 30 20 49 408 408 Both Sides 60 36 49 735 723 Both Sides 90 42 48 875 787 Both Sides 120 45 49 918 844 One Side 15 5 49 102 102 One Side 30 13 49 265 265 One Side 60 25 49 510 488 One Side 90 34 47 723 529 One Side 120 40 43 930 866 Note that when preparing data for statistical analysis all observation for each replicate treatment should appear on the same line This is the most common format that modern statistical programs receive and handle data A probit analysis on the above data was run with the following results only the One Side treatment is shown in the output table below Calculated Data from Probit Analysis of Time to Mortality Experiment with Neonate Codling Moth Larvae Exposed to Trees Sprayed on One Side with Guthion Insecticide Probability Mortality TIME 95 Lower FL 95 Upper FL 001 1 523 946 270 002 2 379 753 154 003 3 287 630 80 004 4 219 538 24 005 5 163 463 22 006 6 115 400 61 007 7 73 344 95 008 8 36 295 126 009 9 01 250 154 010 10 30 208 180 015 15 160 38 289 020 20 263 95 377 ESRP531 Lecture 6doc Page 10 of 12 ESRP 531 Fundamentals of Environmental Toxicology Fall 2005 025 25 351 207 455 030 30 431 305 527 035 35 504 393 598 040 40 574 473 668 045 45 642 547 739 050 50 709 616 813 055 55 775 681 890 060 60 843 745 972 065 65 913 809 1058 070 70 986 874 1151 075 75 1066 942 1254 080 80 1154 1017 1369 085 85 1257 1103 1504 090 90 1387 1209 1676 091 91 1419 1235 1718 092 92 1453 1263 1764 093 93 1490 1293 1813 094 94 1532 1327 1869 095 95 1580 1366 1933 096 96 1636 1411 2008 097 97 1705 1467 2101 098 98 1796 1540 2223 099 99 1940 1656 2418 Note that probability represents the proportion of the tested population of insect larvae that has been estimated to die after the indicated time The probability was transformed to Mortality M by multiplying by 100 95 FL are fiducial limits analogous to confidence intervals that represent intervals likely to capture the true population mortalitytime response 95 per 100 times the experiment was conducted ie the probability of not capturing the true population response at any time interval would be 5 The calculations data along with the actual observed data points were graphed in a program called DeltaGraph Red Rock Software PC and MAC compatible and then edited for presentation using Corel Draw PC and MAC compatible Figures 6 and 7 From Figure 6 we can conclude that the LT50 for neonate larvae exposed to leaves from the unsprayed side of a tree is about 71 minutes This time to death for 50 of the population is about 17 minutes greater than the LT50 for larvae exposed to leaves from the sprayed side of the tree LT50 54 minutes Figure 7 However be aware of overlapping 95 Fiducial Limits At a probability of 5 we cannot resolve the difference between treatments in the observed distribution of larval responses ESRP531 Lecture 6doc Page 11 of 12 ESRP 531 Figure 6 Fundamentals of Environmental Toxicology Fall 2005 Calculated Probit Function 100 Mortality LT50 71 min 62 81 150 260 250 Time minutes The doseiresponse actually the timeiresponse function and associated 95 fiducial limits for neonate codling moth larvae exposed to leaves collected from the unsprayed side of an apple tree The values for the 95 fiducial limits are shown in parentheses adjacent to the LTSO of 71 minutes Calculated Probit Function lOO 90 y 80 3 i 732 Observed Mortality t o l S ra ed side oftree 2 501 p y g 40 o Unsprayed slde oftree 30 20 LT50 71 min 62 81 10 4 3 LT50 54 min 45 63 0 V 10 50 0 50 100 150 200 Time minutes Figure 7 Comparison of the timeiresponse function for treatment one sidequot sprayed and ESRP531 Lecture 6doc treatment both sidesquot sprayed Note the relative position of each function but beware of the overlapping fiducial limits Page 12 of12

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