ENV U6220 THURSDAY, 7/14/05 – LAB #1: HAZARD IDENTIFICATION PAGE 1 Name: _____________________________________Lab 1:Quantitative Analysis of the Implications of Uncertainty in Hazard IdentificationThis lab is based on a recent publication of Dr. Ennever’s, “Implications of the lack of accuracy of the lifetime rodent bioassay for predicting human carcinogenicity”, by Fanny K. Ennever and Lester B. Lave, Regulatory Toxicology and Pharmacology 38 (2003) 52–57.Please fill in all the blanks below and hand this in as your lab report. A few questions require the use of a calculator. You may work with others on all parts of the lab except the final essay, whichmust be your own work. I. Read the article.II. Examine the following concepts concerning test accuracy:REAL STATENEGATIVE POSITIVETEST RESULTNEGATIVE True Negative (TN) False Negative (FN)POSITIVE False Positive (FP) True Positive (TP)Prevalence = Percentage of real positivesSensitivity =Number of true positive resultsNumber of true positives plus false negativesSpecificity =Number of true negative resultsNumber of true negatives plus false positivesIII. Answer the following 8 questions (the last one is an essay):1. In the task described in the paper, the “test” is the lifetime rodent bioassay (LRB) and the “real state” is human carcinogenicity. What are the two different definitions offered in the paper for “a positive test result”? [the second (harder) answer has been filled in foryou]i. LRB is positive if _____________________________________________________; using this definition, ______ of all chemicals are positive in the LRBii. LRB is positive if rats and mice both give a positive result (trans-species carcinogen); in this definition, 6.8% of all chemicals are positive in the LRBENV U6220 THURSDAY, 7/14/05 – LAB #1: HAZARD IDENTIFICATION PAGE 2 2. Fill in the following blanks with the appropriate numbers from the paper for the two differentdefinitionsi. Of the _____ known human carcinogens, LRB is positive in ____, giving a sensitivityequal to _______ii. Of the _____ known human carcinogens, LRB is positive in ____, giving a sensitivityequal to _______3. The information value of a test depends on sensitivity, specificity and prevalence. The paper states: “Specificity cannot be estimated directly, because epidemiologic studies can only givean upper limit on potency, not prove a lack of carcinogenic effect”. Explain this in your own words:4. “Prevalence”, in the task described in the paper, is the percentage of actual human carcinogens among all chemicals. Explain why we do not know this number:ENV U6220 THURSDAY, 7/14/05 – LAB #1: HAZARD IDENTIFICATION PAGE 3 5. Tables 2 and 3 in the paper illustrate the calculation of RLB performance with an assumed prevalence. The first table below is an expansion of paper Table 2 with explanations:HUMAN CARCINOGENNO YES TOTALLRBTESTRESULTNEGATIVE 77h1d78fPOSITIVE 13g9c22eTOTAL 90b10a100aAssumed prevalence = 10% (see paper Table 2 legend and NOTE* below)bIf 10% of 100 chemicals are actually human carcinogens, then 90 are notcSpecificity is 90% (definition i, see answer in 1.i.) so 9 out of 10 human carcinogens are positive (true positives)dThe other human carcinogen is negative (false negative)eIn definition i, 22% of all chemicals are positive in the LRB (see your answer in 1.i.)fAnd so 78% of all chemicals are negative in the LRBgThe number of false positives must be 13 because the sum of false positives and true positives (9) is equal to the total number of positives (22) hThe number of true negatives must be 77 because  the sum of the true negatives plus false positives (13) must be equal to the total number of human noncarcinogens (90) the sum of the true negatives plus false negatives (1) must be equal to the total number of chemicals negative in the LRB (78)The specificity is a result of these calculations; in this case, the specificity is 77/90 = 85%ENV U6220 THURSDAY, 7/14/05 – LAB #1: HAZARD IDENTIFICATION PAGE 4 To make sure you understand this, fill in the explanations for paper Table 3:HUMAN CARCINOGENNO YES TOTALLRBTESTRESULTNEGATIVE 90.7h2.5d93.2fPOSITIVE 4.3g2.5c6.8eTOTAL 95b5a100abcdefghSpecificity = *NOTE: The prevalence is not known (see your answer to question 4), but we can know the minimum (zero) and the maximum. The maximum possible prevalenceis set by the fact that the specificity cannot exceed 100%. This maximum prevalence is about 25% for definition i and 13% for definition ii (trust me on this). The choices of 10% and 5% seemed like reasonable mid-point values to present; paper Figures 1 and 2 are the graphs of the results for all possible prevalences.ENV U6220 THURSDAY, 7/14/05 – LAB #1: HAZARD IDENTIFICATION PAGE 5 6. Remember, if we are looking at a test result from the LRB, all we know is whether the test result is positive or negative, and we do not know which of the positives are true positives andwhich are false positives, and we do not know which of the negatives are true negatives and which are false negatives. We must compare our new knowledge to what we knew before the ($2,000,000) test: for an untested chemical, its chance of being a human carcinogen is equal tothe prevalence.The tables below have an added column “% Real Positives”, which represents the percentage of the LRB negative or positive chemicals that are actually human carcinogens. Fill in the blank column in the second table below:i HUMAN CARCINOGEN% REALPOSITIVESNO YES TOTALLRBTESTRESULTNEGATIVE 77 1 78 1.28%POSITIVE 13 9 22 40.9%TOTAL 90 10 100ii HUMAN CARCINOGEN% REALPOSITIVESNO YES TOTALLRBTESTRESULTNEGATIVE 90.7 2.5 93.2POSITIVE 4.3 2.5 6.8TOTAL 95 5 100Calculate the factor increase or decrease from the prevalence and summarize your results:Definition i:A positive LRB result increases the chance of human carcinogenicity from 10% to _____, a factor of _______A negative LRB result decreases the chance of human carcinogenicity from 10% to _____, a factor of _______Definition ii:A positive LRB result increases the chance of human carcinogenicity from 5% to _____, a factor of _______A negative LRB result decreases the chance of human carcinogenicity from 5% to _____, a factor of _______ENV U6220 THURSDAY, 7/14/05 – LAB #1: HAZARD IDENTIFICATION PAGE 6 7. The comparison between definitions i and ii shows the inevitable trade-off between sensitivity and specificity. If we have a chemical that causes cancer in mice but not