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SURVIVAL OF PATIENT It is of interest to determine whether a patient will survive a disease given a dosage level of a treatment. Given below is the summary of the dosage levels, number of individuals who received each dose level, & the number of individuals who survived the disease. Dose No. of Individuals No. of individuals who survived 10 20 30 40 50 60 R codes with Software output: 96 115 105 99 > shapiro.test (dose) 111 102 Shapiro-Wilk normality test > lm (ye-logdose) data: dose W = 0.98189, p-value = 0.9606 Coefficients: (Intercept) 2.122 Call: Im(formula = ye ~ logdose) 17 25 23 29 51 78 logdose 1.679 a. Compute for the percentage of individuals who survived the disease for each dose level. b. Compute the log of each dose level. C. Determine the empirical probits (ye) for estimating LD50. Finney's table is shown below (Finney, 1952):

SURVIVAL OF PATIENT It is of interest to determine whether a patient will survive a disease given a dosage level of a treatment. Given below is the summary of the dosage levels, number of individuals who received each dose level, & the number of individuals who survived the disease. Dose No. of Individuals No. of individuals who survived 10 20 30 40 50 60 R codes with Software output: 96 115 105 99 > shapiro.test (dose) 111 102 Shapiro-Wilk normality test > lm (ye-logdose) data: dose W = 0.98189, p-value = 0.9606 Coefficients: (Intercept) 2.122 Call: Im(formula = ye ~ logdose) 17 25 23 29 51 78 logdose 1.679 a. Compute for the percentage of individuals who survived the disease for each dose level. b. Compute the log of each dose level. C. Determine the empirical probits (ye) for estimating LD50. Finney's table is shown below (Finney, 1952):

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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SURVIVAL OF PATIENT It is of interest to determine whether a patient will survive a disease given a dosage level of a treatment. Given below is the summary of the dosage levels, number of individuals who received each dose level, & the number of individuals who survived the disease. Dose No. of Individuals 10 20 30 40 50 60 R codes with Software output: SA No. of individuals who survived > shapiro.test (dose) 96 115 105 99 111 102 Shapiro-Wilk normality test > lm (ye~logdose) data: dose W = 0.98189, p-value = 0.9606 Coefficients: (Intercept) 2.122 Call: Im(formula = ye~ logdose) 17 25 23 29 51 78 logdose 1.679 a. Compute for the percentage of individuals who survived the disease for each dose level. b. Compute the log of each dose level. C. Determine the empirical probits (ye) for estimating LD50. Finney's table is shown below (Finney, 1952):
Transcribed Image Text:SURVIVAL OF PATIENT It is of interest to determine whether a patient will survive a disease given a dosage level of a treatment. Given below is the summary of the dosage levels, number of individuals who received each dose level, & the number of individuals who survived the disease. Dose No. of Individuals 10 20 30 40 50 60 R codes with Software output: SA No. of individuals who survived > shapiro.test (dose) 96 115 105 99 111 102 Shapiro-Wilk normality test > lm (ye~logdose) data: dose W = 0.98189, p-value = 0.9606 Coefficients: (Intercept) 2.122 Call: Im(formula = ye~ logdose) 17 25 23 29 51 78 logdose 1.679 a. Compute for the percentage of individuals who survived the disease for each dose level. b. Compute the log of each dose level. C. Determine the empirical probits (ye) for estimating LD50. Finney's table is shown below (Finney, 1952):
Table 3.2 Transformation of percentages to probits 1 2 3 4 5 6 7 8 9 % 0 0 2.67 2.95 3.12 3.25 3.52 3.59 3.66 10 3.72 3.77 3.82 3.87 3.92 4.05 4.08 4.12 4.26 4.29 40 3.36 3.45 3.96 4.01 20 4.16 4.19 4.23 4.33 4.36 4.39 4.42 4.45 30 4.48 4.50 4.53 4.50 4.59 4.61 4.64 4.67 4.69 4.72 4.75 4.77 4.80 4.82 4.85 4.87 4.90 4.92 4.95 4.97 50 5.00 5.03 5.05 5.08 5.10 5.13 5.15 5.18 5.20 5.23 60 5.25 5.28 5.31 5.33 5.36 5.39 5.41 5.44 5.47 5.50 70 5.52 5.55 5.58 5.61 5.64 5.67 5.71 5.74 5.77 5.81 80 5.84 5.88 5.92 5.95 5.99 6.04 6.08 6.13 6.18 6.23 90 6.28 6.34 6.41 6.48 6.55 6.64 6.75 6.88 7.05 7.33 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 99 7.33 7.37 7.41 7.40 7.51 7.58 7.65 7.75 7.88 8.09 Ref:http://userwww.sfsu.edu/efc/classes/biol710/probit/ProbitAnalysis.pdf d. Fit a linear regression model using the empirical probit as the dependent variable and the log dose level as the independent model - that is, set-up your probit model. d. Estimate LD50 using the model constructed. NOTE: For items requiring test of hypotheses, specify the null & alternative hypothesis in words, test procedure, p-value, decision, & conclusion. Use α=0.05
Transcribed Image Text:Table 3.2 Transformation of percentages to probits 1 2 3 4 5 6 7 8 9 % 0 0 2.67 2.95 3.12 3.25 3.52 3.59 3.66 10 3.72 3.77 3.82 3.87 3.92 4.05 4.08 4.12 4.26 4.29 40 3.36 3.45 3.96 4.01 20 4.16 4.19 4.23 4.33 4.36 4.39 4.42 4.45 30 4.48 4.50 4.53 4.50 4.59 4.61 4.64 4.67 4.69 4.72 4.75 4.77 4.80 4.82 4.85 4.87 4.90 4.92 4.95 4.97 50 5.00 5.03 5.05 5.08 5.10 5.13 5.15 5.18 5.20 5.23 60 5.25 5.28 5.31 5.33 5.36 5.39 5.41 5.44 5.47 5.50 70 5.52 5.55 5.58 5.61 5.64 5.67 5.71 5.74 5.77 5.81 80 5.84 5.88 5.92 5.95 5.99 6.04 6.08 6.13 6.18 6.23 90 6.28 6.34 6.41 6.48 6.55 6.64 6.75 6.88 7.05 7.33 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 99 7.33 7.37 7.41 7.40 7.51 7.58 7.65 7.75 7.88 8.09 Ref:http://userwww.sfsu.edu/efc/classes/biol710/probit/ProbitAnalysis.pdf d. Fit a linear regression model using the empirical probit as the dependent variable and the log dose level as the independent model - that is, set-up your probit model. d. Estimate LD50 using the model constructed. NOTE: For items requiring test of hypotheses, specify the null & alternative hypothesis in words, test procedure, p-value, decision, & conclusion. Use α=0.05
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Fit a linear regression model using the empirical probit as the dependent variable and the log dose level as the independent model – that is, set-up your probit model. What would be the visual Linear regression Models of c and d.

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