MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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):
expand button
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
expand button
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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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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