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):

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
100%
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
Expert Solution
steps

Step by step

Solved in 6 steps with 1 images

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

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.

Solution
Bartleby Expert
SEE SOLUTION
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman