jamesmartinn11
03-13-2010, 11:21 AM
Five different doses of an insecticide were applied under standardized conditions to samples of an insect species. The data were:
Dose (ml/ g): 2.6 3.8 5.1 7.7 10.2
Number killed: 7 16 20 48 54
Total number of insects: 60 60 59 57 60
Use SAS to fit a logistic regression model which says that the logit of the chance of death increases linearly with the natural log of dose of insecticide. Answer the following questions:
1) Calculate the predicted probability of death at a dose of 6 ml/G
2) Estimate the dose for which there is a 50% kill rate
3) Give an approximate 95% likelihood-ratio confidence interval for B. Translate this interval into an interval for the effect on the odds of death of increasing the dose by 50% (i.e. multiplying the dose by 1.5) and interpret. Hint: First translate the multiplying dose factor to the log scale
4) Set up an approximate 95% confidence interval for the rate of change of the chance of death per unit increase in ln concentration at the median effective level.
Answers:
My Alpha estimate was: -5.5811. My Beta estimate was 3.3364. SE of Beta estimate = .3690
1) pi(x) = 1 / (1+e^(-(-5.5811 +3.3364*LnDose)))
Since its asking for a dose of 6 ml/g, I took ln(6) = 1.79175947.
pi(1.79175947) = 1 / (1+e^(-(-5.5811 +3.3364*1.79175947))) = .596948946
Therefore, the predicted probability of insect death at a dose of insecticide equal to 6 mg/l is about 59.69%
2)
EL50 = -alpha/beta = -(-5.5811)/3.3364 = 1.67279103
e^(1.67279103) = 5.32701493
Therefore, a dose of insecticide of about 5.327 mg/l will result in a 50% probability of insect death.
3) The likelihood-ratio confidence interval for B = (2.6478, 4.0989). I'm not sure how to proceed, I'm getting confused with the logarithms and what not.
4) Not sure.
Please help!
Thanks in advance!
Dose (ml/ g): 2.6 3.8 5.1 7.7 10.2
Number killed: 7 16 20 48 54
Total number of insects: 60 60 59 57 60
Use SAS to fit a logistic regression model which says that the logit of the chance of death increases linearly with the natural log of dose of insecticide. Answer the following questions:
1) Calculate the predicted probability of death at a dose of 6 ml/G
2) Estimate the dose for which there is a 50% kill rate
3) Give an approximate 95% likelihood-ratio confidence interval for B. Translate this interval into an interval for the effect on the odds of death of increasing the dose by 50% (i.e. multiplying the dose by 1.5) and interpret. Hint: First translate the multiplying dose factor to the log scale
4) Set up an approximate 95% confidence interval for the rate of change of the chance of death per unit increase in ln concentration at the median effective level.
Answers:
My Alpha estimate was: -5.5811. My Beta estimate was 3.3364. SE of Beta estimate = .3690
1) pi(x) = 1 / (1+e^(-(-5.5811 +3.3364*LnDose)))
Since its asking for a dose of 6 ml/g, I took ln(6) = 1.79175947.
pi(1.79175947) = 1 / (1+e^(-(-5.5811 +3.3364*1.79175947))) = .596948946
Therefore, the predicted probability of insect death at a dose of insecticide equal to 6 mg/l is about 59.69%
2)
EL50 = -alpha/beta = -(-5.5811)/3.3364 = 1.67279103
e^(1.67279103) = 5.32701493
Therefore, a dose of insecticide of about 5.327 mg/l will result in a 50% probability of insect death.
3) The likelihood-ratio confidence interval for B = (2.6478, 4.0989). I'm not sure how to proceed, I'm getting confused with the logarithms and what not.
4) Not sure.
Please help!
Thanks in advance!