How Do You Interpret Logistic Regression Output and Translate Dose Effects?

[jamesmartinn]

Hello all, I've performed a simple logistic regression and could use some help in interpretations/minor calculations.

Five different doses of insecticide were applied under standardized conditions to samples of an insect species. The data were:

Dose: ---2.6---3.8---5.1---7.7---10.2---
Dead: ----7----16---20----48----54----
Total: ---60----60---59----57----60---

So I was asked to fit a logistic regression model that says the logit of chance of death increases linearly with the natural logarithm of dose (ml/G). So, I did a ln transformation of the dose variable, and then proceeded with the logistic regression.

Some important output from the analysis:

Beta_hat = 3.3364
95% Likelihood Ratio Confidence Interval for Beta = (2.6478, 4.0989)This is pretty much a multi-step type question... I've answered questions a) through f), but I am getting really confused on questions g) and h)

Here are the questions, verbatim.

g) Given 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% (ie., multiplying the dose by 1.5) and interpret. Hint: First translate the multiplying dose factor to the natural log scale.

For this question, I've been going with this interpretation.

e^Beta_hat = e^3.3364 = 28.12. Thus, for a one-unit increase in the log dose, there is a 28.12 multiplicative effect on the odds in favor of insect death. I'm just having trouble proceeding with the next parts...logarithms and all.

I need help converting the interval so I can say something like this. For a 50% increase in Dose (Not Log dose), there is a ___ multiplicative effect on the odds in favor of insect death, CI (___, ____)

h) Setup an approximate 95% CI for the rate of change of the chance of death per unit increase in log concentration at the median effective level.

Any help would be great. Like I said, its just these last two questions that are really confusing me.

Cheers

 

[mmwave]

Hello,

Based on the information provided, it appears that you have correctly performed the initial steps of fitting a logistic regression model and calculating the beta_hat and confidence interval. To answer your questions g) and h), you will need to use the information from the output and apply it to the specific scenarios given.

For question g), you are asked to interpret the confidence interval for the effect on the odds of death of increasing the dose by 50%. In order to do this, you will need to first translate the multiplying dose factor of 1.5 to the natural log scale.

To do this, you can use the fact that ln(1.5) = 0.4054. This means that a 50% increase in the dose corresponds to a 0.4054 increase in the natural log of the dose. Now, using the beta_hat and confidence interval from your output, you can calculate the corresponding interval for the effect on the odds of death.

To do this, you can use the formula e^(beta_hat + 0.4054) to get the upper bound of the interval and e^(beta_hat - 0.4054) to get the lower bound. This will give you the interval for the odds ratio, which you can then interpret as the multiplicative effect on the odds of death.

For question h), you are asked to set up an approximate 95% confidence interval for the rate of change of the chance of death per unit increase in log concentration at the median effective level. The median effective level is the point at which the logit of the chance of death is equal to 0.5, which corresponds to an odds ratio of 1.

To set up the interval, you can use the formula (beta_hat + or - 2 * standard error), where the standard error can be found in your output. This will give you an approximate interval for the rate of change, which you can then interpret as the slope of the line.

I hope this helps clarify the last two questions for you. Let me know if you have any further questions or need any additional assistance. Best of luck with your analysis!