# Dose Response Curve (log logistic regression)

#### hlsmith

##### Not a robit
Hey,

I had someone ask me if I could create a dose response curve for them. They have a dose amount and associated response which is a time to event. I believe everyone will have an event, so I have a continuous response value to work with (but I have a feeling there will only be 2-3 dose amounts - e.g., 1.2, 1.4, 1.6). I have not seen these data yet. Last part is they have subgroupings, say males/females and also other drugs with comparable data (dose, time).

I have not met with the person, but I wouldn't be surprised if they want me to calculate dose response curves for subgroups or compare response curves between groups. A quick look showed these data are usually analyzed with log logistic model. I was going to see if anyone had some insights or references. I can post example data when I get them, but I imagine it will be like the following with few dose amounts and with multiple units per dose amount. Also each unit is unique, these aren't repeat measures.

does response
1.2 123
1.2 134
1.4 100
1.4 90

@Miner
@rogojel
@GretaGarbo
Do you all have any experience with such data?

#### GretaGarbo

##### Human
They have a dose amount and associated response which is a time to event.
I had never heard of log logistics distribution. (So, thanks!) (Here is the wiki page I looked at.) But maybe you should look at other distributions used in survival analysis.

If they want a dose response curve, I would suggest to take more levels of doses, say six or more.

#### hlsmith

##### Not a robit
I am watching this useR video (below), and from it and another source, it seems like the log logistic model is the go to method. I will post more once I learn about it. But this is a clipped image.

#### GretaGarbo

##### Human
I don’t understand this. What is the log-logistics used for?

It can either be used as a distribution for the time to event, given that the dose is e.g. 1.4. (Just like given that x=1.4 the distribution of Y will be normal. Just like in the usual anova.)

OR it (the log-logistics formula) is used as a description of the dose response relationship, like when the x increases the expected value of Y will follow the logistic equation (or the log-logistic equation).

#### hlsmith

##### Not a robit
Yes, the latter - to describe characteristics of a dose response relationship. After applying it to relationships you can make comparisons between exposures agent.

#### ondansetron

##### TS Contributor
I would look at Agresti's Categorical Data Analysis 3rd edition (978-0470463635). Chapter 8 discussed cumulative logit proportional odds (example 8.2.4 "Happiness") and continuation-ratio logit (example 8.3.7 "developmental toxicity") and these may be useful for you to look at depending on the actual nature of the study.