# Trend analysis with non-binary variable

#### zihuatanejo

##### New Member
Hi, I have a data set where I have a number of organs that fall into 5 treatment groups. These treatment groups can be organized based on increasing dose (0, 1, 2, 3, 4), with 0 being my vehicle or placebo control. I have about 10 organs per treatment group. I then have 6 different characteristics that have been measured in the organs. So for each ovary, I have a % occurrence of each characteristic.

What I'm trying to do, for a given characteristic, is test to see if there is a significant trend for increasing occurrence with increase dose. I've never done this sort of analysis before, so looking for some suggestions. I stumbled upon the Cochrane-Armitage Trend Test, which seems to be just what I'm looking for, except my result variable needs to be binary - ie, yes/no. Instead, my response variable for each characteristic is a percentage, somewhere from 0-100%.

I've compared each group to the placebo individually with an ANOVA, but was looking to add in this analysis as well. Any feedback would be greatly appreciated. Thanks!

#### mmercker

##### Member
Hi, are the dose-values on a continuous scale? I.e., is dosis 4 really 4 times the amount of dosis 1? In this case you can take for each characteristic all values of this characteristic from the different participants, and make a linear regression with the dose as predictor and the characteristic as outcome. If the outcome is approximately normally distributed, you can use simple linear regression, if not, it is a little bit more complicated: If the percentage outcome is based on counts (i.e., you can express it in terms of "number of success for a number of trials"), you would choose a Generalized Linear Model (GLM) with a Binomial distributed stochastic part, if your percentage outcome is continuos (i.e. percentage of cream in milk), beta-regression would be a common choice.

If your dose is only ordinal (i.e., you can only say that dose 3 is more than dose 2) you would use an ANOVA which allows for trend analysis, since your outcome is probably not normally distributed, the Jonckheere-Terpstra Test would be appropriate

#### zihuatanejo

##### New Member
Hey, I think so. So Dose 2 is 10 times Dose 1, Dose 3 is 10 times Dose 2, etc. All one order of magnitude off from each other.

In terms of the outcome variable, it is based off of counts. So there are 6 outcome variables, and in total, they will add up to 100% for each organ of interest. We get there by doing raw counts of multiple slides from each organ - so there is no upper limit - we don't stop at say, 100. We count everything on every slide and then use the total count for that particular organ to generate the %s for each outcome for that organ.

Does that make sense? I think all my outcome variables are normally distributed, or I was able to normalize them without too much difficulty. I'm only looking at one outcome at a time, so a change in outcome 1 based on treatment - even though outcome 1 is by default associated with outcomes 2-6. So I don't think it should matter that some are normalized vs others being not.

So it sounds like perhaps beta-regression? I can do some reading up on how I'd go about that - not familiar to me. PROC NLMIXED?

Thanks for the help!!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I think it may help us to ensure we know what you are planning, if you can now try to rephrase the question and then put it in a model equation.

y = beta

and define these terms and how they are formatted.