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I am conducting a study on patients with small follicles in their ovaries, diagnosed by ultrasound. Different drugs are administered to these patients, and they also have varying hormonal levels. After the last dose of the drug, we count the number of grown follicles using ultrasound. We define the ratio of "grown follicle count" to "total small follicle count before drug initiation" as FGR (Follicle Growth Ratio). I am interested in evaluating the effect of hormonal levels and drug types on FGR using an appropriate generalized regression model.

Intuitively, the FGR ratio should be lower than 1, but due to limitations of ultrasound assessment at the initiation, the number of grown follicles can sometimes exceed the number of small follicles, resulting in FGR values greater than 1. Additionally, there are instances where no small follicles are visible at the start, but a very small follicle that was initially undetectable may grow. In such cases, the FGR ratio can take the value of 1/0, which is +Inf.

I have excluded the very rare +Inf values from the FGR dataset. The histogram and distribution, generated using the Fitdistrplus package in R, are shown in the following images:

the distribution according to Fitdistrplus package in R

histogram of FGR

Now, I would like to know the proper way or model to analyze the effect of hormonal levels, while considering drug type as a confounding variable, on FGR or on the probability of a follicle to grow. If necessary, I am open to excluding the +Inf values from the FGR dataset.

Additionally, as the FGR ratio derived from patients with a higher count of small follicles at the treatment initiation is considered more valuable, I would like to explore the possibility of using a weighted approach based on the number of small follicles.

Any guidance or suggestions on the appropriate statistical approach or model to address this research question would be greatly appreciated.

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