In many clinical experiments a random number of severity measurements are collected on an experimental unit. We refer to data arising from such experiments as multivariate random length data. Often, in data of this type, both the number of measurements as well as the severity of each measurement inform on treatment effect. Consider two examples: In a cardiovascular clinical trial both the number of arterial blockages as well as the degree of occlusion of each blockage is informative on the performance of a cholesterol lowering medication; In a reproductive toxicology study each fetus from a litter of random size is assessed for developmental abnormalities, both the number of fetuses as well as the developmental status of each fetus can inform on the effect of a toxin. We present both parametric and semi parametric models for such ``random length" data and use these models to effectively incorporate information from both event frequency and severity. We conduct simulation studies and apply these methodologies to data examples from cardiology and toxicology studies.
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