What is a reasonable type of model to fit these data? Write out the model, and explain what the terms mean?

Ophthalmology

Data were collected on TBUT, a measure of how long it takes for tears to form. This is a commonly used measure to assess dry-eye patients, with a smaller number indicating more severe disease. One issue is how reproducible this measure is. For this purpose, replicate values of this measure were obtained from the right eye of 14 dry-eye patients 5 minutes after instillation of a placebo drop. The data for the first 7 patients are given in Table 12.45.

Table 12.45 loge (TBUT) obtained 5 minutes after instillation of a placebo drop (seconds)

 

Assume overall that the ln_e (TBUT) is approximately normally distributed. The sd [ln_e (TBUT)] over the 14 observations) is 0.459.

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Mean (7,) Replicate 1 Replicate 2 1.57 1.87 1.72 2,55 2.59 2.51 2.53 2.82 2.675 2.14 1.34 1.74 2.00 2.28 2.14 1.50 1.70 1.60 2.39 2.365 2.36 overall mean (7) 2.113