Assignment III for Biostats Course VHM 801 at AVC - Fall semester 2020

The assignment is worth 15% of the final course mark. Please be aware that by handing in the home assignment you implicitly acknowledge to have read and accepted the instructions for home assignments as described on the VHM 801 homepage. Recall that all solutions should be accompanied by text explaining the procedures used; in particular, all statistical models and assumptions should be specified. The level of detail provided should at least conform to the main principles of the recommendations for statistical reporting, as discussed in the course.

The data for the assignment are from an older study carried out among breeders of German shepherd dogs in Denmark. Hip dysplasia (HD) is a quite common and hereditary disease among dogs of this breed, and it is important to monitor the occurrence of the disease in breeding programs. One type of monitoring uses X-ray diagnostics for young dogs to assess their predisposition to HD, based on evaluation of X-rays by a panel of trained personnel. For simplicity, we will refer to this outcome as the HD-status (of a young dog). Over two consecutive years, data were obtained for the offspring of 3 dogs (sires). Some changes were undertaken in the panel of X-ray assessors, so it was of particular interest to compare data from these two years. It was also of interest to compare the sires.

The data are shown in the table below; no data file is provided so you will have to set up the data for the software yourself (note: it may be easiest to use different datasets for different questions).

	Year 1		Year 2
	HD-status of offspring		HD-status of offspring
Dog (sire)	negative	positive	negative	positive
Caesar	109	84	42	52
Quatro	19	17	36	24
Obelix	24	8	52	20

The following four questions should all be answered (and have approximately equal weight).

1. When making decisions about sires in a breeding program, it is of interest to know not only estimated proportions of offspring predisposed to HD but also to know approximate ranges of these parameters (because substantial differences in the number of offspring tested may lead to quite different ranges). Use the data for year 1 to estimate, with a 99% interval, the proportion of offspring predisposed to HD for each of the sires.
   
   
2. Relevant and more recent data indicate the proportion of young German shepherd dogs with positive HD-status based on this type of X-ray evaluation to be about 37%. Use the data of the study to compare each of the three sires to the present level of disease, and discuss what conclusions may be drawn from this comparison. You may assume that the HD diagnostic and evaluation procedure of year 2 is the one most similar to recent procedures.
   
   
3. For the data of the first year, examine whether any differences between the HD-status seem to exist between the offspring of the three sires. Carry out a similar analysis for the data of the second year, and draw conclusions.
   
   
4. The primary purpose of the study was to assess whether the changes in the panel of assessors were noticeable in the HD assessments. Use statistical test(s) to examine whether this seemed to be the case.
   (Hint: For this question you have a choice between analysing the dogs combined or separately. No matter which method you choose, make sure to include your arguments for your chosen method. As the statistical approach to the choice of method is beyond the coverage in the course (and the textbooks), you are expected to base your choice only on your common sense and the information the previous questions and simple tabulations of the data give you.)