One method to estimate the amount of sodium excreted each day is via a morning urine sample test based on the so-called Kawasaki formula . O'Donnell et al. (2011) report the findings of a longitudinal study incorporating the participants in two separate, but comparable, clinical trials involving subjects who were deemed susceptible to cardiovascular disease (CVD). All the subjects included in the study provided a urine sample from which the amount of sodium excreted per day was estimated. Subjects were then monitored over a period of around five years, with any health issues arising being recorded. We focus here on the number of deaths due to CVD. Suppose the data in the study were as follows:



M. J. O'Donnell, S. Yusuf, A. Mente, P. Gao, J. F. Mann, K. Teo, M. McQueen, P. Sleight, A. M. Sharma, A. Dans, J. Probstfield, R. E. Schmieder (2011): Urinary Sodium and Potassium Excretion and Risk of Cardiovascular Events. Journal of the American Medical Association 306 , No.20, 2229-2238.

Part a) If modelling the number of deaths due to CVD in one of the seven levels of estimated daily sodium excretion, which probability distribution would be most useful?








Part b) Assuming a sensible model for the number of deaths within each of the seven levels of estimated daily sodium excretion, how many free parameters would be required to model the data?


Part c) It is of interest to test the null hypothesis that the chances of death by CVD are the same in each of the seven levels of estimated daily sodium excretion. Under such an assumption and a reasonable model for the data above, how many free parameters are required?


Part d) Compute Pearson's test statistic here, giving your answer to two decimal places.


Part e) If testing the null hypothesis at the 5% significance level, what would you conclude?





You can earn partial credit on this problem.