Question

In the United States, among a representative group of 6,006 white men and 1,126 black men aged 70–79 years at diagnosis with stage IV prostate cancer, 2,337 whites and 344 blacks were alive after 5 years of follow-up. Compare the white and black patient survival at 5 years.

Answer 1

The table to represent the data given in problem is as shown below:

Survival

Race Survived Not Survived

White 2337 3669

Black 344 782

The formula and computation of risk ratio is as follows:

Since,is the number of whites not alive after five years, it is calculated by subtracting survived whites from total number of whites. Similarly, calculateby subtracting survived number of blacks from total.

Thus, the risk ratio is. It means that white men diagnosed with stage IV prostate cancer in the age range 70-79 years are 1.27 times or 27% more expected to survive 5 years after diagnosis than black men.

To determine the, apply the steps of hypothesis testing for this cohort study as follows. The value ofis calculated as:

The null hypothesis is written below:

The alternative hypothesis is written below:

The formula and computation ofatlevel of significance with 1 degree of freedom and is as shown below:

Thus, the value ofis. From theDistribution values table given in the appendix, the critical value is 3.84, since it is less than the calculated value, reject and conclude that there is an association between group of men diagnosed with stage IV prostate cancer aged 70-79 and survival after 5 years.

The formula and calculation of 95% confidence interval for the risk ratio is given is as shown below:

Thus, the 95% confidence interval for the prevalence ratio is.

Since the 95% confidence interval does not contain 1, it can be concluded that there is a statistical association between group of men diagnosed with stage IV prostate cancer aged 70-79 and survival after 5 years.