Question

A randomized experimental study was conducted to evaluate the effectiveness of a new cancer vaccine. One-thousand healthy adults were randomized to receive either the new vaccine (500 adults) or the old vaccine (500 adults). The adults were followed for 10 years to monitor the incidence of colon cancer. At the end of the study, the risk ratio for developing colon cancer was 0.5 among the adults who received the new vaccine compared to adults who received the old vaccine. The 95% confidence interval for this relative risk was 0.2-0.8 and the p value was 0.01.

a. ) State in words your interpretation of the risk ratio. Be as descriptive as possible.

b.) State in words your interpretation of the p value. Be as descriptive as possible.

c.) State in words your interpretation of the 95% confidence interval. Be as descriptive as possible, and do not simply repeat the interpretation given in part b.

d.) Suppose that the same experimental study was conducted and that the same risk ratio was observed (RR=0.5) using a much larger population - -1,000 adults in each group instead of 500 in each group. Would the 95% confidence interval be narrower or wider in the study with 2,000 adults as compared to the study with 1,000 adults?

Answer 1

a) The risk ratio is given as probability of getting cancer given they were on new vaccine upon probability of getting cancer given they were on old vaccine. The risk ratio of means that their is no effect on(no diffrence) in patients getting cancer whether they were on new vaccine or old vaccine. If the risk ratio is greater than one then the risk of cancer is higher and if the risk ratio is less than one then the risk of cancer is lower in the new vaccine group.

b)

The p value denotes the probability of getting the observed association due to chance alone. The higher the p-value, the higher the chance of getting the association due to purely chance. Therefore to conclude that the association is significant the p-value must be small.

c) The 95% confidence interval tells that, we are 95% confidence that the risk ratio is between 0.2-0.8. If we draw 100 such samples then 95 of the times the risk ratio will fall between 0.2-0.8.

d) If same risk ratio is observed for larger population (1000 adults in each group instead of 500 adults). Therefore the 95% confidence interval be narrower. The confidence interval gets smaller as the number of samples increase.