Question

Another team of investigators reviewed medical records to determine which military personnel among several basic training units had received a previous type of meningitis vaccine during training two decades ago. Two study groups were formed, those who had not received the vaccine and those who had. These were followed forward by record review throughout the duration of their active military service, and if they had a record of care through the VA system, these records were searched as well. The outcome of interest was the occurrence of any of a number of autoimmune diseases that were thought to have a possible association with the vaccine. In this study, of a vaccine group of 70, 4 individuals were found to have been diagnosed with lupus at some subsequent point in time. In the non-vaccine group of 105, only 2 individuals had that diagnosis

a. What is the independent variable in this scenario, and what type is it? What is the dependent variable in this scenario, and what type is it?

b. State a null hypothesis

c.  What is the most appropriate measure of association to compare the rates of occurrence of autoimmune disease between the two groups and Why? Calculate that measure of association

d. What is the most appropriate statistical test of significance of this measure of association and Why?

Answer 1

a) Here the independent variable is the meningitis vaccine, that is , whether the military personnel received vaccine or not. It is of nominal type(qualitative). The predictor variable is the occurence of any autoimmune diseases. It is also nominal type variable. Both the variables can also be said to be a dichotomous variable taking yes or no values.

b)The primary interest is to see whether the occurrence of any of a number of autoimmune diseases were thought to have a possible association with the vaccine. So, here we would like to test whether the vaccinated and the non-vaccinated personnels are independent of the occurences of autoimmune diseases. This is our null hypothesis.

c)Here, we have the 2x2 contingency table as:

	Vaccinated	Not vaccinated	Total
Occurence	4=$f_1_1$	2=$f_1_2$	6=$f_1_0$
Non-occurence	66=$f_2_1$	103=$f_2_2$	169=$f_2_0$
Total	70=$f_0_1$	105=$f_0_2$	175=$f_0_0$

Cramer's coefficient of Association (given below) is the appropriate measure of association.

VAB = ($11.922 - f12f21)/Vf10 foi f20 fo2

If the two variables are independent then $V_A_B$ will be zero, else will be positive or negative depending on whether they are positively or negatively associated.

The value of the measure is obtained as 0.10256 .

Another measure that can be appropriate is the relative risk.

let p1=proportion of individuals who suffered from the disease from among those who were vaccinated=4/70=0.0571

p2=proportion of individuals who suffered from the disease from among those who were not vaccinated=2/105=0.0190

Note that p1/p2 is approximately 3, that is the proportion of individuals who suffered from the disease among those who were vaccinated is approximately 3 times the proportion of individuals suffering from the disease among those who were not vaccinated. Thus clearly the two variables are associated.

d)To statistically conclude the presence of association, we can perform chi-squared test for independence in the large sample setup. This will provide a statistical evidence for the association. The chi-square test for independence is appropriate for finding the association among the nominal variables.