Consider the data table showing epidemiology data for 25 individuals with a disease and 25 healthy comparison individuals. Their deaths are recorded over a period of 12 months.

$\begin{array}{c}\underline { \text { Diseased } } \quad \quad \quad \quad \quad \quad \quad \quad\underline { \text { Healthy}}\\\begin{array}{cccc}\text { Time } & \text { \# at risk } & \text { Deaths } & \text { \# at risk } & \text { Deaths } \\2 & 25 & 1 & 25 & 2 \\4 & 24 & 3 & 23 & 5 \\6 & 21 & 1 & 18 & 4 \\8 & 20 & 2 & 13 & 3 \\10 & 18 & 0 & 10 & 1 \\12 & 18 & 1 & 9 & 2\end{array}\end{array}$
-What is the ?² value we obtain from a ?² test of the hazard ratio for the disease group relative to the healthy group?

Question

Consider the data table showing epidemiology data for 25 individuals with a disease and 25 healthy comparison individuals. Their deaths are recorded over a period of 12 months.

\begin{array}{c}\underline { \text { Diseased } } \quad \quad \quad \quad \quad \quad \quad \quad\underline { \text { Healthy}}\\\begin{array}{cccc}\text { Time } & \text { \# at risk } & \text { Deaths } & \text { \# at risk } & \text { Deaths } \\2 & 25 & 1 & 25 & 2 \\4 & 24 & 3 & 23 & 5 \\6 & 21 & 1 & 18 & 4 \\8 & 20 & 2 & 13 & 3 \\10 & 18 & 0 & 10 & 1 \\12 & 18 & 1 & 9 & 2\end{array}\end{array}

-What is the ?² value we obtain from a ?² test of the hazard ratio for the disease group relative to the healthy group?

Quizplus · Accepted Answer

The ?² value for the ?² test of the hazard ratio for the disease group relative to the healthy group is 5.743. This is calculated by taking the sum of the squared differences between the observed and expected deaths in each group, and dividing by the expected deaths. In this case, the expected deaths are calculated by multiplying the number of individuals at risk in each group by the overall death rate. The ?² value is then compared to a critical value to determine if there is a statistically significant difference between the two groups.

Consider the Data Table Showing Epidemiology Data for 25 Individuals