A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 6294 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). The counts of deaths over the course of the study are reported for each group in the following two-way table.
$$\begin{array}{l}
\begin{array} { | l | r r r r | }
\hline &{ \text { sleep-disordered breathing } } \
& \text { none } & \text { mild } & \text { moderate } & \text { severe } &\text { total }\
\hline \text { death } & 476 & 320 & 165 & 86&1047 \
\text { no death } & 2953 & 1477 & 562 & 255&5247 \
\hline \text { total } & 3429 & 1797 & 727 & 341 \
\hline

\end{array}
\end{array}$$ We want to know whether the study findings give evidence of a significant relationship between the extent of sleep-disordered breathing and death. Under the null hypothesis of no relationship, what is the expected count of individuals with severe sleep-disordered breathing who died?

Question

A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 6294 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). The counts of deaths over the course of the study are reported for each group in the following two-way table.
$$\begin{array}{l}
\begin{array} { | l | r r r r | } 
\hline &{ \text { sleep-disordered breathing } } \
& \text { none } & \text { mild } & \text { moderate } & \text { severe } &\text { total }\
\hline \text { death } & 476 & 320 & 165 & 86&1047 \
\text { no death } & 2953 & 1477 & 562 & 255&5247 \
\hline \text { total } & 3429 & 1797 & 727 & 341 \
\hline

\end{array}
\end{array}$$ We want to know whether the study findings give evidence of a significant relationship between the extent of sleep-disordered breathing and death. Under the null hypothesis of no relationship, what is the expected count of individuals with severe sleep-disordered breathing who died?

Quizplus · Accepted Answer

To calculate the expected count under the null hypothesis for individuals with severe sleep-disordered breathing who died, use the formula for expected counts in a contingency table: $(\text{Row Total} \times \text{Column Total}) / \text{Grand Total}$. For deaths among those with severe sleep-disordered breathing, the calculation is $(1047 \times 341) / 6294 = 56.7$.

A Study Prospectively Examined Whether Sleep-Disordered Breathing Was Associated with an Increased