4.9: Cases and Rates
- Page ID
- 116196
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)What do we count when we are monitoring or measuring health? Usually we count cases of a certain disease or injury. Often, thinking about prevention, we also monitor health behaviors(like smoking, drinking, driving fast)and community conditions that affect health (like the number of liquor stores in a neighborhood).
When we count how many cases happened, we get a sense of HOW MANY or HOW MUCH. The number of cases is sometimes referred to as a count, not surprisingly. For example, in 2013 there were 135 new cases of bladder cancer reported in San Francisco.
But was 135 new cases of bladder cancer in San Francisco a lot or a little? Was it an unexpectedly large number (an epidemic)? Increasing or decreasing? To answer this kind of question, we need to look at rates.
MorBIDity is a word that refers to illness. A morbidity rate tells us how many people are sick or injured.
MorTALity is a word that refers to death (like a "mortal wound" is a deadly wound). A mortality rate tells us how many people have died.
The Importance of Rates
Rates allow for comparison of outbreaks at different times or in different places
- Cases =people afflicted (those who are sick)
- Rates = number of events in a given population over a given period of time
- Examples of common rates:
- natality (birth)
- morbidity (sickness)
- mortality or fatality (death) rates
- attack rates (rate of illness in a specific outbreak)
- Population at Risk: those susceptible to particular disease or condition
For example, in 2016 there were 88 homicides in Oakland, CA. In New York, NY there were 335 homicides. Clearly, that means there were more total deaths by homicide in New York than in Oakland , 247 more. But which city had a higher homicide rate?
To answer that, you would need to know the size of the population at risk. For homicide, the population at risk is everyone who is a resident of that city -- it isn't an injury that can only happen to one gender, one age group, etc. (This is true, even though some populations are at MORE risk that others.) In contrast, for a disease like testicular cancer the population at risk would only include male-bodied individuals.
New York City had a population of roughly 8.5 million (that's 8,500,000, rounded off).
Oakland had a population of roughly 383,000.
So, New York hada homicide rate of 335 divided by 8.5 million -- which comes out roughly to 4 homicides for every 100,000 people. Oakland had a homicide rate of 88 divided by 383,000, and that number is roughly 23 homicides for every 100,000 people.
So, while New York has a higher number of cases, Oakland has a higher rate of homicides.
Rates let us compare apples to apples and oranges to oranges, as the saying goes. You can use rates to compare the scope of a disease, injury, or health behavior in cities (or countries) of different populations, or across different times.