BIOSTATISTICS

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  BIOSTATISTICS


         5.5
MEASURES OF FREQUENCY




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          BIOSTATISTICS
• TERMINAL OBJECTIVE:

5.5 Prepare a Food Specific Attack Rate
  Table IAW PEF 5.5.




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• DEFINE:
5.5.1 Incidence Rate.
5.5.2 Prevalence Rate.
5.5.3 Attack Rate.
5.5.4 Mortality Rate.
5.5.5 Relative Risk.
5.5.6 Attributable Risk.
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             Incidence Rate
• Expresses the probability of or risk of
  illness in a population over a period of time.

• The frequency of new events (illness) for a
  specified population over a given period of
  time, multiplied by a population base.


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            Prevalence Rate
• Proportion of persons in a population who
  have a particular disease over a specified
  period of time.




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               Attack Rate
• Incidence rates which are calculated for
  narrowly defined populations, during
  limited periods of time, such as an epidemic




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               Mortality Rate
• Frequency of death in a population during a
  specified period of time
  – Crude mortality rate
     • The mortality rate from all causes of death for a
       population.




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           Mortality Rate
– Case-fatality Rate
Number of cause-specific deaths among the
incident cases divided by the number of
new cases of that disease.




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              Relative Risk
• The ratio of the incidence of the exposed
  group to the incidence of the unexposed
  group

• Risk group of primary interest is in the
  numerator, while the comparison group is in
  the denominator

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            Relative Risk
– A value greater than 1 indicates a positive
  association, or an increased risk among the
  exposed.




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             Relative Risk
• Used as the measure of association for
  illness with the Food Specific Attack Rate
  Table.
• Data derived from a two-by-two table




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           Attributable Risk
• Measures the difference between incidence
  rates in the exposed group and nonexposed
  group.
  – A measure of the excess risk of disease in those
    exposed compared with those nonexposed.




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           Attributable Risk
• With no association between incidence
  rates, the attributable risk = 0.

• Positive values indicate the number of cases
  of disease that can be attributed to exposure.



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           Attributable Risk

• A useful measure of the public health
  impact of a particular exposure.




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• CALCULATE:
5.5.7 Incidence Rate.
5.5.8 Prevalence Rate.
5.5.9 Attack Rate.
5.5.10 Case Fatality Rate.
5.5.11 Absolute Risk.
5.5.12 Relative Risk.
5.5.13 Attributable Risk.
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         Calculate Incidence Rate
• Formula:

new cases occurring over a period of time
                                            x 10n
population at risk during same time


   – 10n = base power of ten,
     n = 2, 3, 4, 5


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   Calculate Incidence Rate
• Example
  – In CY 2000, 51 new cases of
    hepatitis B were reported in a county
    with a mid-year population of
    552,000. Calculate the incidence rate
    using a base of 100,000 (105).




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   Calculate Incidence Rate
– Numerator = 51
– Denominator = 552,000
– 51/552,000 x 105
  = 0.0000924 x 100,000
– = 9.24 per 100,000




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    Calculate Incidence Rate
A population of 200 experienced an Ebola
outbreak between March and October.
There were 17 cases, 9 which died. What is
the six month incidence rate? Use base of
100.




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           Incidence Rate
(1) Over time, 200 – 9 (deaths) = 191 people
 are included in the calculation
Numerator = 17
Denominator = 191
17/191 x 100 = 8.9 cases per 100
                 population

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      Calculate Prevalence Rate
• Formula:

all new and existing cases during a given time period
population during same the time period

                       x 100%


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       Calculate Prevalence Rate
• Example
  – In a survey of records at a major medical
    center, 80 out of 500 patients were treated
    for one or more nosocomial infections in
    the past six months. Calculate prevalence.




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  Calculate Prevalence Rate
– Numerator = 80
– Denominator = 500
– Prevalence = 80/500 x 100%
  = 16%




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         Calculate Attack Rate
• Formula

 # of new cases among the population during the
                   time period
                Population at risk


             x 100%

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        Calculate Attack Rate
• Example
  – A cohort of 75 persons (45 male, 30 female)
    attended a picnic. Of these, 46 developed
    gastroenteritis. Of the ill, 12 were females.
    Calculate the crude and sex-specific attack
    rates.




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        Calculate Attack Rate
• Crude attack rate
  – New cases = 46
  – Population at risk = 75


  – AR = 46/75 x 100 = 61%




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        Calculate Attack Rate
• Female sex-specific attack rate
  – Cases = 12
  – Population at risk = 30


  – AR = 12/30 x 100 = 40%




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        Calculate Attack Rate
• Male sex-specific attack rate
  – Cases = 46-12=34
  – Population at risk = 45


  – AR = 34/45 x 100 = 75.5%




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       Calculate Mortality Rate
• Crude mortality rate
Formula:

Deaths during calendar year
                                  x 10n
Population at mid-year




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     Calculate Mortality Rate
• Example
  – In 1998 there were 21,000 deaths in a mid-year
    population of 3,750,000. Calculate crude
    mortality.




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   Calculate Mortality Rate
– Numerator = 21,000
– Denominator = 3,750,000
– CDR = 21,000/3,750,000 x 105
  = 560 deaths per 100,000 pop.




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        Calculate Mortality Rate
• Case fatality rate
Formula:

number of cause-specific deaths among
incident cases
number of new cases of disease

                    x 100%

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   Calculate Case Fatality Rate
• Example
A hospital treated 80 individuals for
malaria. There were 39 deaths. Numerator =
  39
 Denominator = 80
 39  80 x 100%
 = 49%
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         Calculate Absolute Risk
• Formula
Risk for group of interest (Ie)

Same as the incidence rate         1

Ie = incidence for exposed group




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      Calculate Absolute Risk
• Use 2x2 observed table

• Formula: a / H 1 x 100

  – Example: a = 46; H1 = 1484
  Risk = 46/1484 x 100
       = 3.1%

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         Calculate Relative Risk
• Formula

Risk for group of interest (Ie)
Risk for comparison group (I0)       x 1 1

Ie = incidence for exposed group
I0 = incidence for unexposed group



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      Calculate Relative Risk
• Two-by-two contingency table
                 TABLE 5.5A
     NUMBER OF CASES FOR PELLAGRA BY SEX,
           SOUTH CAROLINA, 1920'S

                    Pellagra
                   Yes    No      Total
       Female   a =         b =   1,484
                46        1,438
        Male    c =         d =   1,419
                18        1,401
       Total                      2,903
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       Calculate Relative Risk
 Ie = a  a+b = 46/1484 = .031

Io = c  c+d    = 18/1419 = .013


        RR = Ie/Io

            = .031/.013 = 2.4
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 Calculate Attributable Risk
– Ie = Incidence rate of persons exposed to a
  disease or other event.
– I0 = Incidence rate of persons not exposed to
  the disease or event.
– Expressed as a rate per base population.




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           Attributable Risk
• Using a 2x2 contingency table
      INCIDENCE OF HEPATITIS C IN SYRINGE SHARING
                        N = 256*

                                          HCV
            Shared               Yes               No
            Syringe                                           Total

             Yes                  37               89          126

             No                  13               117          130_
             Total                                             256_
           *Hagan, H. et al., Sharing of Drug Preparation Equipment as a
            Risk Factor for Hepatitis C, Am J Public Health, Jan 01, Vol.   42
            91, No. 1, pp. 42-46.
         Attributable Risk
  Ie = 37/126 = .29


Io = 13/130 = .10

AR = 0.29 – 0.10 = 0.19

19 per 100
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        Attributable Risk
Using a rate table
      DEATH RATES FROM LUNG CANCER BY DAILY
                  CIGARETTE USE
    DOLL AND HILL PHYSICIAN FOLLOW-UP STUDY,
                    1951-1961

         Cigarettes   Death Rates per 1000
           per Day          per Year
               0              0.07
             1-14             0.57




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  Calculate Attributable Risk

 (1) Ie = 0.57

(2) I0 = 0.07

(3) AR = 0.57 - 0.07 = 0.50
 0.50 per 1,000 per year
    (50 per 100,000)

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Food Specific Attack Rate Table

IAW PEF 5.5:

5.5.14 Prepare a Food Specific Attack Rate
  Table




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Food Specific Attack Rate Table

• Description:

  – Used to ascertain which food or foods caused
    the illness when the incriminating meal is
    known




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Food Specific Attack Rate Table

• Data is obtained by interviewing:

  – Cases: the persons that became ill.


  – Controls: The persons who did not become ill
    (well).


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Food Specific Attack Rate Table

 – Compare the attack rates of those who ate the
   specific foods served, with the attack rates of
   those who did not eat the foods.




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Food Specific Attack Rate Table

 – The food items which present the greatest
    difference in the attack rates are considered
   the prime suspects as the source of the illness.




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Food Specific Attack Rate Table

• Construction
  – The table has three major headings (columns):
     • Food/Beverage
     • Ate Specified Item
     • Did Not Eat Specified Item




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Food Specific Attack Rate Table

• Subheadings under major headings
  – Food/Beverage

     • Foods served during the implicated meal.




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Food Specific Attack Rate Table

 – Ill
    • Total number of persons ill.
 – Well
    • Total number of persons not ill.




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Food Specific Attack Rate Table

 – Total
    • Total number of persons Ill and the number Well.




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Food Specific Attack Rate Table

 – Attack Rate %
   • Ill divided by Total x (100)%




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Food Specific Attack Rate Table

 – Difference (%)
   • The last column under Did Not Eat Specified Item

   • The difference between the attack rates (%) from
     those who ate the specified food and those who did
     not eat it.




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Food Specific Attack Rate Table

   •         This value is obtained by subtracting the attack
       rate of those who did not eat the food from those
       who did eat.
          Negative values can occur.




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Food Specific Attack Rate Table

 – Fill in the columns with the appropriate data
   from food histories obtained during the
   outbreak investigation.


 – The total columns for each food item should
   equal the number of persons (ill and well) in the
   investigation.


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Food Specific Attack Rate Table
• Identify the food item(s) with the largest
  positive difference in attack rates
  (Attributable Risk). This is the food(s)
  which is suspected as the source of the
  illness.




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Food Specific Attack Rate Table

• Statistical analysis is performed on the
  values of the suspected food(s) to determine
  if there is a statistical association between
  its consumption and the occurrence of the
  illness..


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