Frequency Measures Used in Epidemiology Introduction In epidemiological studies, many qualitative variables have only two possible categories, such as Alive or dead Case or control Exposed and unexposed The frequency measures for dichotomous variable include: Ratio Proportion Rate ( All the above 3 measure are based on the same formula: ) Ratios, Proportion, and Rates Compared In a ratio, the values of x and y may be completely independent from each other or x is a part of y For example , the gender of the children attending a specific program could be compared in one of the following ways: Proportion is a ratio in which X is included in Y For example , the gender of the children attending a specific program Rate is a proportion that measures the occurrence of an event in a population over time Rate = X Ratios, Proportion, and Rates Compared Example 1: The following table was part of an article published by Dr. Mshana and his colleagues. The title of this study is “Outbreak of a novel Enterobacter sp. carrying blaCTX-M-15 in a neonatal unit of a tertiary care hospital in Tanzania. ". Please use this table to answer the following questions. Source: Mshana SE, Gerwing L, Minde M, Hain T, Domann E, Lyamuya E, et al. Outbreak of a novel Enterobacter sp. carrying blaCTX-M-15 in a neonatal unit of a tertiary care hospital in Tanzania. International journal of antimicrobial agents. 2011;38(3):265-9. 4 Example 1 What is the ratio of males to females? 7 : 10 What proportion of premature babies? 12/17=0.706 What proportion of patients were discharged? 11/17=0.647 What is the ratio of prematurity to birth asphyxia ? 12 : 5 Source: Mshana SE, Gerwing L, Minde M, Hain T, Domann E, Lyamuya E, et al. Outbreak of a novel Enterobacter sp. carrying blaCTX-M-15 in a neonatal unit of a tertiary care hospital in Tanzania. International journal of antimicrobial agents. 2011;38(3):265-9. 5 Example 2: In 1989, 733,151 new cases of gonorrhea were reported among the United States civilian population. The 1989 mid-year U.S. civilian population was estimated to be 246,552,000. What is the 1989 gonorrhea incidence rate for the U.S. civilian population? (For these data we will use a value of 105 for 10n ). Answer: Incidence rate = X Incidence rate = X = 297.4 per 100,000 6 Measures of association: They are used to quantify the relationship between exposure and disease among two groups They are used to compare the disease occurrence among one group with the disease occurrence in the another group They include the following measures based on the study design: Risk Ratio (RR): It also called relative risk It is used to compare the risk of health related events in two groups The following formula cis used to calculate the RR: A risk ratio of 1.0 indicates identical risk in the two groups A risk ratio greater than 1.0 indicates an increased risk for the numerator group A risk ratio greater than 1.0 ...

1. Frequency Measures Used in Epidemiology
Introduction
In epidemiological studies, many qualitative variables have only
two possible categories, such as
Alive or dead
Case or control
Exposed and unexposed
The frequency measures for dichotomous variable include:
Ratio
Proportion
Rate
( All the above 3 measure are based on the same formula:
)
Ratios, Proportion, and Rates Compared
In a ratio, the values of x and y may be completely independent
from each other or x is a part of y
For example , the gender of the children attending a specific
program could be compared in one of the following ways:
Proportion is a ratio in which X is included in Y
For example , the gender of the children attending a specific

2. program
Rate is a proportion that measures the occurrence of an event in
a population over time
Rate = X
Ratios, Proportion, and Rates Compared
Example 1: The following table was part of an article published
by Dr. Mshana and his colleagues. The title of this study is
“Outbreak of a novel Enterobacter sp. carrying blaCTX-M-15 in
a neonatal unit of a tertiary care hospital in Tanzania. ". Please
use this table to answer the following questions.
Source: Mshana SE, Gerwing L, Minde M, Hain T, Domann E,
Lyamuya E, et al. Outbreak of a novel Enterobacter sp. carrying
blaCTX-M-15 in a neonatal unit of a tertiary care hospital in
Tanzania. International journal of antimicrobial agents.
2011;38(3):265-9.
4
Example 1
What is the ratio of males to females? 7 : 10
What proportion of premature babies? 12/17=0.706
What proportion of patients were discharged? 11/17=0.647
What is the ratio of prematurity to birth asphyxia ? 12 : 5

3. Source: Mshana SE, Gerwing L, Minde M, Hain T, Domann E,
Lyamuya E, et al. Outbreak of a novel Enterobacter sp. carrying
blaCTX-M-15 in a neonatal unit of a tertiary care hospital in
Tanzania. International journal of antimicrobial agents.
2011;38(3):265-9.
5
Example 2:
In 1989, 733,151 new cases of gonorrhea were reported among
the United States civilian population. The 1989 mid-year U.S.
civilian population was estimated to be 246,552,000. What is
the 1989 gonorrhea incidence rate for the U.S. civilian
population? (For these data we will use a value of 105 for 10n
).
Answer:
Incidence rate = X
Incidence rate = X = 297.4 per 100,000
6
Measures of association:
They are used to quantify the relationship between exposure
and disease among two groups
They are used to compare the disease occurrence among one
group with the disease occurrence in the another group
They include the following measures based on the study design:
Risk Ratio (RR):
It also called relative risk
It is used to compare the risk of health related events in two
groups
The following formula cis used to calculate the RR:

4. A risk ratio of 1.0 indicates identical risk in the two groups
A risk ratio greater than 1.0 indicates an increased risk for the
numerator group
A risk ratio greater than 1.0 indicates an decreased risk for the
numerator group (protective effect)
http://www.cdc.gov/ophss/csels/dsepd/SS1978/SS1978.pdf
7
Measures of association:
Rate ratio
It is used to compare the incidence rates, person-time rates, or
mortality rated of two groups
The following formula cis used to calculate the rate ratio:
X 1
A risk ratio of 1.0 indicates equal rates in the two groups
A risk ratio greater than 1.0 indicates an increased risk for the
numerator group
A risk ratio greater than 1.0 indicates an decreased risk for the
numerator group (protective effect)
http://www.cdc.gov/ophss/csels/dsepd/SS1978/SS1978.pdf
9
Measures of association:
Odds ratio (OR)

5. It is used to quantify the relationship between an exposure and
health-related outcome from a comparative study
It is also called the cross-product ratio
The following formula is used to calculate the OR:
a = number of persons exposed and with disease
b = number of persons exposed but without disease
c = number of persons unexposed and with disease
d = number of persons unexposed and without disease
If the health-related outcome uncommon (rare disease
assumption), OR provides a good estimation for the relative risk
It is commonly used in case-control studies
http://www.cdc.gov/ophss/csels/dsepd/SS1978/SS1978.pdf
10
Measures of association:
Odds ratio (OR)
A odds ratio of 1.0 indicates that there is no difference in odds
of the two groups
A odds ratio greater than1.0 indicates that people in the
numerator group are more likely to develop the event of interest
A odds ratio less than1.0 indicates that people in the numerator
group are less likely to develop the event of interest (protective
effect)
Example
= = 0.997

6. 11
12
Multiple Regression Analysis
Multiple Regression
Analysis that involves multiple variables
A multiple regression equations expresses a relationship
between a dependent variable (y) and two or more independent
variables (X1, X2 , X3, ….., X k).
The general form of a multiple regression equation is
y= a + b1X1+ b2X2+ b3X3, …..+ b
k X k
Where :
a = constant
b1 = regression coefficient for variable X1
b2 =regression coefficient for variable X2
b3 =regression coefficient for variable X3
b k =regression coefficient for variable X k
Three Types of Multiple Regression Analysis
Multiple Linear Regression
Used when the dependent variable is quantitative
Adjusted R-squared should be used instead of R-squared to
assess the percent of the variation in the dependent variable

7. accounted for by the independent variables
Multiple Logistic Regression
Used when the dependent variable is qualitative
If confidence interval of the odds ratio includes the value of
one, we fail to reject the null hypothesis
If confidence interval of the odds ratio does not include the
value of one, we reject the null hypothesis
Three Types of Multiple Regression Analysis
Cox Regression (Survival Analysis)
Used when the dependent variable is time to event
If confidence interval of the hazard ratio includes the value of
one, we fail to reject the null hypothesis
If confidence interval of the hazard ratio does not include the
value of one, we reject the null hypothesis
Example 1:
High blood pressure is a serious health problem in the U.S.
adult population. The task of the study is to investigate how
baseline diastolic blood pressure is affected by obesity (BMI)
after adjusting for important potential confounders. The
literature review conducted by the researchers indicates that age
and sex are important variables that have to be adjusted for .
Dependent Variable:
Baseline diastolic blood pressure
Independent variables :
BMI
Age
Gender

8. Since the dependent variable is quantitative, thus Multiple
Linear Regression is the appropriate method of analysis.
Interpretation:
The multiple linear regression analysis indicates that there is a
statistically significant linear relationship between diastolic
blood pressure at baseline and BMI after adjusting for age and
gender (p< 0.001).
For every 1 unit increase in BMI, diastolic blood pressure at
baseline will increase by 0.584 units after adjusting for other
variables (β= 0.584, p-value <0.001 with R2 (adjusted) = 0.109)
Example 2:
High blood pressure is a serious health problem in the U.S.
adult population. The task of the study is to investigate how to
investigate how blood pressure (abnormal vs. normal) is
affected by stress after adjusting for important potential
confounders. The literature review conducted by the
researchers indicates that age and sex are important variables
that have to be adjusted for .
Dependent Variable:
Blood pressure (abnormal vs. normal)
Independent variables :

9. Stress
Age
Gender
Since the dependent variable is dichotomous, thus Multiple
Logistic Regression is the appropriate method of analysis.
Interpretation:
People in high stress level group are 1.044 times more likely to
experience hypertension compared with people in the low stress
level group after adjusting for age and gender (Odds
ratio=1.044 [95% CI: 0.638, 1.711]).
Example 3:
The table 3 (shown in slide# 9) was part of an article by Deegan
and others in the July 2014 issue of Orthopedics titled: Impact
of chronic kidney disease stage on lower-extremity arthroplasty.
Dependent Variables :
Mortality (time to death)
Independent variables :
Stages of chronic kidney disease (stage 3 vs. stage 1-2)
Age
Sex
BMI
Joint replaced
Since the dependent variables are time to an event ( time to

10. death) , thus the appropriate statistical test is survival analysis
(Cox Regression)
Interpretation:
Mortality (time to death): The mortality rate was 2.09 times
higher in the patients with stage 3 chronic kidney disease than
in the patients with stage 1 to 2 after adjusting for age, sex,
BMI, and joint replaced (hazard ratio=2.09 [95% CI: 1.14 ,
3.80]).
Multiple Linear Regression
Used when the dependent variable is quantitative
Multiple Logistic Regression
Used when the dependent variable is qualitative
Cox Regression (Survival Analysis)
Used when the dependent variable is time to an event
Summary: Multiple Regression Analysis