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Statistics for Infection Control
Practitioners
Presented By:
Shana O’Heron, MPH, CIC
Infection Prevention and Management Associates
Role of Statistics in Hospital
Epidemiology
Aid in organizing and summarizing data
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Population characteristics
Frequency distributions
Calculation of infection rates
Make inferences about data
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Suggest association
Infer causality
Communicate findings

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Prepare reports for the ICC
Monitor the impact of interventions
Study Design
Observational Studies

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Draw inferences from patterns of exposure
Descriptive or Analytic
Experimental Studies
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Prospective
Manipulation of variables
Randomization
Observational Studies
Descriptive Studies
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Identify population at risk
Characterize disease by person, place, time
Estimate disease frequency and generate rates
Study Design: Cross-Sectional
Analytic Studies

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Designed to test etiologic hypotheses
Suggest mechanisms of causation
Study Design: Case-Control, Cohort
Descriptive Epidemiology
Descriptive Statistics: techniques
concerned with the organization,
presentation, and summarization of
data.

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Measures of central tendency
Measures of dispersion
Use of proportions, rates, ratios
Measures of Central Tendency
Mean- mathematical average of the
values in a data set.
Median- the value falling in the middle
of the data set.
Mode- most frequently occurring value
in a data set.
Average Length of Stay
Mean = The sum of each patient’s length of stay
The number of patients
=12 + 9 + 3 + 5 + 7 + 6 + 13 + 8 + 4 + 15 + 6 = 88 = 8 days
11
11
Median = 3, 4, 5, 6, 6, 7, 8, 9, 12, 13, 15 = 7 days
Mode = 6 days
Measures of Dispersion
Range- the difference between the smallest
and largest values in a data set.
Standard Deviation- measure of dispersion
that reflects the variability in values around
the mean.
Variance- a measure of variability that is
equal to the square of the standard deviation.
Dispersion in Procedure Length
Range = 2-7 hours
SD = √(14.80) = √3.70 = 1.94
√4
note: mean=4.2
V = 3.70
Use of Proportions, Rates, and Ratios
Proportions- A fraction in which the
numerator is part of the denominator.
Rates- A fraction in which the denominator
involves a measure of time.
Ratios- A fraction in which there is not
necessarily a relationship between the
numerator and the denominator.
Prevalence Proportion
Prevalence- proportion of persons with a particular
disease within a given population at a given time.
Proportion of S. aureus Nosocomial
Infections Resistant to Oxacillin (MRSA)
Among Intensive Care Unit Patients,
1989-2003*
Percent Resistance
70
60
50
40
30
20
10
0
1989
1991
1993
1995
1997
1999
2001
Year
*Source: NNIS System, data for 2003 are incomplete
2003
Device-associated Infection Rate
Calculation of a Device-associated
Infection Rate

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Step 1: Decide upon the time period for your
analysis.
Step 2: Select the patient population for analysis.
Step 3: Select the infections to be used in the
numerator.
Step 4: Determine the number of device-days
which is used as the denominator of the rate.
 Device days: total number of days of exposure to the
device by all patients in the selected population during
the time period.
Device-associated Infection Rate

Step 5: Calculate the device-associated infection
rate (per 1000 device-days) using the following
formula: Number of device-associated infections x 1000
Number of device-days
Example: Foley-Associated UTIs in the ICU
# of Infections: 2
Foley-days in ICU: 920
Rate: 2 x 1000 = 2.17 per 1000 Foley-days
920
NNIS Comparison
Quarters
Q1 2004
Q4 2003
Q3 2003
Q2 2003
Q1 2003
Q4 2002
Q3 2002
Q2 2002
Q1 2002
Q4 2001
Q3 2001
Q2 2001
Q1 2001
Q4 2000
Q3 2000
Q2 2000
Q1 2000
# of Infections/ 1000 Foley Days
Control Charts
Foley Catheter Associated UTIs in the ICU
14
12
10
Infection Rate
8
Ubar
-2 Sigma
6
2 Sigma
-1 Sigma
4
1 Sigma
Benchmark
2
0
Device Utilization Ratio
Calculation of Device Utilization (DU)
Ratio
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Step 1: Decide upon the time period for your
analysis.
Step 2: Select the patient population for analysis.
Step 3: Determine the number of device-days.
Step 4: Determine the number of patient-days.
 Patient-days are the total number of days that patients
are in the selected population during the time period.
Device Utilization Ratio

Step 5: Calculate the device-utilization ratio using
the following formula: Number of device-days
Number of patient-days
Example: Foley Utilization Ratio in the ICU
Foley-days in ICU: 920
Patient-days in ICU: 1176
Ratio: 920 = 0.78
1176
NNIS Comparison
What does this tell you?
When examined together, the deviceassociated infection rate and device utilization
ratio can be used to appropriately target
preventative measures.

Consistently high rates and ratios may signify a
problem and further investigation is suggested.
 Potential overuse/improper use of device

Consistently low rates and ratios may suggest
underreporting of infection or the infrequent use
or short duration of use of devices.
Analytic Epidemiology
Inferential statistics: procedures used to
make inferences about a population
based on information from a sample of
measurements from that population.
Hypothesis Testing Studies
Null Hypothesis (Ho): a hypothesis of no
association between two variables.

The hypothesis to be tested
Alternate Hypothesis (Ha): a hypothesis
of association between two variables.
Error
Type I Error (): Probability of rejecting the
null hypothesis when the null hypothesis is
true.

p-value = 
Type II Error(): Probability of accepting the
null hypothesis when the alternate hypothesis
is true.

Power = 1 - 
Significance Testing
p-value (): probability that the findings
observed could have occurred due to chance
alone.

p-value = 0.05
Confidence Interval: a computed interval of
values that, with a given probability, contains
the true value of the population parameter.

95% CI- 95% of the time the true value falls
within this interval.
Significance of a p-value
If p > .05, then the results are considered not
statistically significant.
If .01 ≤ p < .05, then the results are significant.
If .001 ≤ p < .01, then the results are highly
significant.
If p < .001, then the results are very highly
significant.
Examples of Significance
Study A found that the patient’s average
length of stay was associated with C. difficile
colitis (p = .002).

Highly Significant
Study B found that men were more likely to
develop a BSI than women (P = .09)

Not Significant
Normal Distribution
Properties of a Normal Distribution
Continuous distribution
Bell shaped curve
Symmetric around the mean
Study Design
Case-Control Study: a retrospective study
that compares individuals with and without a
disease in order to examine differences in
exposures or risk factors for the disease.
Cohort Study: a prospective study that
compares individuals with and without
exposures or risk factors for a disease in
order to examine differences in the
development of disease.
Components of Study Design
Precision (reliability)- the ability of a
measuring instrument to give consistent
results on repeated trials.
Validity (accuracy)- the ability of a
measuring instrument to give a true
measure.
Study Precision
Sample Size- a portion of the population
under study that is representative of
that population.
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Random Sampling: Simple, Stratified,
Cluster, Sequential
Nonrandom Sampling: Convenience,
Volunteer, Quota
Study Validity
Sensitivity- percentage of people with a disease who
test positive for the disease.
Specificity- percentage of people without a disease
who test negative for the disease.
Predictive Value Positive- percentage of people who
test positive for the disease who actually have the
disease.
Predictive Value Negative- percentage of people who
test negative for the disease who actually do not
have the disease.
2x2 Table
Patients with
disease
Patients without
disease
Test is
positive
a
b
Test is
negative
c
d
Sensitivity
True Positives =
All diseased persons
Sensitivity= 80
(80+40)
Sensitivity=0.67
a/(a + c)
Patients
with disease
Patients
w/out
disease
Test is
positive
80
20
Test is
negative
40
860
Specificity
True negatives = d/(b + d)
All non-diseased
Specificity= 860
(20+860)
Specificity=0.98
Patients
with disease
Patients
w/out
disease
Test is
positive
80
20
Test is
negative
40
860
Predictive Value Equations
Predictive Value Positive
=
true positives
=
true + false positives
a/(a + b)
Predictive Value Negative
=
true negatives
=
true + false negatives
d/(c + d)
Case-Control Study
Measure of Association: Odds Ratio

OR = (a*d)/(b*c)
Significance Test: 95% CI
Disease
No Disease
Exposure
a
b
No Exposure
c
d
Case-Control Study
Ho: C. difficile colitis is not associated with
prolonged antimicrobial use.
Ha: C. difficile colitis is associated with
prolonged antimicrobial use.
OR= (332)*262)
(164)*(230)
OR = 2.3
Exposure
No
Exposure
Disease
No Disease
332
164
230
262
Case-Control Study
95% CI of the Odds Ratio
CI = e(OR) +- 1.96(1/A + 1/B + 1/C + 1/D)^0.5
OR=2.3
CI = e(2.3) +- 1.96(1/332 + 1/164 + 1/230 + 1/262)^0.5
CI = [1.78, 2.98]
SSI Rate Comparison
Z-test Calculation

Test statistic (Z) based on normal
distribution.
Chi-Square Analysis
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Test statistic (X2) based on Chi-Square
distribution.
Z-test Calculation
Risk-Stratified Rate Comparison
Z-test Calculation
Z-test Calculation
Z = 21.8
*The critical values -1.6 and 1.6 correspond to a p-value of 0.05.
Chi-Square Analysis
Comparing Dr. X’s surgical site infection
rate to Dr. Y’s surgical site infection rate.
Disease
No Disease
Exposure
(Dr. X)
40
10
No
Exposure
(Dr. Y)
25
25
Chi-Square Analysis
Expected Values
Disease
No Disease
Exposure
(Dr. X)
32.5
17.5
No
Exposure
(Dr. Y)
32.5
17.5
X2= 8.615
Chi-Square Analysis
X2 = 8.615
df = 1
0.001< p < 0.01
Questions?
Questions?
References
Rosner, B. (2000). Fundamentals of
Biostatistics (5th ed). United States:
Brooks/Cole.
Friis, RH & Sellers, TA. (2004). Epidemiology
for Public Health Practice (3rd ed). Sudbury:
Jones and Bartlett Publishers, Inc.
www.apic.org
www.cdc.gov
http://www.slack.ser.man.ac.uk/theory/associ
ation_odds.html