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 Population characteristics Frequency distributions Calculation of infection rates Make inferences about data Suggest association Infer causality Communicate findings Prepare reports for the ICC Monitor the impact of interventions

Study Design Observational Studies Draw inferences from patterns of exposure Descriptive or Analytic Experimental Studies Prospective Manipulation of variables Randomization

Observational Studies Descriptive Studies Identify population at risk Characterize disease by person, place, time Estimate disease frequency and generate rates Study Design: Cross-Sectional Analytic Studies 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. 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 = = 88 = 8 days 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 note: mean=4.2 SD = √(14.80) = √3.70 = 1.94 V = 3.70 √4

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.

Device-associated Infection Rate Calculation of a Device-associated Infection Rate 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

Control Charts

Device Utilization Ratio Calculation of Device Utilization (DU) Ratio 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 =

NNIS Comparison

What does this tell you? When examined together, the device- associated 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 (H o ): a hypothesis of no association between two variables. The hypothesis to be tested Alternate Hypothesis (H a ): 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. 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 ab Test is negative c d

Sensitivity True Positives = a/(a + c) All diseased persons Sensitivity= 80 (80+40) Sensitivity=0.67 Patients with disease Patients w/out disease Test is positive 8020 Test is negative

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 8020 Test is negative

Predictive Value Equations Predictive Value Positive = true positives = a/(a + b) true + false positives Predictive Value Negative = true negatives = d/(c + d) true + false negatives

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 H o : C. difficile colitis is not associated with prolonged antimicrobial use. H a : C. difficile colitis is associated with prolonged antimicrobial use. OR= (332)*262) (164)*(230) OR = 2.3 Disease No Disease Exposure No Exposure

Case-Control Study 95% CI of the Odds Ratio CI = e (OR) (1/A + 1/B + 1/C + 1/D)^0.5 OR=2.3 CI = e (2.3) (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 Test statistic (X 2 ) based on Chi-Square distribution.

Z-test Calculation Risk-Stratified Rate Comparison

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) 4010 No Exposure (Dr. Y) 25

Chi-Square Analysis Expected Values X 2 = Disease No Disease Exposure (Dr. X) No Exposure (Dr. Y)

Chi-Square Analysis X 2 = df = < p < 0.01

Questions?

References Rosner, B. (2000). Fundamentals of Biostatistics (5 th ed). United States: Brooks/Cole. Friis, RH & Sellers, TA. (2004). Epidemiology for Public Health Practice (3 rd ed). Sudbury: Jones and Bartlett Publishers, Inc ation_odds.html