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Statistics for Infection Control Practitioners

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

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Statistics for Infection Control Practitioners

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  1. Statistics for Infection Control Practitioners Presented By: Shana O’Heron, MPH, CIC Infection Prevention and Management Associates

  2. 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

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

  4. 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

  5. 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

  6. 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.

  7. 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

  8. 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.

  9. Dispersion in Procedure Length Range = 2-7 hours note: mean=4.2 SD = √(14.80) = √3.70 = 1.94 V = 3.70 √4

  10. 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.

  11. Prevalence Proportion • Prevalence- proportion of persons with a particular disease within a given population at a given time.

  12. Device-associatedInfection 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.

  13. 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 Device-associated Infection Rate

  14. NNIS Comparison

  15. Control Charts

  16. 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.

  17. 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

  18. NNIS Comparison

  19. 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.

  20. Analytic Epidemiology • Inferential statistics: procedures used to make inferences about a population based on information from a sample of measurements from that population.

  21. 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.

  22. 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 - 

  23. 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.

  24. 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.

  25. 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

  26. Normal Distribution

  27. Properties of a Normal Distribution • Continuous distribution • Bell shaped curve • Symmetric around the mean

  28. 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.

  29. 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.

  30. 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

  31. 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.

  32. Patients with disease Patients without disease Test is positive a b Test is negative c d 2x2 Table

  33. Patients with disease Patients w/out disease Test is positive 80 20 Test is negative 40 860 Sensitivity • True Positives = a/(a + c) All diseased persons Sensitivity= 80 (80+40) Sensitivity=0.67

  34. 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

  35. 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

  36. 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

  37. Disease No Disease Exposure 332 164 No Exposure 230 262 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

  38. 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]

  39. SSI Rate Comparison • Z-test Calculation • Test statistic (Z) based on normal distribution. • Chi-Square Analysis • Test statistic (X2) based on Chi-Square distribution.

  40. Z-test Calculation • Risk-Stratified Rate Comparison

  41. Z-test Calculation

  42. Z-test Calculation • Z = 21.8 *The critical values -1.6 and 1.6 correspond to a p-value of 0.05.

  43. 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

  44. Disease No Disease Exposure (Dr. X) 32.5 17.5 No Exposure(Dr. Y) 32.5 17.5 Chi-Square Analysis • Expected Values • X2= 8.615

  45. Chi-Square Analysis X2 = 8.615 df = 1 0.001< p < 0.01

  46. Questions? Questions?

  47. 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/association_odds.html

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