1. Intro to Statistics for Infection Preventionists Presented By: Jennifer McCarty, MPH, CIC Shana O’Heron, MPH, PhD, CIC

2. Objectives Describe the important role statistics play in infection prevention. Describe the most common types of statistics used in hospital epidemiology Provide examples on how statistics are utilized in hospital epidemiology.

3. 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 committees Monitor the impact of interventions

4. Role of Statistics in Hospital Epidemiology When evaluating a study or white paper Are the findings statistically significant? Was the sample size large enough to show a difference if there is one? Are the groups being compared truly similar? When investigating and unusual cluster Describe the outbreak Select control subjects Determine the appropriate test to use when measuring exposure

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. Descriptive Statistics Variable: “Anything that is measured or manipulated in a study” Types of variables: Qualitative  Nominal, Ordinal Quantitative  Interval, Ratio Independent vs. Dependent Variables Continuous vs. Discrete variables

7. Variables

8. Measures of Central Tendency

9. Mean: mathematical average of the values in a data set. Calculation: Patient Length of Stay: 12, 9, 3, 5, 7, 6, 13, 8, 4, 15, 6 Mean (x)= 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

10. Measures of Central Tendency Median: the value falling in the middle of the data set. Calculation: Patient Length of Stay: 12, 9, 3, 5, 7, 6, 13, 8, 4, 15, 6 Median = 3, 4, 5, 6, 6, 7, 8, 9, 12, 13, 15 = 7 days

11. Measures of Central Tendency Mode: the most frequently occurring value in a data set. Calculation: Patient Length of Stay: 12, 9, 3, 5, 7, 6, 13, 8, 4, 15, 6 Mode = 3, 4, 5, 6, 6, 7, 8, 9, 12, 13, 15 = 6 days

12. Measures of Dispersion

13. Range: the difference between the smallest and largest values in a data set. Calculation: Patient Length of Stay: 12, 9, 3, 5, 7, 6, 13, 8, 4, 15, 6 Range = 15 – 3 = 12 days

14. Measures of Dispersion Standard Deviation: measure of dispersion that reflects the variability in values around the mean. Deviation: the difference between an individual data point and the mean value for the data set. SD = √(X-X) 2 / n-1  “Take all the deviations from the mean, square them, then divide their sum by the total number of observations minus one and take the square root of the resulting number” Variance: a measure of variability that is equal to the square of the standard deviation.

16. Normal Distribution Continuous distribution Bell shaped curve Symmetric around the mean

17. Non-Normal Distributions Skew Non-symmetric distribution Positive or Negative  Refers to the direction of the long tail Bi/Multi-Modal May have distinct peaks with its own central tendency No central tendency

18. Proportions

19. Use of Proportions, Rates & 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.

20. Proportions Prevalence: proportion of persons with a particular disease within a given population at a given time.

21. Rates Rate = x/y × k x = The number of times the event (e.g., infections) has occurred during a specified time interval. y = The population (e.g., number of patients at risk) from which those experiencing the event were derived during the same time interval. k = A constant used to transform the result of division into a uniform quantity so that it can be compared with other, similar quantities.

22. Rates Example: Foley-Associated UTIs in the ICU Step 1: Time period  April 2014 Step 2: Patient population  Patients in the Medical / Surgical ICU of Hospital X who have Foley catheters Step 3: Infections (numerator)  April CAUTI infections in the ICU = 2 Step 4: Device-days (denominator)  Total number of days that patients in the ICU had Foley catheters in place = 920 Step 5: Device-associated infection rate  Rate = 2 x 1000 = 2.17 per 1000 Foley-days 920

23. NHSN Comparison

24. Ratios Calculation of Device Utilization Ratio Step 1: Time period  April 2014 Step 2: Patient population  Patients in the Medical / Surgical ICU of Hospital X who have Foley catheters Step 3: Device-days (numerator)  Total number of days that patients in the ICU had Foley catheters in place = 920 Step 4: Patient-days (denominator)  Total number of days that patients are in the ICU = 1176 Step 5: Device utilization ratio  Ratio = 920= 0.78 1176

25. NHSN Comparison

26. 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.

27. Analytic Epidemiology Inferential statistics: procedures used to make inferences about a population based on information from a sample of measurements from that population. Z-test/T-test Chi Square SIR

28. Hypothesis Testing

29. 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.

30. Hypothesis Testing: Error Reality Treatments are not different Treatments are different Conclude that treatments are not different Correct Decision Type II Error (Probability =  ) Conclude that treatments are different Type I Error (Probability =  ) Correct Decision (Probability = 1-  = Power) Decision

31. Significance Testing A p value is not the probability that your finding is due to random chance alone But of collecting a random sample of the same size from the same population that yields a result at least as extreme as the one you just calculated Level of Significance (  level) is the probability of rejecting a null hypothesis when it is true The level of risk a researcher is willing to take of being wrong Usually set to 0.05 or 0.01

32. Hypothesis Testing: Error Type I Error: Probability of rejecting the null hypothesis when the null hypothesis is true.  = probability of making a type I error Type II Error: Probability of accepting the null hypothesis when the alternate hypothesis is true.  = probability of making a type II error Power: Probability of correctly concluding that the outcomes differ 1 -  = power

33. Hypothesis Testing: Error Reality Treatments are not different Treatments are different Conclude that treatments are not different Correct Decision Type II Error (Probability =  ) Conclude that treatments are different Type I Error (Probability =  ) Correct Decision (Probability = 1-  = Power) Decision

34. Parametric Tests Assume Normal distribution of the sample population Usually continuous-interval variables z Test Student’s t Test

35. z Test Test the difference in means of two proportions (two tailed) Use when: Sample size is greater than 30 Requires a normal distribution Example: Comparing your mean infection rate to NHSN mean rates

36. t Tests http://www.dimensionresearch.com/resources/calculators/ztest.html

37. t Tests Test the difference in means (one or two tailed) Use when: Sample size is less than 30 Assumes  Independence of populations & values  Variance is equal for both sets of data  No confounding variables Types of t Tests: Independent sample (experiment vs. control) Paired sample (before and after)

38. t Tests http://www.dimensionresearch.com/resources/calculators/ttest.html

39. t Tests http://www.usablestats.com/calcs/2samplet

40. Non-Parametric Tests Do not assume normal distribution Used with more types of data: Nominal, Ordinal, Interval, Discrete (infection vs no infection) Chi Square (X 2 ) Compares observed values against expected values  Example: Comparing SSI rates for Dr. X and Dr. Y http://www.gifted.uconn.edu/siegle/research/ChiS quare/chiexcel.htm http://www.gifted.uconn.edu/siegle/research/ChiS quare/chiexcel.htm

41. 2x2: Exposures and Outcomes Patients With Disease Patients With No Disease Patients Exposed ab Patients Not Exposed cd

42. Chi square http://faculty.vassar.edu/lowry/newcs.html

43. Relative Risk Comparing the risk of disease in exposed individuals to individuals who were not exposed Patients With Disease Patients With No Disease Patients Exposed ab Patients Not Exposed cd ___Disease incidence in exposed___ _a / (a + b)_ Disease incidence in non-exposed c / (c + d) __a__ ____a + b____ __c__ c + d RR = = ( ( ) )

44. Relative Risk RR = 1 Risk in exposed equal to risk in non-exposed No association RR > 1 Risk in exposed greater than risk in non-exposed Positive association, possibly causal RR < 1 Risk in exposed less than risk in non-exposed Negative association, possibly protective

45. Odds Ratio Comparing the odds that a disease will develop Patients With Disease (Cases) Patients With No Disease (Controls) Patients With History of Exposure ab Patients Without History of Exposure cd __Odds that a case was exposed_ _a / c_ _ad_ Odds that a control was exposed b / d bc OR ===

46. Odds Ratio OR = 1 Exposure not related to the disease OR > 1 Exposure positively related to disease OR < 1 Exposure negatively related to the disease

47. 95% Confidence Interval 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 the interval given. Allows you to assess variability of an estimated statistic If the confidence interval includes the value of 1, then the stat is not significant

48. Standardized Infection Ratio (SIR) Compare the HAI experience among one or more groups of patients to that of a standard population’s (e.g. NHSN) Risk-adjusted summary measure Available for CAUTI, CLABSI, and SSI data Details can be found in the SIR Newsletter, available at: http://www.cdc.gov/nhsn/PDFs/Newsletters/NHSN_N L_OCT_2010SE_final.pdf

49. SIR Observed # of HAI – the number of events that you enter into NHSN Expected or predicted # of HAI – comes from national baseline data* The formula for calculating the number of expected CLABSI infections is: # central line days *(NHSN Rate/1000) *Source of national baseline data: NHSN Report, Am J Infect Control 2009;37:783- 805 Available at: http://www.cdc.gov/nhsn/PDFs/dataStat/2009NHSNReport.PDF

50. SIR – CLAB Data for CMS IPPS

51. Overall SIR Interpretation During the first half of 2011, our facility observed 15 CLABSIs in our ICU locations. The number of expected CLABSIs during this timeframe, based on national data, was 10.397 CLABSIs This yields an SIR of 1.443, indicating that we observed approx. 44% more infections than expected Based on statistical evidence, we can conclude that our SIR is no different than 1

52. SIR for SSI Data SSI Rates output options have been moved to “Advanced” folder You can still obtain your facility’s SSI rates using Basic Risk Index, however NHSN pooled mean and comparison statistics for SSI Rates will no longer be available SIRs use several risk factors to build logistic regression models for improved risk adjustment

53. Expected SSIs The number of expected SSIs is calculated by summing the procedure risk for all procedures included in the summarized calculation (e.g., all procedures for 2011, H1) The procedure risk is calculated from improved risk models* The “Basic Risk Index” is no longer used for national SSI analyses New risk models provide improved risk adjustment in the prediction of SSIs *Mu Y et al. Infect Control Hosp Epidemiol 2011;32(10):970-986.

54. Available NHSN Risk Factors

55. Logistic Regression Model

56. Logistic Model for VHYS

57. Sum Probability of SSI for #Expected SSIs

58. Overall SSI SIR

59. Questions?

60. Useful Resources:

61. APIC EpiGraphics: Statistics and Surveillance Tools for IPs APIC Manual, Chapter 5 – Use of Statistics. (2009) PDQ Statistics. GR Norman & DL Streiner (2003). BC Decker. Fundamentals of Biostatistics. B Rosner (2000). Brooks/Cole. Epidemiology for Public Health Practice. RH Friis & TA Sellers (2004). Jones and Bartlett Publishers, Inc. Excel Hacks. DE Hawley (2007). O’Reilly www.graphpad.com/quickcalcs http://www.danielsoper.com/statcalc/default.aspx Free statistics calculators http://nccphp.sph.unc.edu/training/index.php Free online epi training from North Carolina Center of Public Health Preparedness

62. Images From: National prevalence of methicillin-resistant Staphylococcus aureus in inpatients at US health care facilities, 2006. W Jarvis et al. AJIC December 2007 National Healthcare Safety Network (NHSN) report: Data summary for 2006 through 2008, issued December 2009. Edwards et al. AJIC December 2009. PDQ Statistics. GR Norman & DL Streiner (2003). BC Decker. Pertussis: A Disease Affecting All Ages. DS Gregory. American Family Physician. August 2006. www.aafp.org/afp/2006/0801/p420.html www.aafp.org/afp/2006/0801/p420.html Summarizing Your Data. Science Buddies. www.sciencebuddies.org/mentoring/project_data_analysis_sum marizing_data.shtml www.sciencebuddies.org/mentoring/project_data_analysis_sum marizing_data.shtml