Week 3: Ratios, s, and Proportions (Part I) Dan Bronson Lowe, PhD, CIC Senior Clinical Manager Baxter Healthcare Corporation DISCLOSURES The speaker, Daniel Bronson Lowe, discloses no actual or potential conflict of interest in relation to this program/presentation. The following planning staff report no actual or potential conflict of interest in relation to this program/presentation. Carol McLay DrPH, MPH, RN, CIC Bill Bridges PhD 1
Healthcare Worker Flu Vaccination Clinic A Clinic B 20 vaccinated 5 vaccinated 100 total 5 total 20% vaccinated 100% vaccinated Counts Frequency Measures Ratios Proportions s 2
Ratios Proportions s Counts Frequency Measures Ratios Proportions s Numerator Denominator x 10n Where: 10 0 = 1 10 1 = 10 10 2 = 100 10 3 = 1,000 10 4 = 10,000 and so on Ratios Number or rate of events/items/persons/etc. in group 1 Number or rate of events/items/persons/etc. in group 2 x 10 n A hospital with 420 inpatient beds has 3 IPs. 420 / 3 (x 1) = 140 inpatient beds per IP Ratio of inpatient beds to IPs is 140:1. 3
Proportions events/persons with a particular characteristic Total number of events/persons (of which the numerator is a subset) x 10 n During 2015 a hospital had 50, of which 18 were in male patients. 18 / 50 (x 100) = 36 in males per 100 = 36% of were in males s Number or rate of events during the time period Number or rate of events/items/persons/etc. at risk during the time period x 10 n A hospital with 80,000 admissions in 2014 had 120 cases of healthcare acquired C. difficile infections in 2014. 120 / 80,000 (x 1) = 0.0015 infection per admission per year 120 / 80,000 (x 10,000) = 15 infections per 10,000 admissions per year So What is It? 1. Is it based on (Numerator/Denominator) x 10 n? No = Not a Ratio. Stop here. Yes = Ratio. Go to Question 2. Example A 24 patients Example C Example B 16 males / 8 females = 2 males per female Example D 16 males/24 patients (x100) = 67% 8patients per day 4
So What is It? 2. Is the Numerator a subset of the Denominator? No = Not a Proportion. Go to Question 3. Yes = Proportion. Go to Question 3. Example B 16 males / 8 females = 2 males per female Example C 16 males/24 patients (x100) = 67% Example D 8patients per day So What is It? 3. Is time part of the Denominator? No = Not a. Stop here. Yes =. Stop here. Example B 16 males / 8 females = 2 males per female Example C 16 males/24 patients (x100) = 67% Example D 8patients per day Mortality or Cure Prevalence 5
Prevalence Prevalence = existing cases at a given point in time Total population at a given point in time Point Prevalence Specific point in time Period Prevalence Specific period in time Point vs. Period Data by minute Point = one minute Period = multiple minutes (hour/day/week/ ) Data by day Point = one day Period = multiple days (week/month/year/ ) Point Prevalence Prevalence = isolation patients on W on June 4th Total population on W on June 4th 6
Patients on Isolation on W June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month Patient Presence on W June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month Point Prevalence Prevalence = isolation patients on W on June 4th Total population on W on June 4th Prevalence = 5 isolation patients 7 patients total Prevalence = 0.71 71% 7
Period Prevalence Prevalence = isolation patients on W in June Total population on W in June Patients on Isolation on W June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month Patient Presence on W June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month 8
Period Prevalence Prevalence = isolation patients on W in June Total population on W in June Prevalence = 8isolation patients 12 patients total Prevalence = 0.67 67% = new cases during a given time period Total at risk population (or time) observed Proportion Cumulative Person based; uses people at risk Density Time based; uses time at risk Proportion Proportion = new cases during a given time period Total at risk population observed 9
CAUTI Events on Z June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month Patient Presence on Z June 2015 Foley Catheter Use on Z June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month Proportion Proportion = Proportion = new cases during a given time period Total at risk population observed 3 new in June 12 patients in June = 0.25 25% Proportion 10
Proportion Proportion = Proportion = new cases during a given time period Total at risk population observed 3 new in June 9 patients with urinary catheters in June = 0.34 34% Proportion Foley Catheter Use on Z June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month = new cases during a given time period Total at risk time observed 11
CAUTI Events on Z June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month Foley Catheter Use on Z June 2015 Patient A B C D E F G H I J K L 1 7 14 21 28 Day of the Month Catheter Days 11 0 4 7 30 6 0 0 14 30 3 9 114 = new cases during a given time period Total at risk time observed = 3 new in June 114 urinary in June = 0.026 per catheter day = 26 per 1000 12
Attack Attack = new cases during a given time period Total at risk population observed Overall Attack = 8 new cases of norovirus this week 420 in patients Overall Attack = 0.02 2% Attack Attack = new cases during a given time period Total at risk population observed Food Specific Attack = Food Specific Attack = 7 new cases of norovirus this week (ate salad) 120 in patients (ate salad) 0.06 6% Mortality Mortality = deaths Total at risk population observed x10 n (per year) Crude Mortality = 100 deaths 20,000 total population x1,000 (per year) Crude Mortality = 5 deaths per 1,000 population per year 13
Mortality Mortality = deaths Total at risk population observed x10 n (per year) Cause Specific Mortality = 2 tuberculosis deaths 20,000 total population x100,000 (per year) Cause Specific Mortality = 10 TB deaths per 100,000 population per year Crude vs. Category-Specific s Hospital A Hospital B 25 11 8000 8000 3.1 per 1,000 1.4 per 1,000 Hospital A Medical 24 6000 4.0 Rehab 1 2000 0.5 Total 25 8000 3.1 Hospital B Medical 8 2000 4.0 Rehab 3 6000 0.5 Total 11 8000 1.4 14
Hospital A Hospital B ICU 12 6000 2.0 Medical 3 1000 3.0 Oncology 3 1500 2.0 Ortho 0 750 0.0 Rehab 1 2000 0.5 Stepdown 3 1500 2.0 Surgical 18 3000 6.0 Telemetry 0 250 0.0 Total 40 16000 2.5 ICU 2 200 10.0 Medical 3 3000 1.0 Oncology 10 2500 4.0 Ortho 1 450 2.2 Rehab 0 1200 0.0 Stepdown 0 50 0.0 Surgical 10 15000 0.7 Telemetry 1 80 12.5 Total 27 22480 1.2 Direct Standardization Standardization Your Population Category Specific s Standard Population Indirect Standardization Your Population Category Specific s Standard Population Direct Standardization Hospital A s Hospital B s Standard Population denominator (e.g. ) Infections for Standard Population using Hospital A rates versus Infections for Standard Population using Hospital B rates 15
Hospital A Direct Standardization Medical 24 6000 4.0 Rehab 1 2000 0.5 Total 25 8000 3.1 Standard Hospital Medical 4000 Rehab 4000 Total 8000 Hospital B Direct Standardization Medical 8 2000 4.0 Rehab 3 6000 0.5 Total 11 8000 1.4 Standard Hospital Medical 4000 Rehab 4000 Total 8000 Hospital A Hospital B 25 11 8000 8000 Crude : 3.1 per 1,000 Standardized : 2.3 per 1,000 Crude : 1.4 per 1,000 Standardized : 2.3 per 1,000 16
Indirect Standardization Hospital A s Hospital B s Hospital A denominator (e.g. ) Actual Infections for Hospital A versus Infections for Hospital A using Hospital B rates Hospital A (Standardized) Indirect Standardization Medical 24 6000 4.0 Rehab 1 2000 0.5 Total 25 8000 3.1 Hospital B (Standard Population) Medical 8 2000 4.0 Rehab 3 6000 0.5 Total 11 8000 1.4 Hospital A (Expected) Indirect Standardization Medical 24 6000 4.0 Rehab 1 2000 0.5 Total 25 8000 3.1 Hospital A (Observed) Medical 24 6000 4.0 Rehab 1 2000 0.5 Total 25 8000 3.1 17
Standardized Infection Ratio SIR = Observed number of infections Expected number of infections Better Same Worse 0 1 2 SIR Standardized Infection Ratios Null hypothesis: Your infection rate and the benchmark infection rate are the same. Alternative hypothesis: Your infection rate and the benchmark infection rate are different. Better Same Worse 0 1 2 SIR Standardized Infection Ratios α = 0.05 CABG Related Surgical Site Infections Procedures Expected SIR 95% Confidence Facility Performed Infections Infections SIR p value Interval for SIR A 290 1 5.8 0.2 0.03 0.0, 0.9 B 80 4 1.5 2.6 0.65 0.7, 6.7 C 1500 75 28.5 2.6 0.01 2.1, 3.3 Better Same Worse 0 1 2 SIR 18
Standardized Infection Ratios α = 0.05 95% Confidence Facility SIR SIR p value Interval for SIR A 0.2 0.03 0.0, 0.9 B 2.6 0.65 0.7, 6.7 C 2.6 0.01 2.1, 3.3 0 1 2 3 4 5 6 7 SIR Crude s Category Specific s Standardized s 19
Module 3 Takeaways It takes more than one measure to get the whole story. Nomenclature is iffy. Focus on what s actually being calculated rather than what it is called. Watch out for confounding if the denominators of the groups are different. 20