1. The Mathematics of Biostatistics Chapter 6 and 7 Copyright Kaplan University 2009

2. Our Progress So Far Week 1,2 and 3: Examination of the theory of epidemiology How this theory relates to biostatistics Week 4: Delving into the numbers game of biostatistics How biostatistics related to epidemiology

3. Simplifying Statistics To make a statistical operation more simple do the following: Write out the formula Plug in all the numbers in the appropriate places (make sure you have the right numbers) Work from the inside of the equation to the outside in terms of solving things Solve the equation, remember we are simply working with +, -, x, and ∙∕∙ all of your basic functions

4. Attributable Risk (AR) Defined: An estimate of the amount of risk which is attributable to the risk factor Formula: AR = [a/(a+b)] – [c/(c+d)]

5. Problem # 1 Refer to Pp. 92, Table 6-1 Using Table 6-1 (pp. 92) as our guide to what a,b,c, and d mean, lets use the data shown in Figure 6-1. Therefore: A = 191 (smokers dying of lung cancer) B = 999809 (100,000 population – A) C = 8.7 (non-smokers dying of lung cancer) D = 99991.30 (100,000 population – C)

6. Working the Equation Step 1: AR = [a/(a+b)] – [c/(c+d)] Step 2: AR = [191/(191+999809)] – [8.7/(8.7+99991.30)] Step 3 : 191-8.7 100,000 Step 4: 182.3/100,000

7. ANY QUESTIONS ON THIS FORMULA?

8. Try One On Your Own History: For a given year there was a heart attack death rate in people 50 pounds over their ideal weight of 1346 per 100,000 population. Among people of a normal weight there was a heart attack death rate in people within their ideal body weights of 200 per 100,000 population. Please identify a,b,c and d Determine the AR (you have 3 minutes)

9. AR = [a/(a+b)] – [c/(c+d)] AR = [1346/(1346+98654)] – [200/(200+99800)] AR = 1346 – 200/100,000 AR = 1146/100,000

10. Relative Risk Defined: This is somewhat of a comparison of the ratio of risk in an exposed group to the ratio of risk in the unexposed group. Formula: RR = [a/(a+b)]/[c/(c+d)] Hint: Notice that we are dividing the two sets of numbers not subtracting them as we did with AR

11. Use Data From Slide # 5 RR = [a/(a+b)] / [c/(c+d)] RR = [191/(191+999809)] / [8.7(8.7+99991.3)] RR = [191/100,000] / [8.7/100,000] RR = 191 / 8.7 100,000 RR = 21.95 100,000 RR = 22 (round up)

12. Your Turn Using the information from our obesity example, solve for RR You have 3 minutes Here are the values for your convenience A = 1346 B = 98654 C = 200 D = 99800

13. RR = [a/(a+b)] / [c/(c+d)] RR = [1346/(1346+98654)/[200/(200+99800 ) RR = 1346/200 100,000 RR = 6.73/100,000

14. ? ? ? ? ? So what does all of this data mean? Slide 11 = Smokers are 22 times more likely to die from lung cancer than non-smokers Slide 12 = People weighing 50 pounds over their ideal body weight are 7 times more likely to die from heart attacks than people within their normal weight range.

15. Ratio Defined: An estimate of a odds ratio Formula: OR = (a/c) / (b/d) HINT: Do not use the step in the book that instructs you to convert the above formula to OR = ad/bc. The reason is because the numbers sometimes become too large to work with and muddy the waters.

16. Using Slide # 12 Data OR = (a/c) / (b/d) OR = (1346 / 200) / (98654 / 99800) OR = 6.73 /.989 OR = 6.80

17. Your Turn… Using the data from Slide # 5 solve for OR Data is below for your convenience A = 191 B = 999809 C = 8.7 D = 99991.30 You have 3 minutes

18. OR = (a/c) / (b/d) OR = (191/8.7) / (999809/99991.30) OR= 21.95/10 OR = 2.195 or 2.2

19. Attributable Risk Percent Defined: A method of determining the total risk of death due to a condition found in the group practicing a particularly “risky” behavior. Formula AR% (exposed) = Risk ex – Risk unex X 100 Risk ex

20. Back to Slide 5 Data AR% = Risk ex – Risk unex x 100 Risk ex AR% = 191-8.7 x 100 191 AR% = 182.3 X 100 191 AR% = 95.4

21. So… According to this data, 95.4% of the lung cancer found in the smokers population is caused by the risk factor of smoking.

22. Key Concepts Accuracy: Ability of a measurement to be correct on the average Precision: Ability of a measurement to give the same results with repeated measurements of the same thing Both of these are necessary in statistics and neither takes a back seat to the other

23. Variability Who looks can make all the difference…or none at all Intraobserver variability = A difference of observation/interpretation of data when studied by the same person Interobserver variability = A difference of observation/interpretation of data when studied by more than one person

24. False is False and True is True Or is it? Type I Error Also known as a false-positive error or Alpha error The error is in the fact that a positive reading is registered when the results are actually negative

25. Continued… Type II Error Also known as a false-negative error or a beta error The error is in the fact that a negative reading is registered when the results are actually positive

26. Sensitive Vs. Specific Sensitivity – Ability of a test to detect the disease when present Specificity – Ability of a test to indicate non-disease status when no disease is present

27. A Summary of Tonight’s Class Mathematical manipulation of data Relationship between the data and the population it was taken from Support of epidemiological reckoning with statistical analysis of data

28. QUESTIONS

29. Future Plans Utilize the statistical tools conquered tonight Build on those tools with more tools Become junior statisticians who can use statistics to understand epidemiological principles