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The Mathematics of Biostatistics

The Mathematics of Biostatistics. Chapter 6 and 7. 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. Our Progress So Far.

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The Mathematics of Biostatistics

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  1. The Mathematics of Biostatistics Chapter 6 and 7

  2. 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 Our Progress So Far

  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 # 1Refer 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 – 200/100,000AR = 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 = 1346/200100,000RR = 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= 21.95/10OR = 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) = Riskex – Riskunex X 100 Riskex

  20. Back to Slide 5 Data • AR% = Riskex – Riskunex x 100 Riskex 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. VariabilityWho 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

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