1. GOALs pre-test Did you complete the pre-test? A Yes B No

2. Last lecture… Population: The entire collection of all objects under study Sample: is all the cases that we have collected data on (a subset of the population) Statistical inference is the process of using data from a sample to gain information about the population Sample statistics vs Population parameters Summary statistics for the location or central tendency: Mean, Median, Quartiles. Summary statistics for the variability in data: Range, Inter-quartile range (IQR), Variance, Standard deviation Data presentation: Dot-diagram, Stem-and-leaf diagram, Histogram and Box-plot

3. Association and Causation Two variables are associated if values of one variable tend to be related to values of the other variable Two variables are causally associated if changing the value of the explanatory variable influences the value of the response variable ASSOCIATION IS NOT NECESSARILY CAUSAL.

4. Does the headline imply a causal association? “Daily Exercise Improves Mental Performance” A Association (not necessarily causal) B Causal Association B is correct, This implies that exercising daily will improve (change) your mental performance

5. Does the headline imply a causal association? “Want to lose weight? Eat more fiber!” A Association (not necessarily causal) B Causal Association B is correct, This implies that eating fiber will cause you to lose weight.

6. Does the headline imply a causal association? “Cat owners tend to be more educated than dog owners” A Association (not necessarily causal) B Causal Association A is correct, there is no claim that owning a cat will change your education level.

7. Confounding Variable A third variable that is associated with both the explanatory variable and the response variable is called a confounding variable A confounding variable can offer a plausible explanation for an association between the explanatory and response variables Whenever confounding variables are present (or may be present), a causal association cannot be determined

8. Let's imagine that… Population: all patients with index vertebral fractures. Is this physical or concepetual population? Sample: we evaluate 400 patients with index vertebral fractures. 200 of whom received vertebroplasty and 200 did not. How should we assign treatments. We wanted to know if treating index osteoporotic vertebral fractures with vertebroplasty increased the risk of subsequent vertebral fractures. Index osteoporotic vertebral fractures: weakening and thinning in the bones that lead to fracture. Vertebroplasty: a treatment to stabilize the fractures. Bone cement is injected into back bones (vertebrae) that have cracked or broken, often because of osteoporosis.

9. We identified 45 subsequent fractures with the following fictitious distribution: After two years… VertebroplastyConservative careRelative risk (95% confidence interval) 30/200 (15%)15/200 (7.5%)2.0 (1.1–3.6) Can we conclude that those who received vertebroplasty were at a much higher risk ? A Yes B No

10. Further investigation… Patient Status: Vertebroplasty N = 200 Conservative care N = 200 Age, y, mean ± SD78.2 ± 4.179.0 ± 5.2 Weight, kg, mean ± SD54.4 ± 2.353.9 ± 2.1 Smoking status, No. (%)110 (55)16 (8) What do you think went wrong in this research study?

11. And further investigation… SmokeNo smoke VertebroplastyConservativeRR (95% confidence interval) VertebroplastyConservativeRR (95% confidence interval) 23/110 (21%)3/16 (19%)1.1 (0.4, 3.3)7/90 (8%)12/184(7%)1.2 (0.5, 2.9) If we stratify the results by smoking status, we note that the risk of subsequent fractures is similar between treatment groups in each stratum (smoking and nonsmoking) such that the relative risk (RR) is closer to 1 (no effect) compared with the overall results above where RR was 2.