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Statistical analyses in the real world

Statistical analyses in the real world. Paul Williams Lawrence Berkeley National Laboratory. Statistical significance. Theory: The probably of observing something by chance Practice: The accepted threshold P<0.05 is publishable P>0.05 is not publishable

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Statistical analyses in the real world

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  1. Statistical analyses in the real world Paul Williams Lawrence Berkeley National Laboratory

  2. Statistical significance • Theory: The probably of observing something by chance • Practice: The accepted threshold • P<0.05 is publishable • P>0.05 is not publishable • The promise to produce P<0.05 is a primary consideration for NIH funding

  3. Choice of an appropriate statistical test • Familiarity to the reader, reviewer, granting agency • Succinctness, in consideration of journal space, simplicity in presenting results • Statistical tests promise the world, which we can then promised to funding agencies, journals, etc.

  4. Classical regression model

  5. 1. The real world may befuddle the description of even the simplest relationships

  6. Relationship of average BMI to weekly distance walked in women kg/m2 Williams PT.Med Sci Sports Exerc. 2005 371893-901.

  7. Relationship of percentiles of the BMI distribution to weekly distance walked in women kg/m2 Williams PT.Med Sci Sports Exerc. 2005 371893-901.

  8. Convex regression curve

  9. Regression slope by percentile Slope (kg/m2 per km/wk) Williams PT.Med Sci Sports Exerc. 2005 371893-901.

  10. Decline in BMI per km/wk run or walked Slope (∆BMI per 1km difference in weekly distance) Williams PT.Med Sci Sports Exerc. 2005 371893-901.

  11. Correspondence between BMIs of female runners and walkers

  12. Q-Q plot of female runners’ and walkers’ BMI distribution Walkers’ BMI distribution

  13. Estimated change in BMI per one km/wk difference in running distance Slope (∆BMI per 1km difference in weekly distance)

  14. Published applications: “… the effects of physical activity, alcohol, and weight reduction on HDL-C levels may be, to a large extent, dependent on the initial level with the greatest improvement achieved in subjects with high HDL and the least improvement in those having low HDL-C levels.” Williams PT.The relationships of vigorous exercise, alcohol, and adiposity to low and high high-density lipoprotein-cholesterol levels.Metabolism. 2004 Jun;53(6):700-9.

  15. Published applications: “We speculate that the reported greater increases in triglycerides per unit of adiposity in whites than blacks, in men than women, and in low-density lipoprotein (LDL) pattern B than A are all consistent with the relationships we observe.” Williams PT. Relationship of adiposity to the population distribution of plasma triglyceride concentrations in vigorously active men and women. Atherosclerosis. 2004 Jun;174(2):363-71.

  16. Published applications: “We speculate that the reported greater increases in triglycerides per unit of adiposity in whites than blacks, in men than women, and in low-density lipoprotein (LDL) pattern B than A are all consistent with the relationships we observe.” Williams PT. Relationship of adiposity to the population distribution of plasma triglyceride concentrations in vigorously active men and women. Atherosclerosis. 2004 Jun;174(2):363-71.

  17. Published applications: “These results are consistent with the hypothesis that running promotes the greatest weight loss specifically in those individuals who have the most to gain from losing weight.” Williams PT. Vigorous exercise and the population distribution of body weight.Int J Obes Relat Metab Disord. 2004 Jan;28 (1):120-8

  18. 2. The complexities of the real world may negate most statistical analyses

  19. Classical regression model

  20. After assigning significance, the second most important contribution of statistics to research scientist is adjustment • For example, walkers may be leaner than nonwalkers but is it because they eat better. • Statistical adjustment is usually a sufficient argument for journals, funding agencies, etc.

  21. Classical statistical adjustment Triglycerides (mmol/L)

  22. Alternative statistical adjustment % reduction Williams PT.Metabolism . 2004;53:700-9.

  23. 3. Analysis of change data DBMI=a +bDdistance

  24. DBMI=a +bDdistance Cross-sectional relationship BMI Distance

  25. Translating change data into a relationship Doesn’t correspond To: DBMI=a + bDdistance gDdistance2 Cross-sectional relationship BMI The amount of change depends upon the starting and ending distance

  26. Annual change in men’s BMI by reported running distance

  27. Exposure model relating DBMI to change in running distance Estimated DBMI due to a “dj-cj” km/wk change in running distance Williams PT, Wood PD. Int J Obes (Lond). 2006 30:543-51

  28. Exposure model to weight change by Drunning

  29. 4. Measurement error

  30. Original interpretation of ACLS Blair SN, et al. JAMA. 1995;273:1093-8.

  31. Variables measured with error Second fitness measurement (Treadmill duration) Williams PT. Med Sci Sports Exerc. 2003;35:736-40.

  32. Our interpretation of ACLS Fitness measured Fitness measured Williams PT. Med Sci Sports Exerc. 2003;35:736-40.

  33. Measurement error model

  34. Simulation of measurement error

  35. Simulation results

  36. Simulation versus reported results Williams PT. Med Sci Sports Exerc. 2003;35:736-40.

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