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A Conceptual Approach to Statistics

A Conceptual Approach to Statistics. Mitchell H. Katz, MD Director of Health. City & County of San Francisco Department of Public Health Mitch.Katz@sfdph.org. Why is statistic analysis so important for clinical research?. Because most treatments are not that effective!.

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A Conceptual Approach to Statistics

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  1. A Conceptual Approach to Statistics Mitchell H. Katz, MD Director of Health City & County of San Francisco Department of Public Health Mitch.Katz@sfdph.org

  2. Why is statistic analysis so important for clinical research? Because most treatments are not that effective!

  3. Should you anticoagulate persons with Afib and normal heart values? Answer: Anticoagulate

  4. What result would make you believe that the coin is biased? Beyond quantitation: Chance. * Probability of the observed data (or a more extreme result in either direction) when the expected probability is 0.50.

  5. Beyond quantitation: Chance. What result would make you believe that the coin is biased? * Probability of the observed data (or a more extreme result in either direction) when the expected probability is 0.50.

  6. Beyond quantitation: Chance. What result would make you believe that the coin is biased? * Probability of the observed data (or a more extreme result in either direction) when the expected probability is 0.50.

  7. Principles of Statistical Analysis • Quantifying experience • Determine probability of a particular result assuming that chance is the explanation (null hypothesis) • If probability is low, reject null hypothesis and consider alternative hypothesis

  8. Choose correct statistic

  9. Univariate Statistics FREQUENCIES %

  10. Anavekar, NS, et al. New Engl J Med. 2004;351:1285-95. Univariate Statistics • Histogram • Mean ≈ Median Interval variable: Normally distributed

  11. Shlipak, MG, et al. J Am Med Assoc. 2000; 283:1845-52. Univariate Statistics • Histogram • Mean ≠ Median • Interquartile Range (25% - 75%) Interval variable: Skewed

  12. Maisel, AS, et al. New Engl J Med. 2002;347:161-7. Univariate Statistics Non-normally distributed variables Box plot

  13. Univariate Statistics Time to event data (survival experience) Kaplan-Meier curves Incorporate censored observations including persons lost to follow-up.

  14. Kyrle, PA, et al. New Engl J Med. 2000; 343:457-62.

  15. Bivariate Statistics • Association between two variables. • Choose statistic based on the type of variables you have.

  16. Statistics for assessing an association between two variables, unpaired data Katz, MH. Study Design and Statistical Analysis: A Practical Guide for Clinicians. Cambridge University Press. 2006

  17. Inferential Statistics • Test the probability that the null hypothesis (no association) is correct. • When the probability is low (i.e., <.05) we reject the null hypothesis and consider alternative hypothesis.

  18. Common features of Inferential Statistics • Observations are independent of one another. Therefore: • Special statistics are needed when: • Multiple observations of the same subjects at different times • Multiple observations of the same subjects after receiving different treatments • Multiple observations of the same subjects by different observers • Multiple observations of different body parts of the same subjects • Clustered study design • Cases matched to a control

  19. Comparison of Bivariate tests for unpaired and paired data Katz, MH. Study Design and Statistical Analysis: A Practical Guide for Clinicians. Cambridge University Press. 2006

  20. Why do Multivariable Analyses? • Diseases have multiple causes • Apparent associations between a risk factor and an outcome may actually be due to a third factor: a confounder.

  21. Relationship among risk factor, confounder, and outcome. Katz MH. Multivariable Analysis: A Practical Guide for Clinicians. (2nd Ed.) Cambridge University Press, 2006.

  22. [RH = 2.66 (95% CI 2.34-3.03)] [RH = 1.21 (95% CI 0.98-1.50)] Does periodontitis cause CAD?

  23. Multivariable analysis • Enables us to identify the unique contribution of multiple risk factors to an outcome. • Minimize the effect of confounders especially in situations where randomization is not possible.

  24. Why is multivariable analysis harder? • Multidimensional instead of a flat plane. • Harder to assess whether the model fits the data.

  25. Type of outcome variable determines choice of multivariable analysis. Katz MH. Multivariable Analysis: A Practical Guide for Clinicians. (2nd Ed.) Cambridge University Press, 2006.

  26. Checking the assumptions of the model • Plot the residuals (the difference between the observed and the estimated value). • Assess the pattern.

  27. Limitations of multivariable analysis • Can only statistically adjust for those confounders you know (have measured). • Models are chosen that we believe fit the data, but the fit is always imperfect.

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