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Biostat 200 Introduction to Biostatistics

Biostat 200 Introduction to Biostatistics . Lecture 1. Course instructors. Judy Hahn, M.A., Ph.D. Judy.hahn@ucsf.edu (415) 206-4435 TAs Michelle Odden, Ph.D., M.S. Megumi Okumura, M.D. Maya Vijayaraghavan, M.D. Robin Wallace. M.D. The details. Lectures: Tuesdays 10:30-12:30

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Biostat 200 Introduction to Biostatistics

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  1. Biostat 200Introduction to Biostatistics

  2. Lecture 1

  3. Course instructors • Judy Hahn, M.A., Ph.D. • Judy.hahn@ucsf.edu • (415) 206-4435 • TAs Michelle Odden, Ph.D., M.S. Megumi Okumura, M.D. Maya Vijayaraghavan, M.D. Robin Wallace. M.D.

  4. The details • Lectures: Tuesdays 10:30-12:30 • Labs: Thursday 10:30-12 • Lab 1: Room CB 6702 • Lab 2: Room CB 6704 • Office hrs: Thursday 12-1 Room CB 5715 • Course credits: 3

  5. The details • Readings • Required readings will be from Principles of Biostatistics by M. Pagano and K. Gauvreau. Duxbury. 2nd edition. • Please read the assigned chapters before lecture, and review them after lecture

  6. The details • Assignments will be posted on Thursdays with due dates Sunday at 5 p.m. 1.5 weeks later • Data collection (Assignment 1 only) • Data analysis and interpretation • Exercises in the book • Reading and interpretation of scientific publications • You must attend Lab 1 to receive assignment 1

  7. The details • Grading: • Homework (75%) • 5 Assignments • Varying in length; each homework problem is worth (usually 10) points toward final homework score • Final exam (25%) • LATE ASSIGNMENTS WILL NOT BE ACCEPTED!!!

  8. Assigments • Send to your TAs • Lab 1: Megan Okumura, Robin Wallace ticr.biostat200.1@gmail.com • Lab 2: Michelle Odden, Maya Vijayaraghavan ticr.biostat200.2@gmail.com

  9. What I do and why

  10. Course goals • Familiarity with basic biostatistics terms and nomenclature • Ability to summarize data and do basic statistical analyses using STATA • Ability to understand basis statistical analyses in published journals • Understanding of key concepts including statistical hypothesis testing – critical quantitative thinking • Foundation for more advance analyses

  11. Today’s topics • Variables- numerical versus categorical • Tables (frequencies) • Graphs (histograms, box plots, scatter plots, line graphs) • Required reading: Pagano Chapter 2

  12. Types of data • Data are made up of a set of variables • Categorical variables: any variable that is not numerical (values have no numerical meaning) (e.g. gender, race, drug, disease status) • Nominal variables • Ordinal variables Pagano and Gauvreau, Chapter 2

  13. Types of data • Categorical variables • Nominal variables: • The data are unordered (e.g. RACE: 1=Caucasian, 2=Asian American, 3=African American) • A subset of these variables are Binary or dichotomous variables: have only two categories (e.g. GENDER: 1=male, 2=female) • Ordinal variables: • The data are ordered (e.g. AGE: 1=10-19 years, 2=20-29 years, 3=30-39 years; likelihood of participating in a vaccine trial) Pagano and Gauvreau, Chapter 2

  14. Types of data • Numerical (quantitative) variables: naturally measured as numbers for which meaningful arithmetic operations make sense (e.g. height, weight, age, salary, viral load, CD4 cell counts) • Discrete variables: can be counted (e.g. number of children in household: 0, 1, 2, 3, etc.) • Continuous variables: can take any value within a given range (e.g. weight: 2974.5 g, 3012.6 g) Pagano and Gauvreau, Chapter 2

  15. Types of data • Manipulation of variables • Continuous variables can be discretized • E.g., age can be rounded to whole numbers • Continuous or discrete variables can be categorized • E.g., age categories • Categorical variables can be re-categorized • E.g., lumping from 5 categories down to 2 Pagano and Gauvreau, Chapter 2

  16. Frequency tables • Categorical variables are summarized by • Frequency counts – how many are in each category • Relative frequency or percent (a number from 0 to 100) • Or proportion (a number from 0 to 1) Pagano and Gauvreau, Chapter 2

  17. Frequency tables • Continuous variables can categorized in meaningful ways • Choice of cutpoints • Even intervals • Meaningful cutpoints related to a health outcome or decision • Equal percentage of the data falling into each category Pagano and Gauvreau, Chapter 2

  18. Frequency tables Pagano and Gauvreau, Chapter 2

  19. Bar charts • General graph for categorical variables • Graphical equivalent of a frequency table • The x-axis does not have to be numerical Pagano and Gauvreau, Chapter 2

  20. Histograms • Bar chart for numerical data – The number of bins and the bin width will make a difference in the appearance of this plot and may affect interpretation histogram cd4count, fcolor(blue) lcolor(black) width(50) name(cd4_by50) title(CD4 among new HIV positives at Mulago) xtitle(CD4 cell count) percent Pagano and Gauvreau, Chapter 2

  21. Histograms • This histogram has less detail but gives us the % of persons with CD4 <350 cells/mm3 histogram cd4count, fcolor(blue) lcolor(black) width(350) name(cd4_by350) title(CD4 among new HIV positives at Mulago) xtitle(CD4 cell count) percent Pagano and Gauvreau, Chapter 2

  22. What does this graph tell us?

  23. Box plots • Middle line=median (50th percentile) • Middle box=25th to 75th percentiles (interquartile range) • Bottom whisker: Data point at or above 25th percentile – 1.5*IQR • Top whisker: Data point at or below 75th percentile + 1.5*IQR Pagano and Gauvreau, Chapter 2

  24. Box plots graph box cd4count, box(1, fcolor(blue) lcolor(black) fintensity(inten100)) title(CD4 count among new HIV positives at Mulago) Pagano and Gauvreau, Chapter 2

  25. Box plots by another variable • We can divide up our graphs by another variable • What type of variable is gender?

  26. Histograms by another variable

  27. Numerical variable summaries • Mode – the value (or range of values) that occurs most frequently • Sometimes there is more than one mode, e.g. a bi-modal distribution (both modes do not have to be the same height) • The mode only makes sense when the values are discrete, rounded off, or binned Pagano and Gauvreau, Chapter 3

  28. Scatter plots Pagano and Gauvreau, Chapter 2

  29. The importance of good graphs http://niemann.blogs.nytimes.com/2009/09/14/good-night-and-tough-luck/

  30. Numerical variable summaries • Measures of central tendency – where is the center of the data? • Median – the 50th percentile == the middle value • If n is odd: the median is the (n+1)/2 observations (e.g. if n=31 then median is the 16th highest observation) • If n is even: the median is the average of the two middle observations (e.g. if n=30 then the median is the average of the 15th and16th observation • Median CD4 cell count in previous data set = 234.5 Pagano and Gauvreau, Chapter 3

  31. Numerical variable summaries • Range • Minimum to maximum or difference (e.g. age range 15-58 or range=43) • CD4 cell count range: (0-1368) • Interquartile range (IQR) • 25th and 75th percentiles (e.g. IQR for age: 23-36) or difference (e.g. 13) • Less sensitive to extreme values • CD4 cell count IQR: (92-422) Pagano and Gauvreau, Chapter 3

  32. Numerical variable summaries • Measures of central tendency – where is the center of the data? • Mean – arithmetic average • Means are sensitive to very large or small values • Mean CD4 cell count: 296.9 • Mean age: 32.5 Pagano and Gauvreau, Chapter 3

  33. Interpreting the formula • ∑ is the symbol for the sum of the elements immediately to the right of the symbol • These elements are indexed (i.e. subscripted) with the letter i • The index letter could be any letter, though i is commonly used) • The elements are lined up in a list, and the first one in the list is denoted as x1 , the second one is x2 , the third one is x3 and the last one is xn . • n is the number of elements in the list. Pagano and Gauvreau, Chapter 3

  34. Numerical variable summaries • Sample variance • Amount of spread around the mean, calculated in a sample by • Sample standard deviation (SD) is the square root of the variance • The standard deviation has the same units as the mean • SD of CD4 cell count = 255.4 • SD of Age = 11.2 Pagano and Gauvreau, Chapter 3

  35. Numerical variable summaries • Coefficient of variation • For the same relative spread around a mean, the variance will be larger for a larger mean • Can use to compare variability across measurements that are on a different scale (e.g. IQ and head circumference) • CV for CD4 cell count: 86.0% • CV for age: 34.5% Pagano and Gauvreau, Chapter 3

  36. Pocket/wallet change • Histogram , boxplot • Mode, Median, 25th percentile, 75th percentile • Mean, SD • Differ by gender?

  37. For next time • Read Pagano and Gauvreau • Chapters 1-3 (Review of today’s material) • Chapter 6

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