Biostat 200 Introduction to Biostatistics

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Biostat 200Introduction to Biostatistics
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Lecture 1
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Course instructors

• Judy Hahn, M.A., Ph.D.
• Judy.hahn_at_ucsf.edu
• [phone]
• TAs
• Michelle Odden, Ph.D., M.S.
• Megumi Okumura, M.D.
• Maya Vijayaraghavan, M.D.
• Robin Wallace. M.D.

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The details

• Lectures Tuesdays 1030-1230
• Labs Thursday 1030-12
• Lab 1 Room CB 6702
• Lab 2 Room CB 6704
• Office hrs Thursday 12-1 Room CB 5715
• Course credits 3

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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

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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

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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!!!

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Assigments

• Send to your TAs
• Lab 1 Megan Okumura, Robin Wallace
• ticr.biostat200.1_at_gmail.com
• Lab 2 Michelle Odden, Maya Vijayaraghavan
• ticr.biostat200.2_at_gmail.com

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What I do and why
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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

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Todays topics

• Variables- numerical versus categorical
• Tables (frequencies)
• Graphs (histograms, box plots, scatter plots,
  line graphs)
• Required reading Pagano Chapter 2

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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
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Types of data

• Categorical variables
• Nominal variables
• The data are unordered (e.g. RACE 1Caucasian,
  2Asian American, 3African American)
• A subset of these variables are Binary or
  dichotomous variables have only two categories
  (e.g. GENDER 1male, 2female)
• Ordinal variables
• The data are ordered (e.g. AGE 110-19 years,
  220-29 years, 330-39 years likelihood of
  participating in a vaccine trial)

Pagano and Gauvreau, Chapter 2
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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
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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
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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)

Gender of new HIV clinic patients, 2006-2007, Mbarara, Uganda. Gender of new HIV clinic patients, 2006-2007, Mbarara, Uganda.
n ()
Male 415 (39)
Female 645 (61)
Total 1060 (100)
Pagano and Gauvreau, Chapter 2
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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
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Frequency tables
CD4 cell counts (mm3) of newly diagnosed HIV positives at Mulago Hospital, Kampala (N268) CD4 cell counts (mm3) of newly diagnosed HIV positives at Mulago Hospital, Kampala (N268)
n ()
50 40 (14.9)
50-200 72 (26.9)
201-350 58 (21.6)
350 98 (36.6)
Pagano and Gauvreau, Chapter 2
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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
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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
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Histograms

• This histogram has less detail but gives us the
  of persons with CD4 lt350 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
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• What does this graph tell us?

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Box plots

• Middle linemedian (50th percentile)
• Middle box25th to 75th percentiles
  (interquartile range)
• Bottom whisker Data point at or above 25th
  percentile 1.5IQR
• Top whisker Data point at or below 75th
  percentile 1.5IQR

Pagano and Gauvreau, Chapter 2
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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
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Box plots by another variable

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

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Histograms by another variable
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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
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Scatter plots
Pagano and Gauvreau, Chapter 2
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The importance of good graphs
http//niemann.blogs.nytimes.com/2009/09/14/good-n
ight-and-tough-luck/
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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 (n1)/2
  observations (e.g. if n31 then median is the
  16th highest observation)
• If n is even the median is the average of the
  two middle observations (e.g. if n30 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
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Numerical variable summaries

• Range
• Minimum to maximum or difference (e.g. age range
  15-58 or range43)
• 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
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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
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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
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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
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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
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Pocket/wallet change

• Histogram , boxplot
• Mode, Median, 25th percentile, 75th percentile
• Mean, SD
• Differ by gender?

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For next time

• Read Pagano and Gauvreau
• Chapters 1-3 (Review of todays material)
• Chapter 6