Title: UCSF - Data Exploration

Slide 1: Multiple Predictor Regression

• Assess the relationship between an outcome and multiple predictors
• Powerful tool for:
  • understanding complex relationships
  • controlling confounding
  • prediction / risk stratification
• Regression models differ by outcome type, but all have much in common

Slide 2: Data Types

Slide 3: More on Data Type

• Data type implies plausible probability distn
• Different data summaries the sample mean not always interpretable
• Distinctions between different types can be flexible

Slide 4: Model depends on outcome type

• Continuous -- linear or gamma model
• Discrete (counts)- Poisson/negative binomial
• Binary -- logistic, relative risk models, survival models when follow-up varies
• All easily implemented in Stata

Slide 5: Data Exploration

• Find data errors
• Assess missingness
• Detect anomalous observations and outlying data values
• Select appropriate analysis methods
• Support a formal data analysis

Slide 6: Data Example

• Western Collaborative Group Study
• Large early observational study (n=3154)
• Association between "type A" behavior and coronary heart disease (CHD)
• Example variable: systolic blood pressure

Slide 7: Descriptive Output

Slide 8: Cholesterol Data with Outlier

Slide 9: Histograms

• Shows location, spread, and shape of the distribution
• Horizontal axis: intervals or "bins" in which data values are grouped
• Vertical axis: number, fraction, or percent of the observations in each bin

Interpreting Histograms

• Pattern of bar heights conveys shape of distribution:
  • number of modes
  • skewness
  • long or short tails
• Usefulness depends on number of bins
  • too many defeats goal of summarization
  • too few obscures shape of distribution

Slide 10: Stata Commands

• histogram varname to graph a histogram
• histogram varname, bin(x) histogram with x bars
• histogram varname, freq histogram with frequency not fractions

Slide 11: Boxplot

• Box with upper & lower hinges
• Box: 25% tile, median, 75% tile
• Length of box: interquartile range (IQR)
• Lower hinge: 25% tile minus 1.5*IQR
• Upper hinge: 75% tile plus 1.5*IQR
• Values outside hinges: outliers 100

Slide 12: Using a Boxplot

• Location: given by lines in box, median
• Spread: given by size of box, IQR
• Skewness: distance between the lines
• Outliers are clearly marked can usually tell how many and their values

Slide 13: Stata Command

• graph box varname to graph a boxplot
• graph box varname, over( grpvar) side-by-side boxplots based on grpvar
• group varname1 varname2, over( grpvar) side-by-side boxplots for two variables

Slide 14: qq Normal Plot

• Graphical approach to assessing Normality
• Horizontal axis (x axis) sorted data values
• Vertical axis (y axis) expected data values if data Normal
• If plot straight, data is nearly Normal
• Shape indicates nature violation, if any

Slide 15: Using qqNormal Plot

• Right skew: plot curved up
• Left skew: plot curved down
• Outlier: values far off line
• STATA: qnorm varname

Slide 16: Transforming variables

• Make outcome more normally distributed
• Linearize predictor effects, remove interactions, equalize outcome variance

• Untransformed variable more credible,interpretable
• Natural scale may be more meaningful: cost vs log cost

Slide 17: Frequency Tables

• Used for categorical data loses no information
• Display raw numbers of percentages
• Can be used for continuous data
  • discards lots of information
  • may create relevant groups

Slide 18: Summary

• Types of Data: Numerical v. Categorical
• Numerical: mean, SD, 5 numbers
• Numerical: histogram, boxplot, qq normal
• Categorical: Tables
• Transformations: potentially useful