1. Biost 511 DL Discussion Section Announcements Quiz 1 (CEU students only) Will be available on Canvas.uw.edu Friday 12 pm – Sunday 11:59 pm One hour to complete (from time you begin) Questions? Fall 2013Biostat 5110

2. Fall 2013Biostat 5111 (Biostatistics 511) Discussion Section Week 2 Mike Garcia Medical Biometry I

3. Fall 2013Biostat 5112 Lecture Outline Review of HW #1 Key Concepts/Topics from Weeks 1 & 2 Computer lab

4. Fall 2013Biostat 5113 Homework #1 Overall very good responses A few of you did not submit a response for problem 0. Note that future assignments with missing responses will receive a zero, regardless of the quality of the rest of the submission.

5. Fall 2013Biostat 5114 Homework #1: Formatting Please don’t include raw Stata (or other software) output! Extract the relevant information and summarize neatly. Rounding to 2 or 3 decimal places helps make your responses more readable.

6. Fall 2013Biostat 5115 Homework #1: Random sampling/bias A common mistake was thinking that only sampling a subset of the population of freshman women would lead to biased estimates. It really depends on how the sampling is done. If it is completely random, we expect the random subset to be, on average, similar to the population and would not expect bias. (e.g. 100 letters randomly sent out). If the subset differs from the population, then we would not expect them to be similar and there may be bias (e.g. more sexually active women responding to the study.

7. Fall 2013Biostat 5116 1. Scientific question/ Research hypothesis 2. Define measurable quantity to answer question 3. Design experiment/study to gather data 4. Collect data 5. Analyze data 6. Make decision about research question Scientific Method/Statistical thinking

8. Fall 2013Biostat 5117 Cystic fibrosis (CF) affects 30,000 individuals in the U.S. The condition is complicated by recurrent pulmonary infection. A study was conducted to determine if the aerosolized antibiotic tobramyacin was effective in treating recurrent bacterial infection in CF patients. 520 CF patients, 10 to 60 years of age, were randomized to receive tobramycin or placebo in a double-blind controlled trial. The primary endpoint was the pulmonary function test forced expiratory volume in one second (FEV1 ). Measurements were collected at baseline and again at the end of the 24-week study period. Example: Infection in Cystic fibrosis

9. Fall 2013Biostat 5118 Cystic fibrosis example What is the scientific question? What is the Experimental Design? What is the measured quantity used to investigate the scientific question?

10. Fall 2013Biostat 5119 Population vs. Sample POPULATION: the entire group of individuals of interest. SAMPLE: a subset of individuals selected from the population Populations are characterized by parameters. Samples are characterized by statistics. Parameters and statistics typically summarize the distribution of measured values on population/sampling units.

11. Fall 2013Biostat 51110 Cystic fibrosis example What is the population? What is the sample? What is one population parameter of interest? What is the corresponding statistic?

12. Fall 2013Biostat 51111 Types of Variables Binary (0/1) Categorical Nominal Ordinal Quantitative Discrete Continuous Examples: Department affiliation Sex Weight Number of students in the class Likert scale

13. Fall 2013Biostat 51112 Y0: FEV1 pre-treatment Y1: FEV1 post-treatment T: Treatment group (0/1) New variable: diff=Y1-Y0 What kind of variables are in the CF dataset?

14. Fall 2013Biostat 51113 Not hypothesis driven Goal: summarize data --univariate: location, spread of individual measures --bivariate: relationships between two variables Explore data, numerically and graphically Interesting patterns  lead to new hypotheses Types of statistical analyses: descriptive

15. Fall 2013Biostat 51114 Descriptive statistics: CF example Summarize distributions of baseline Y0, Y1, and the FEV1 difference. central tendencies spread shape of distributions relationship between Y0, Y1 outliers

16. Fall 2013Biostat 51115 A priori scientific question. Translate question into statistical hypothesis or quantity to esitmate Assume a model for the data Test the hypothesis/estimate the parameter Describe uncertainty about the estimate about the estimate or the statistical test Types of statistical analyses: inferential

17. Fall 2013Biostat 51116 CF example: inferential statistics A priori scientific hypothesis: Individuals treated on the drug have on average, less reduction in FEV1 from baseline to follow up compared to the control group. Goal of inferential statistics: Draw conclusions about the population of CF patients from the sample. Test if data support this hypothesis Estimate differences in FEV1 in both groups, with uncertainty bounds

18. Fall 2013Biostat 51117 Univariate summaries: quantitative variables Central Tendency: Mean, Median, Mode Spread Variance, standard deviation, IQR Shape of distribution Skewness Outliers

19. Percentiles The p-th percentile is the value which has p% of the sample values less than or equal to it. Median=50 th percentile Interquartile range 25%-75% percentile (indicator of spread) Fall 2013Biostat 51118

20. Box plots Fall 2013Biostat 51119

21. Histograms and density functions -Histograms tell us the probability of obtaining data in a given interval. -Probability density functions (pdfs) are mathematical functions yielding similar information. -STATA can approximate pdf of a variable. -X is the variable -P(0<X<2) given by area Under the curve between 0,2 Fall 2013Biostat 51120

22. Fall 2013Biostat 51121 Normal distribution --bell-shaped curve --symmetric --parameterized by mean and standard deviation Normal probability density function

23. Fall 2013Biostat 51122 CF example: Y0 Histogram with superimposed normal curve hist Y0, norm

24. Fall 2013Biostat 51123 Computer Lab Problem Investigate the efficacy of an experimental treatment Target Population: children with CF Sample: 520 patients between 3-18 years of age Treatment: Aerosolized antibiotic Variables Treatment assignment indicator (T=1 is treatment; T=0 is control) Y1 = FEV1 at the end of the study (24 weeks) Y0 = FEV1 prior to randomized group assignment Scientific Questions: Is the baseline FEV1 the same between treatment groups prior to randomization? Is there evidence of a treatment effect?

25. Fall 2013Biostat 51124 Conclusions from lab *Are there differences in the baseline FEV1 by treatment group: Why does this matter? *Do you think there is evidence for a treatment effect? Why or why not?

26. Fall 2013Biostat 51125 Week 1 key concepts 1. Scientific method and statistics 2.Types of variables 3.Descriptive versus inferential statistics 4.Population versus samples 5.Univariate summary measures 6.Plots (boxplot, histograms, density plots) 7. Introduction to normal probability density Problem / lab 1. Description and scientific question 2. Summaries (statistics and graphics) 3. Conclusions Summary

27. Fall 2013Biostat 51126 Relationships between 2 variables: scatter plots

28. Fall 2013Biostat 51127 Relationships between 2 variables : correlation Pearson’s correlation coefficient: what is the degree of linear association Between 2 variables? Ranges between -1 to 1. 0 => no correlation (generally). corr Y0 Y1 (obs=520) | Y0 Y1 -------------+------------------ Y0 | 1.0000 Y1 | 0.8932 1.0000