Topics in Biostatistics Part 2

1
Topics in BiostatisticsPart 2

• Sarah J. Ratcliffe, Ph.D.
• Center for Clinical Epidemiology and
  Biostatistics
• University of Penn School of Medicine

2
Outline

• Hypothesis testing
• Examples
• Interpreting results
• Resources

3
Hypothesis testing

• Steps
• Select a one-sided or two-sided test.
• Establish the level of significance (e.g., ?
  .05).
• Select an appropriate test statistic.
• Compute test statistic with actual data.
• Calculate degrees of freedom (df) for the test
  statistic.

4
Hypothesis testing

• Steps contd
• Obtain a tabled value for the statistical test.
• Compare the test statistic to the tabled value.
• Calculate a p-value.
• Make decision to accept or reject null hypothesis.

5
Hypothesis testing

• Steps
• Select a one-sided or two-sided test.
• Establish the level of significance (e.g., ?
  .05).
• Select an appropriate test statistic.
• Compute test statistic with actual data.
• Calculate degrees of freedom (df) for the test
  statistic.

6
Hypothesis testing One-sided versus Two-sided

• Determined by the alternative hypothesis.
• Unidirectional one-sided
• Example
• Infected macaques given vaccine or placebo.
  Higher
• viral-replication in vaccine group has no benefit
  of
• interest.
• H0 vaccine has no beneficial effect on
  viral-replication levels at 6 weeks after
  infection.
• Ha vaccine lowers viral-replication levels by 6
  weeks after infection.

7
Hypothesis testing One-sided versus Two-sided

• Bi-directional two-sided
• Example
• Infected macaques given vaccine or placebo.
• Interested in whether vaccine has any effect on
  viral-
• replication levels, regardless of direction of
  effect.
• H0 vaccine has no beneficial effect on
  viral-replication levels at 6 weeks after
  infection.
• Ha vaccine effects the viral-replication levels.

8
Hypothesis testing

• Steps
• Select a one-sided or two-sided test.
• Establish the level of significance (e.g., ?
  .05).
• Select an appropriate test statistic.
• Compute test statistic with actual data.
• Calculate degrees of freedom (df) for the test
  statistic.

9
Hypothesis testing Level of Significance

• How many different hypotheses are being
  examining?
• How many comparisons are needed to answer this
  hypothesis?
• Are any interim analyses planned?
• e.g. test data, depending on results collect more
  data and re-test.
• gt How many tests will be ran in total?

10
Hypothesis testing Level of Significance

• ?total desired total Type-I error (false
  positives) for all comparisons.
• One test
• ?1 ?total
• Multiple tests / comparisons
• If ?i ?total, then ??i gt ?total
• Need to use a smaller ? for each test.

11
Hypothesis testing Level of Significance

• Conservative approach
• ?i ?total / number comparisons
• Can give different ?s to each comparison.
• Formal methods include Bonferroni, Tukey-Cramer,
  Scheffes method, Duncan-Walker.
• OBrien-Fleming boundary or a Lan and Demets
  analog can be used to determine ?i for interim
  analyses.
• Benjamini Y, and Hochberg Y (1995) Controlling
  the false discovery rate a practical and
  powerful approach to multiple testing. JRSSB,
  57125-133.

12
Hypothesis testing

• Steps
• Select a one-tailed or two-tailed test.
• Establish the level of significance (e.g., ?
  .05).
• Select an appropriate test statistic.
• Compute test statistic with actual data.
• Calculate degrees of freedom (df) for the test
  statistic.

13
Hypothesis testing Selecting an Appropriate test

• How many samples are being compared?
• One sample
• Two samples
• Multi-samples
• Are these samples independent?
• Unrelated subjects in each sample.
• Subjects in each sample related / same.

14
Hypothesis testing Selecting an Appropriate test

• Are your variables continuous or categorical?
• If continuous, is the data normally distributed?
  
• Normality can be determined using a P-P (or Q-Q)
  plot.
• Plot should be approximately a straight line for
  normality.
• If not normal, can it be transformed to
  normality?
• Blindly assuming normality can lead to wrong
  conclusions!!!

15
Hypothesis testing Selecting an Appropriate test
Approximately a straight line normal assumption
okay
16
Hypothesis testing Selecting an Appropriate test
Not a straight line NOT normal Can it be
transformed to normality?
17
Hypothesis testing Selecting an Appropriate test
The natural log transform of the data is
approximately a straight line normal assumption
okay Analyze the transformed data NOT the
original data.
18
Hypothesis testing Geometric versus Arithmetic
mean

• Geometric mean of n positive numerical values is
  the nth root of the product of the n values.
• Geometric will always be less than arithmetic.
• Geometric better when some values are very large
  in magnitude and others are small.
• If geometric is used, log-transform the data
  before analyzing.
• Arithmetic mean of log-transformed data is the
  log of the geometric mean of the data
• E.g. t-test on log-transformed data test for
  location of the geometric mean
• Langley R., Practical Statistics Simply
  Explained, 1970, Dover Press

19
Source Richardson Overbaugh (2005). Basic
statistical considerations in virological
experiments. Journal of Virology, 29(2) 669-676.
20
Hypothesis testing Selecting an Appropriate test

• Other tests are available for more complex
  situations. For example,
• Repeated measures ANOVA gt2 measurements taken
  on each subject usually interested in time
  effect.
• GEEs / Mixed-effects models gt2 measurements
  taken on each subject adjust for other
  covariates.

21
Hypothesis testing

• Steps
• Select a one-tailed or two-tailed test.
• Establish the level of significance (e.g., ?
  .05).
• Select an appropriate test statistic.
• Run the test.

22
Example 1

• Expression of chemokine receptors on CD14/CD14-
  populations of blood monocytes.
• Percent of cells positive by FACS.

23
(No Transcript)
24
Example 1 contd

• Continuous data, 2 samples
• gt t-test, if normal OR
• gt Wilcoxon rank sum or signed-rank sum test, if
  non-normal
• Are samples independent or paired?
• If independent, can test for equality of
  variances using a Levenes test

25
Example 1 contd
1-sided or 2-sided test

• T-tests in excel
• TTEST(L6L15,M6M15,2,2)

Type of t-test 1 paired 2 independent, equal
variance 3 independent, unequal variance
Cells containing data from sample 1
Cells containing data from sample 2
26
(No Transcript)
27
Example 1 contd

• Possible results for different assumptions

28
Example 1 contd

• Which result is correct?
• Data are paired
• The differences for each subject are normally
  distributed.
• gt Paired t-test
• p .0095
• There is a difference in the percentage of
  positive CD14 and CD14- cells.

29
A graph of the 95 CIs for the means would give
the impression there is no difference
30
When its really the differences we are testing.
31
Example 1 contd

• Note paired tests dont always give lower
  p-values.
• A 1-sided test on the CCR5 values would give
  p-values of
• p 0.06 independent samples
• p 0.11 paired samples
• WHY?

32
Example 1 contd

• The differences have a larger spread than the
  individual variables.

33
Example 2

• Does the level of CCR5 expression on PBLs (basal
  or upregulated using lentiviral vector) determine
  the of entry that occurs via CCR5?
• Two viruses
• 89.6
• DH12

34
Example 2 contd
35
Example 2 contd

• How do we know if the slope of the line is
  significantly different from 0?
• Can perform a t-test on the slope estimate. For
  simple linear regression, this is the same as a
  t-test for correlation ( square root of R2).

36
Example 2 contd
37
Interpreting Results

• P-values
• Is there a statistically significant result?
• If not, was the sample size large enough to
  detect a biologically meaningful difference?

38
Online Resources

• Power / sample size calculators
• http//calculators.stat.ucla.edu/powercalc/
• http//www.stat.uiowa.edu/rlenth/Power/
• Free statistical software
• http//members.aol.com/johnp71/javasta2.htmlFreeb
  ies

39
BECC Consulting Center

• www.cceb.upenn.edu/main/center/becc.html
• Hourly fee service
• Design and analysis strategies for research
  proposals
• Selecting and implementing appropriate
  statistical methods for specific applications to
  research data
• Statistical and graphical analysis of data
• Statistical review of manuscripts.