STA 102: Commonly Used Statistical Tests in Medical Research (Part II)

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STA 102 Commonly Used Statistical Tests in
Medical Research (Part II)

• Lecturer Dr. Daisy Dai
• Department of Medical Research

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Core Knowledge in Scholarly Activities
recommended by ABP

• Hypothesis testing
• Distinguish the null hypothesis from an
  alternative hypothesis.
• Interpret the results of hypothesis testing.

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Core Knowledge in Scholarly Activities
recommended by ABP

• Statistical tests
• Understand the appropriate use of the chi-square
  test versus t-test
• Understand the appropriate use of analysis of
  variance (ANOVA)
• Interpret the results of chi-square tests
• Interpret the results of t-tests
• Understand the appropriate use of parametric (eg,
  t-test, ANOVA) versus non-parametric (eg,
  Mann-Whitney U, Wilcoxon) statistical tests

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Core Knowledge in Scholarly Activities
recommended by ABP

• Statistical tests (Continued)
• Understand the appropriate use of a paired and
  non-paired t-test
• Determine the appropriate use of a 1- versus
  2-tailed test of significance
• Interpret a p-value
• Interpret a p-value when multiple comparison have
  been made
• Interpret a confidence interval
• Indentify a type I error
• Identify a type II error.

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Tests covered in the last talk

• Two-independent sample t-test.
• Paired t-test.
• One-way ANOVA
• Chi-square test
• Fishers exact test

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Distributions and Histograms
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Data Distributions

• Discrete distribution
• Binomial distribution
• Poisson distribution
• Continuous distribution
• Normal distribution
• Log-normal distribution
• Uniform distribution
• Exponential distribution
• Chi-square distribution
• F-distribution
• Student t-distribution

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Continuous Variables

• Two or multiple treatment groups

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Case Study Effects of Ocular Wetting Agents

• A research team was interested in evaluating the
  effect of a new ocular wetting agent, Oker-Rinse,
  for improving ocular dryness in patients with
  kerotitis siccs (KCS). Patients (n24) were
  instructed to use Oker-Rinse in one eye and
  Hypotears, as a control, in the other eye 4
  times a day for 3 weeks. Rose-Bengal staining
  scores from four areas of the eye cornea,
  limbus, lateral conjunctiva, and medial
  conjunctiva were added together. Higher scores
  represent a greater number of devitalized cells,
  a condition associated with KCS.

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Case Study Effects of Ocular Wetting Agents
ID Hypotears Oker-Rinse
1 15 8
2 10 3
3 6 7
4 5 13
5 10 2
6 15 12
7 7 14
8 5 8
9 8 13
10 12 3
11 4 9
12 13 3
ID Hypotears Oker-Rinse
13 8 10
14 10 2
15 11 4
16 3 7
17 6 1
18 6 11
19 9 3
20 5 5
21 10 2
22 9 8
23 11 5
24 8 8
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Histogram of Rose-Bengal Scores
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Histogram of Rose-Bengal Scores
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Wilcoxon signed rank test

• It is a non-parametric test that compares the
  medians of two related groups without normality
  assumption.

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Rank difference between two groups
ID Difference Rank
1 7 14.5
2 7 14.5
3 -1 1.5
4 -8 18.5
5 8 18.5
6 3 4.5
7 -7 14.5
8 -3 4.5
9 -5 7.5
10 9 21
11 -5 7.5
12 10 22
ID Difference Rank
13 -2 3
14 8 18.5
15 7 14.5
16 6 11
17 5 7.5
18 -5 7.5
19 6 11
20 0 --
21 8 18.5
22 1 1.5
23 6 11
24 0 --
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P-value
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Case Study Effects of Ocular Wetting Agents

• The mean of Rose-bengal score in Hypotears group
  was 8.6.
• The mean of Rose Bengal score in the Oker Rince
  group was 6.7.
• P0.085 gt 0.05.
• Oker Rince did not significantly reduce the
  number of devitalized cells.

This is a loose statement. We might fail a test
due to a small sample size.
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Wilcoxon rank-sum test

• It is a non-parametric test that compares
  medians of two-independent groups without the
  normality assumption.

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Case Study Seroxatene

• A studied was conducted to evaluate whether a
  new anti-depressant, Seroxatene has a benefit of
  pain relief. Patients (n28) with MRI-confirmed
  disk herniation and symptomatic leg pain were
  enrolled and randomly assigned to receive
  Seroxatene or a placebo for 8 weeks. At the end
  of the study, patients were asked to provide a
  overall rating of their pain, relative to
  baseline.

Deterioration Deterioration Deterioration No Change Improvement Improvement Improvement
Marked Moderate Slight No Change Sight Moderate Marked
-3 -2 -1 0 1 2 3
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Pain Relieving Scores
------- Seroxatene Group ------- ------- Seroxatene Group ------- ------- Seroxatene Group ------- ------- Seroxatene Group -------
ID Score ID Score
2 0 16 -1
3 2 17 2
5 3 20 -3
6 3 21 3
8 -2 22 3
10 1 24 0
12 3 26 2
14 3 27 -1
------- Placebo Group ------- ------- Placebo Group ------- ------- Placebo Group ------- ------- Placebo Group -------
ID Score ID Score
1 3 15 0
4 -1 18 -1
7 2 19 -3
9 3 23 -2
11 -2 25 1
13 1 28 0
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Histograms of Pain Scores
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Histograms of Pain Scores
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P-value
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Case Study Seroxatene

• The mean rank in the control group (n12) was 12.
• The mean rank in the test group (n18) was 16.
• P0.189.
• This experiment failed to demonstrate the pain
  relieving effect from Seroxatene at this
  experiment.

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Kruskal Wallis Test

• It is a non-parametric test that compares
  medians of multiple independent populations
  without the assumption of normally distributed
  data.

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Case study Lesion Size Data

• A study comparing a low dose (0.1) and high
  dose (0.2) of a new, non-steroidal,
  anti-psoriasis medication was conducted using a
  parallel design, including a placebo group as
  control. Thirty-two patients were studied for 4
  weeks of daily treatment. The primary efficacy
  response measure was the degree of psoriatic
  lesion reduction at study termination.

Coded Response Category Reduction in Lesion Size
1 lt0
2 0
3 1-10
4 11-25
5 26-50
6 51-75
7 76-99
8 100
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Lesion size data
Placebo Placebo
ID Lesion Reduction
2 5
4 3
8 7
11 1
13 2
16 4
17 2
21 1
24 4
25 5
29 4
30 5
0.2 Solution 0.2 Solution
ID Lesion Reduction
3 5
5 8
7 2
10 8
14 7
18 4
22 5
26 4
28 6
31 4
0.1 Solution 0.1 Solution
ID Lesion Reduction
1 5
6 4
9 1
12 7
15 4
19 3
20 6
23 7
27 8
32 7
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Histograms of Leisure Reductions
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P-value
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Case study Lesion Size Data
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Categorical Variables
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Binomial test

• Make inference about a proportion of binary
  outcomes by comparing the confidence interval of
  a proportion to target.

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Case Study Genital Wart

• A company markets a therapeutic product for
  genital warts with a known cure rate of 40 in
  the general population. In a study of 25
  patients with genital warts treated with this
  product, patients were also given high doses of
  vitamin C. As shown in Table 15.1, 14 patients
  were cured. Is this consistent with the cure
  rate in the general population?

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Treatment to Genital Wart
ID Effectiveness
1 YES
2 NO
3 YES
4 NO
5 YES
6 YES
7 NO
8 YES
9 NO
10 NO
11 YES
12 NO
13 YES
14 NO
ID Effectiveness
15 YES
16 NO
17 NO
18 YES
19 YES
20 NO
21 YES
22 YES
23 NO
24 YES
25 YES
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Results

• 64 (16/25) of patient were cured by the
  treatment.
• The 95 confidence interval extends from 44 to
  80
• If the probability of "success" in each trial or
  subject is 0.300, then the chance of observing 16
  or more successes in 25 trials is 0.045
  (p-value).
• The cure rate of genital wart by the experimental
  therapy was significantly higher than 30.

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MeNemars test

• Compare response rates in binary data between
  two related populations. Its analogous to
  Chi-square test or Fishers exact test for
  independent populations.

After Before Responders Non-responders
Responders A B
Non-responder C D
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Case Study Bilirubin

• A study was conduct to evaluate the toxicity
  side effect of an experimental therapy. Patients
  (n86) were treated with the experimental drug
  for 3 months. Clinical lab measured bilirubin
  levels of each patient at baseline and 3 months
  after therapy.

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Results of McNemars Test
After Before Normal Abnormally high
Normal 60 14
Abnormally high 6 6

• At baseline, 14 (12/86) of patients had
  abnormally high bilirubin level.
• At 3 months post treatment, 23 (20/86) of
  patients had abnormally high bilirubin level.
• P-value 0.1175
• Odds ratio 2.3 95 CI 0.8 - 7.4
• There is no enough evidence to prove the
  increasing risk of high bilirubin due to
  treatment.

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In summary

• Probability distribution
• Parametric test vs. nonparametric test.
• Three non-parametric tests for continuous
  variables.
• Binomial tests, McNemars test and CMH test for
  categrical variables.
• Confidence interval and odds ratio.

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Thank You

• For more information, visit my website
• http//www.childrensmercy.org/content/view.aspx?id
  9740
• Or go to Scope -gtResearch -gt Medical Research -gt
  Statistics

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References

• Medical Statistics by Campbell et al.
• Common Statistical Methods for Clinical Research
  by Dr. Glenn Walker