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FoSSA: Fundamentals of Statistical Software & Analysis

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  1. Course Information

    Meet the Teaching Team
  2. Course Dataset 1
  3. Course Dataset 2
  4. MODULE A1: INTRODUCTION TO STATISTICS USING R, STATA, AND SPSS
    A1.1 What is Statistics?
  5. A1.2.1a Introduction to Stata
  6. A1.2.2b: Introduction to R
  7. A1.2.2c: Introduction to SPSS
  8. A1.3: Descriptive Statistics
  9. A1.4: Estimates and Confidence Intervals
  10. A1.5: Hypothesis Testing
  11. A1.6: Transforming Variables
  12. End of Module A1
    1 Quiz
  13. MODULE A2: POWER & SAMPLE SIZE CALCULATIONS
    A2.1 Key Concepts
  14. A2.2 Power calculations for a difference in means
  15. A2.3 Power Calculations for a difference in proportions
  16. A2.4 Sample Size Calculation for RCTs
  17. A2.5 Sample size calculations for cross-sectional studies (or surveys)
  18. A2.6 Sample size calculations for case-control studies
  19. End of Module A2
    1 Quiz
  20. MODULE B1: LINEAR REGRESSION
    B1.1 Correlation and Scatterplots
  21. B1.2 Differences Between Means (ANOVA 1)
  22. B1.3 Univariable Linear Regression
  23. B1.4 Multivariable Linear Regression
  24. B1.5 Model Selection and F-Tests
  25. B1.6 Regression Diagnostics
  26. End of Module B1
    1 Quiz
  27. MODULE B2: MULTIPLE COMPARISONS & REPEATED MEASURES
    B2.1 ANOVA Revisited - Post-Hoc Testing
  28. B2.2 Correcting For Multiple Comparisons
  29. B2.3 Two-way ANOVA
  30. B2.4 Repeated Measures and the Paired T-Test
  31. B2.5 Repeated Measures ANOVA
  32. End of Module B2
    1 Quiz
  33. MODULE B3: NON-PARAMETRIC MEASURES
    B3.1 The Parametric Assumptions
  34. B3.2 Mann-Whitney U Test
  35. B3.3 Kruskal-Wallis Test
  36. B3.4 Wilcoxon Signed Rank Test
  37. B3.5 Friedman Test
  38. B3.6 Spearman's Rank Order Correlation
  39. End of Module B3
    1 Quiz
  40. MODULE C1: BINARY OUTCOME DATA & LOGISTIC REGRESSION
    C1.1 Introduction to Prevalence, Risk, Odds and Rates
  41. C1.2 The Chi-Square Test and the Test For Trend
  42. C1.3 Univariable Logistic Regression
  43. C1.4 Multivariable Logistic Regression
  44. End of Module C1
    1 Quiz
  45. MODULE C2: SURVIVAL DATA
    C2.1 Introduction to Survival Data
  46. C2.2 Kaplan-Meier Survival Function & the Log Rank Test
  47. C2.3 Cox Proportional Hazards Regression
  48. C2.4 Poisson Regression
  49. End of Module C2
    1 Quiz

Learning Outcomes

By the end of this section, students will be able to:

  • Explain the key concept of power and what impacts it
  • Estimate the power of a given study
  • Estimate the sample size needed to test hypotheses in different study designs

You can download a copy of the slides here: A2.4: Sample Size Calculations for RCTs

Video A2.4 Sample Size Calculation for RCTs (11 minutes)

A2.4 PRACTICAL: R

Sample size calculation for testing a hypothesis (Clinical trials or clinical interventional studies)

Here is an example:

In a parallel RCT, 25% of the subjects on the standard therapy had a successful outcome. It is only of clinical relevance if a 40% absolute improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?

In this case we need to assess a difference in proportions again, this time with an effect size that has a 0.40 difference between the groups:

> power6<-pwr.2p.test(h=ES.h(p1=0.25, p2=0.65), power=0.8, sig.level=0.05)
>
power6

Difference of proportion power calculation for binomial distribution (arcsine transformation)

          h = 0.8282914
n = 22.88076
sig.level = 0.05
power = 0.8
alternative = two.sided

NOTE: same sample sizes

23 subjects per group and 46 subjects are required in total.

Question A2.4: In the same parallel trial as described in the example above, we still observe that 25% of the subjects on the standard therapy had a successful outcome, but this time it is only of clinical relevance if a 40% relative improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?

Answer

First you need to work out what a 40% relative increase on 25% is: 0.25*1.40=35% of subjects would need to have a successful outcome for there to be clinical relevance.

> power7<-pwr.2p.test(h=ES.h(p1=0.25, p2=0.35), power=0.8, sig.level=0.05)
> power7

Difference of proportion power calculation for binomial distribution (arcsine transformation)

          h = 0.2189061
n = 327.5826
sig.level = 0.05
power = 0.8
alternative = two.sided

NOTE: same sample sizes

We need many more patients than in the example above due to the small effect size that we now wish to detect.

A2.4 PRACTICAL: Stata

Sample size calculation for testing a hypothesis (Clinical trials or clinical interventional studies)

Here is an example:

In a parallel RCT, 25% of the subjects on the standard therapy had a successful outcome. It is only of clinical relevance if a 40% absolute improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?

power twoproportions 0.25 0.65, alpha(0.05) power(0.80)

*– Estimated sample sizes:

            N =        48

  N per group =        24

24 subjects per group and 48 subjects are required in total.

Question A2.4: In the same parallel trial as described in the example above, we still observe that 25% of the subjects on the standard therapy had a successful outcome, but this time it is only of clinical relevance if a 40% relative improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?

Answer

First you need to work out what a 40% relative increase on 25% is: 0.25*1.40=35% of subjects would need to have a successful outcome for there to be clinical relevance.

power twoproportions 0.25 0.35, alpha(0.05) power(0.80)

Estimated sample sizes for a two-sample proportions test
Pearson’s chi-squared test 
Ho: p2 = p1  versus  Ha: p2 != p1
Study parameters:

  alpha =    0.0500
        power =    0.8000
        delta =    0.1000  (difference)
           p1 =    0.2500

p2 =    0.3500

Estimated sample sizes:

            N =       658
  N per group =       329

We need many more patients than in the example above due to the small effect size that we now wish to detect.

A2.4 PRACTICAL: SPSS

Sample size calculation for testing a hypothesis (Clinical trials or clinical interventional studies)

In a parallel RCT, 25% of the subjects on the standard therapy had a successful outcome. It is only of clinical relevance if a 40% absolute improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance? Use the same test as in the previous practical (Independent Samples Binomial Test) but adapt the input values for this scenario. 

In the same parallel trial as described in the example above, we still observe that 25% of the subjects on the standard therapy had a successful outcome, but this time it is only of clinical relevance if a 40% relative improvement is observed in the new therapy. How many subjects are required in order to detect this difference with 80% power at the 5% level of significance?

Answer

In the first part we calculate that 24 subjects per group and 48 subjects are required in total when we are looking for 40% absolute difference.

In the second part, we first need to work out what a 40% relative increase on 25% is (0.25*1.40=35%). Therefore 35% of subjects would need to have a successful outcome for there to be clinical relevance.

When we conduct the test we calculate that we need 329 subjects per group and 658 overall.

We need many more patients than in the example above due to the small effect size that we now wish to detect.

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