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Understanding Hypothesis Testing in Statistics for Clinical Research

This session by Dr. J. C. Horrow from Drexel University College of Medicine focuses on the fundamentals of hypothesis testing within statistical frameworks, particularly in clinical research. Attendees will learn about the significance of null (H0) and alternative hypotheses (HA), how to structure statistical tests, and the four essential steps involved in hypothesis testing. Through practical examples, including the evaluation of DVT rates and initial systolic blood pressures in C-section patients, participants will grasp how to identify test statistics, establish rejection regions, and interpret conclusions drawn from data analysis.

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Understanding Hypothesis Testing in Statistics for Clinical Research

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  1. Statistical Fridays J C Horrow, MD, MSSTAT Clinical Professor, Anesthesiology Drexel University College of Medicine

  2. Previous Session Review • Statistics are functions of the data • Useful statistics have known distributions • Statistical inference = estimation; testing • Tests seek to disprove a “null” hypothesis

  3. Session Review • Tests involve a NULL hypothesis (H0) an ALTERNATIVE hypothesis (HA) • Try to disprove H0 • There are 4 steps in hypothesis testing

  4. Null and Alternative Hypotheses • Together, they describe all possibilities • EXAMPLE: If (H0) : BP=0, then (HA) : BP0. • EXAMPLE: If (H0) : SBP 80, then (HA) : SBP< 80.

  5. How to formulate H0 • GOAL: To DISPROVE H0 • EXAMPLE: If our goal is to show DVT rates with a new oral anticoagulant X are lower than those with warfarin, then: H0 : RX RW and HA : RX < RW • Put the “equals” sign in H0

  6. 4 steps of hypothesis testing • Identify the test statistic • State the null and alternative hypotheses • Identify the rejection region • State your conclusion ------------------------------------------------------------ Example: ALT measured 3-months after starting drug X.

  7. Step 1: Identify the test statistic • A statistic is a function of the data • Examples: average, maximum, rank-sum • Pick a statistic with known distribution • Observations vary, so functions of the data also have variation • The mean, x-bar, is most often used • Distribution is N (,2/n) if n sufficiently large • EX: mean ALT for drug X and drug W

  8. Step 2: State H0 and HA • State in terms of population parameter • Put “equals” signs in H0 • Be sure to cover all possibilities • Example: H0 : X - W = 0HA : X - W  0 • N.B.: “two-sided” hypothesis

  9. Step 3: Identify the rejection region • If T.S. differs “enough” from value “under H0” then we reject H0. • How much is “enough”?  rejection region • EX: T.S. is (x-barX – x-barW)R.R. is |x-barX – x-barW| > X-W  z/2

  10. The Normal Distribution Z=1.965 R.R. -3s -2s -s 0 s 2s 3s

  11. Step 4: State your conclusion • If T.S. is outside R.R., reject H0 • If T.S. within R.R., “cannot reject H0” • we do not “accept H0” if TS within RRmay state: data consistent with H0 • What about HA?If we reject H0, “data consistent with HA” • Why? Can never prove H0: this cohort is one of many possible!

  12. Step 4: State your conclusion • Example: (x-barX – x-barW) = 1.3 (xULN)and X-W= 0.62 • R.R. = X-W  z/2 = 0.62  1.965 = 1.2183 • T.S. lies outside R.R. • Conclude: reject H0, data consistent with different S-ALAT for Xi and W groups.

  13. The Normal Distribution Z=1.965 R.R. Dx=2.1s -3s -2s -s 0 s 2s 3s

  14. Worked Example Do the patients in the C-section cohort have initial systolic BPs that are too low, i.e., less than 85 mmHg? STEP #1: Identify the T.S. T.S. = x-barSBP-init

  15. Worked Example Do the patients in the C-section cohort have initial systolic BPs that are too low, i.e., less than 85 mmHg? STEP #2: State the hypotheses: H0 :   85 HA :  < 85 Note: this is a “one-sided” test

  16. Worked Example Do the patients in the C-section cohort have initial systolic BPs that are too low, i.e., less than 85 mmHg? STEP #3: Identify the rejection region R.R. = (x-barSBP-init – 85)/SBP-init < z R.R. = (80.25 – 85)/1.790 < -1.645

  17. Worked Example Do the patients in the C-section cohort have initial systolic BPs that are too low, i.e., less than 85 mmHg? STEP #4: State your conclusion R.R. -2.65 < -1.645  outside R.R. We reject H0. Data are consistent with initial systolic BPs that are too low.

  18. The Normal Distribution Z=1.645 R.R. Dx=-2.65s -3s -2s -s 0 s 2s 3s

  19. Session Review • Tests involve a NULL hypothesis (H0) an ALTERNATIVE hypothesis (HA) • Try to disprove H0 • There are 4 steps in hypothesis testing • Identify the test statistic • State the null and alternative hypotheses • Identify the rejection region • State your conclusion

  20. Session Homework Use the C-section data Determine whether or not the increase in SBP exceeds 20 mmHg. Hint: first, form paired differences, then perform all 4 steps in testing

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