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Statistics in Medical Research

NGUYÊN LÝ THỐNG KÊ CƠ BẢN TRONG CÁC NGHIÊN CỨU LÂM SÀNG Đối tượng BS CK 1 Y Học Gia Đình PGS,TS LÊ HOÀNG NINH. Statistics in Medical Research. 1. Design phase: Statistics starts in the planning stages of a clinical trial or laboratory experiment to: establish optimal sample size needed

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Statistics in Medical Research

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  1. NGUYÊN LÝ THỐNG KÊ CƠ BẢN TRONG CÁC NGHIÊN CỨU LÂM SÀNGĐối tượng BS CK 1Y Học Gia ĐìnhPGS,TS LÊ HOÀNG NINH

  2. Statistics in Medical Research • 1. Design phase: Statistics starts in the planning stages of a clinical trial or laboratory experiment to: • establish optimal sample size needed • ensure sound study design • 2. Analysis phase: Make inferences about a wider population.

  3. Common problems with statistics in medical research • Sample size too small to find an effect (design phase problem) • Sub-optimal choice of measurement for predictors and outcomes (design phase problem) • Inadequate control for confounders (design or analysis problem) • Statistical analyses inadequate (analysis problem) • Incorrect statistical test used (analysis problem) • Incorrect interpretation of computer output (analysis problem) Therefore, it is essential to collaborate with a statistician both during planning and analysis!

  4. Additionally, errors arise when… • The statistical content of the paper is confusing or misleading because the authors do not fully understand the statistical techniques used by the statistician. • The statistician performs inadequate or inappropriate analyses because she is unclear about the questions the research is designed to answer. • **Therefore, clinical research scientists need to understand the basic principles of biostatistics…

  5. Outline • 1. Primer on hypothesis testing, p-values, confidence intervals, statistical power. 2. Biostatistics in Practice: Applying statistics to clinical research design

  6. Quick review • Standard deviation • Histograms (frequency distributions) • Normal distribution (bell curve)

  7. Variance is the average squared distance from the mean. Standard deviation is the square root of variance (roughly the average distance from the mean). Variance: The standard deviation (original units)= Review: Standard deviation Standard deviation tells you how variable a characteristic is in a population. For example, how variable is height in the US? A standard deviation of height represents the average distance that a random person is away from the mean height in the population.

  8. Percent of total that fall in the 2-inch interval. Data are divided into 2-inch groups (called “bins”). With only three woman <60 inches (5 feet), this bin represents only 2% of the total 150-women sampled. 64-66 66-68 62-64 68-70 60-62 58-60 70-72 Review: Histograms

  9. Roughly, follows a normal distribution Mean height=65.2 inches Median height=65.1 inches Standard deviation (average distance from the mean) is 2.5 inches Review: Histograms 1 inch bins

  10. 68% of the data 95% of the data 99.7% of the data Review: Normal Distribution

  11. -1 SD +1 SD 62.7 67.7 Review: Normal Distribution A perfect, theoretical normal distribution carries 68% of its area within 1 standard deviation of the mean. In fact, here, 101/150 (67%) subjects have heights between 62.7 and 67.7 (1 standard deviation below and above the mean).

  12. -2 SD +2 SD 60.2 70.2 Review: Normal Distribution A perfect, theoretical normal distribution carries 95% of its area within 2 standard deviations of the mean. In fact, here, 146/150 (97%) subjects have heights between 60.2 and 70.2 (2 standard deviations below and above the mean).

  13. -3 SD +3 SD 57.7 72.7 Review: Normal Distribution A perfect, theoretical normal distribution carries 99.7% of its area within 3 standard deviations of the mean. In fact, here, 150/150 (100%) subjects have heights between 57.7 and 72.7 (1 standard deviation below and above the mean).

  14. Review: Applying the normal distribution If women’s heights in the US are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches, what percentage of women do you expect to have heights above 6 feet (72 inches)? From standard normal chart or computer  Z of +2.8 corresponds to a right tail area of .0026; expect 2-3 women per 1000 to have heights of 6 feet or greater.

  15. Statistics Primer • Statistical Inference • Sample statistics • Sampling distributions • Central limit theorem • Hypothesis testing • P-values • Confidence intervals • Statistical power

  16. Truth (not observable) Sample (observation) Make guesses about the whole population Statistical InferenceThe process of making guesses about the truth from a sample.

  17. EXAMPLE: What is the average blood pressure of US post-docs? • We could go out and measure blood pressure in every US post-doc (thousands). • Or, we could take a sample and make inferences about the truth from our sample. • Using what we observe, • 1. We can test an a priori guess (hypothesis testing). • 2. We can estimate the true value (confidence intervals).

  18. Statistical Inference is based on Sampling Variability • Sample Statistic – we summarize a sample into one number; e.g., could be a mean, a difference in means or proportions, an odds ratio, or a correlation coefficient • E.g.: average blood pressure of a sample of 50 American men • E.g.: the difference in average blood pressure between a sample of 50 men and a sample of 50 women Sampling Variability – If we could repeat an experiment many, many times on different samples with the same number of subjects, the resultant sample statistic would not always be the same (because of chance!). Standard Error – a measure of the sampling variability

  19. Examples of Sample Statistics: Single population mean Difference in means (ttest) Difference in proportions (Z-test) Odds ratio/risk ratio Correlation coefficient Regression coefficient …

  20. 110 mmHg The average systolic blood pressure in US post-docs at this moment is exactly 130 mmHg 150 mmHg 105 mmHg 135 mmHg 140 mmHg 129 mmHg Variability of a sample mean The Truth (not knowable) Random Postdocs

  21. 125 mmHg The average systolic blood pressure in US post-docs at this moment is exactly 130 mmHg 137 mmHg 123 mmHg 141 mmHg 134 mmHg 122 mmHg Variability of a sample mean Random samples of 5 post-docs The Truth (not knowable)

  22. The average systolic blood pressure in US post-docs at this moment is exactly 130 mmHg Variability of a sample mean The Truth (not knowable) Samples of 50 Postdocs 129 mmHg 134 mmHg 131 mmHg 130 mmHg 128 mmHg 130 mmHg

  23. The average systolic blood pressure in US post-docs at this moment is exactly 130 mmHg Variability of a sample mean The Truth (not knowable) Samples of 150 Postdocs 131.2 mmHg 130.2 mmHg 129.7 mmHg 130.9 mmHg 130.4 mmHg 129.5 mmHg

  24. How sample means vary: A computer experiment • 1. Pick any probability distribution and specify a mean and standard deviation. • 2. Tell the computer to randomly generate 1000 observations from that probability distributions • E.g., the computer is more likely to spit out values with high probabilities • 3. Plot the “observed” values in a histogram. • 4. Next, tell the computer to randomly generate 1000 averages-of-2 (randomly pick 2 and take their average) from that probability distribution. Plot “observed” averages in histograms. • 5. Repeat for averages-of-5, and averages-of-100.

  25. Uniform on [0,1]: average of 1(original distribution)

  26. Uniform: 1000 averages of 2

  27. Uniform: 1000 averages of 5

  28. Uniform: 1000 averages of 100

  29. ~Exp(1): average of 1(original distribution)

  30. ~Exp(1): 1000 averages of 2

  31. ~Exp(1): 1000 averages of 5

  32. ~Exp(1): 1000 averages of 100

  33. ~Bin(40, .05): average of 1(original distribution)

  34. ~Bin(40, .05): 1000 averages of 2

  35. ~Bin(40, .05): 1000 averages of 5

  36. ~Bin(40, .05): 1000 averages of 100

  37. 1. have mean: 2. have standard deviation: The Central Limit Theorem: If all possible random samples, each of size n, are taken from any population with a mean  and a standard deviation , the sampling distribution of the sample means (averages) will: 3. be approximately normally distributed regardless of the shape of the parent population (normality improves with larger n)

  38. Example 1: Weights of doctors • Experimental question: Are practicing doctors setting a good example for their patients in their weights? • Experiment: Take a sample of practicing doctors and measure their weights • Sample statistic: mean weight for the sample • IF weight is normally distributed in doctors with a mean of 150 lbs and standard deviation of 15, how much would you expect the sample average to vary if you could repeat the experiment over and over?

  39. Relative frequency of 1000 observations of weight Standard deviation reflects the natural variability of weights in the population doctors’ weights mean= 150 lbs; standard deviation = 15 lbs

  40. average weight from samples of 2 1000 doctors’ weights

  41. average weight from samples of 10

  42. average weight from samples of 100

  43. Using Sampling Variability • In reality, we only get to take one sample!! • But, since we have an idea about how sampling variability works, we can make inferences about the truth based on one sample.

  44. Experimental results • Let’s say we take one sample of 100 doctors and calculate their average weight….

  45. What are we going to think if our 100-doctor sample has an average weight of 160? average weight from samples of 100 Expected Sampling Variability for n=100 if the true weight is 150 (and SD=15)

  46. If we did this experiment 1000 times, we wouldn’t expect to get 1 result of 160 if the true mean weight was 150! average weight from samples of 100 Expected Sampling Variability for n=100 if the true weight is 150 (and SD=15)

  47. average weight from samples of 100 “P-value” associated with this experiment “P-value” (the probability of our sample average being 160 lbs or more IF the true average weight is 150) < .0001 Gives us evidence that 150 isn’t a good guess

  48. The P-value P-value is the probability that we would have seen our data (or something more unexpected) just by chance if the null hypothesis (null value) is true. Small p-values mean the null value is unlikely given our data.

  49. The P-value • By convention, p-values of <.05 are often accepted as “statistically significant” in the medical literature; but this is an arbitrary cut-off. • A cut-off of p<.05 means that in about 5 of 100 experiments, a result would appear significant just by chance (“Type I error”).

  50. Hypothesis Testing • The Steps: • Define your hypotheses (null, alternative) • The null hypothesis is the “straw man” that we are trying to shoot down. • Null here: “mean weight of doctors = 150 lbs” • Alternative here: “mean weight > 150 lbs” (one-sided) • Specify your sampling distribution (under the null) • If we repeated this experiment many, many times, the sample average weights would be normally distributed around 150 lbs with a standard error of 1.5 3. Do a single experiment (observed sample mean = 160 lbs) 4. Calculate the p-value of what you observed (p<.0001) 5. Reject or fail to reject the null hypothesis (reject)

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