Download Slide3. Descriptive Statistics - Vanderbilt University School of

Be able to understand statistical concepts in a medical paper Understanding:  p‐value and hypothesis testing
 mean and standard deviation (SD)
 median and inter‐quartile‐range [IQR]
 standard error and confidence interval
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P‐value and hypothesis testing
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“Will you marry me, Mary?” “Yes John, only if you can prove me that love is our destiny.” John (1st Try): Sure I can. Mary, many wonderful things happened since I met you, so love must be our destiny. John (2nd Try): Mary, it is hard to believe that our love happened just by chance alone. If it happened just by chance alone, the probability of us coming from the other side of the universe to Vanderbilt CQS Summer Institute, and fell in love in a stat class is 0.000000001. It COULD NOT happen just by chance alone! Sure, love must be our destiny!!!! 3
What is a scientific evidence？
When you want to prove that a new drug works (or love is their destiny), which approach do you want to take? Alternative hypothesis (Ha)
A. Give evidences to support that the drug works (love is their destiny).
B. Give an evidence to against that the drug does not work (love is NOT their destiny).
Which approach do you think more convincing (or easier to collect evidence)? Null hypothesis (Ho)
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Disproving hypothesis in Evidence Based Medicine
In general, it is much easier to find evidence against a hypothesis than to prove that it is correct. In fact, one view of science is a process of disproving hypothesis. Statistical methods formalize this idea by looking for evidence against a null hypothesis (Ho): that there is no difference between groups or no association between variables (or love is NOT their destiny). Data are then collected and assessed for their consistency with the null hypothesis. (Kirkwood and Sterne, page 72).
P‐value is used as an evidence to against the null hypothesis, it is defined as “probability of observing the observed difference or greater difference when the null hypothesis is true”. (So smaller is better)
The drug does not work.
It in fact does work! 5
But be careful, p>0.05 does not mean that the two drugs are the same.
A. Low dose 60‐80ng/ml
B. High dose 2.5㎎・ｋｇ/day
A.Low dose 60‐80ng/ml
B. High dose 2.5㎎・ｋｇ/day
Meaning of the p‐value：
If the truth is that there is NO difference between the two treatments, the probability of observing this or larger difference is 6 out of 1000, probably hard to believe that it is happening jusy by chance, therefore there must be a difference. Meaning of the p‐value：
If the truth is that there is NO difference between the two treatments, the probability of observing this or larger difference is 6 out of 100. No enough evidence that there is a difference.
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Question：How can I make a p‐value smaller?
Enroll as many patients as you can。
P‐value!?
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What impacts on p-value when comparing new drug v.s. placebo?
The effect of the new drug. ex: Larger reduction (10lbs) in weight by the
new drug!
Variation of data:
Larger variation can result in larger p-value.
Source of variation:
Between-subject variation
Measurement error
And what else??????
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A. Low dose 60‐80ng/ml
B. High dose 2.5㎎・ｋｇ/day
A.Low dose 60‐80ng/ml
B. High dose 2.5㎎・ｋｇ/day
Meaning of the p‐value：
If the truth is that there is NO difference between the two treatments, the probability of observing this or larger difference is 6 out of 1000, probably hard to believe that it is happening jusy by chance, therefore there must be a difference. Meaning of the p‐value：
If the truth is that there is NO difference between the two treatments, the probability of observing this or larger difference is 6 out of 100. No enough evidence that there is a difference.
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❓
Clinical Difference
Statistical Difference
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Probability of Survival Hazard Ratio（95％ CI）
0.63 (0.57 – 1.11) Steroid + Mizoribine
Steroid alone
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43%
36%
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Steroid + Mizoribine
Steroid alone
56%
35%
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Suggestion：
Clinically meaningful reduction of
flare was observed, though it did not reach statistical significance due to a small sample size. 15
What can we do in order not to miss a clinically important difference?
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Steroid + Mizoribine
Sample size computation：
Steroid alone
56%
35%
In order to detect the observed difference statistically with 2‐sided 5% significance level
With 80% power, It requires at least 87 patients per arm. 17
Descriptive Statistics
Measure for central tendency
Ｍｅａｎ (Median)
Measure for variation
Standard deviation (IQR)
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Example 1
Ely, Shintani, Truman et al, JAMA 2003;289:2983‐91
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Mean(SD)
Ely, Shintani, Truman et al, JAMA 2003;289:2983‐91
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Group B
Group A Group B
Ｑ３：７５%
Error bar ：９５％ＣＩ
N=30
N=30
0 5 10 15 20 25 30
Group A Group B
Error bar ：SD
Max
20
30
P=0.01
Significant?
Min
10
10
20
Ｑ２：50%
Ｑ１：２５%
0
Group A
Group A Group B
50
Whisker
30
40
50
Error bar：ＳＥ
Significant?
Ｐ=０．０１
Group B
Box‐Whisker plot
0
Group A
Significant?
40
Significant?
Ｐ=０．１
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
Mean Outcome
Ｐ=０．１
Group A Group B
Box‐Whisker plot with data points
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Standard Deviation (SD)
SD=Average distance from each data point to the sample mean.
SD = 8.1
Mean=25.6
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SD: How to use
When data are normally distributed:
67％ of Patients’ Apache score lie between 1SD.
25.6±8.1 =(17.5, 33.7)
67％
95％ of Patients’ Apache score lie between 2SD.
25.6±2x8.1 =(9.4, 41.8)
95％
Apache II Score 23
Ely, Shintani, Truman et al, JAMA 2003;289:2983‐91
4.8±2 x 12.8 =(‐20.8, 30.4)
使って見よう！
９５％ of patients used lorazepam does between ‐20.8㎎ to 30.4㎎ ????
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９５％ of patients used lorazepam does between ―20.8㎎ to 30.4㎎ ????
Mean＝4.8
SD＝12.8
Median [IQR] ＝ 0 [1, 4.25]
50% 1 mg 25% 0 mg 75% 4.25mg
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Patient’s characteristics
50% 10 ㎎
25% 2 ㎎
75% 41 ㎎
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SD is to describe data （Typically for Table 1）
SE: Multiply by 2, and use as ９５％ Confidence Interval for a statistical inference
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Group B
Group A Group B
Ｑ３：７５%
Error bar ：９５％ＣＩ
N=30
N=30
0 5 10 15 20 25 30
Group A Group B
Error bar ：SD
Max
20
30
P=0.01
Significant?
Min
10
10
20
Ｑ２：50%
Ｑ１：２５%
0
Group A
Group A Group B
50
Whisker
30
40
50
Error bar：ＳＥ
Significant?
Ｐ=０．０１
Group B
Box‐Whisker plot
0
Group A
Significant?
40
Significant?
Ｐ=０．１
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
Mean Outcome
Ｐ=０．１
Group A Group B
Box‐Whisker plot with data points
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Relationship between p‐value and 95% Confidence Interval, CI
95% CI including the null value
P>0.05 No difference detected
95% CI including the null value
P<=0.05 A difference detected
Null Value
Student t-test
ANOVA
Linear regression
absolute difference
in values
0
Logistic regression
Relative difference in
proportions through
a ratio
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Cox regression
Relative difference in
risks through a ratio
1
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95% CI of the difference between two groups.
P‐value is a function of both sample size and treatment effect
Mean
Diff
Sample Size
A.
P>0.05
0 days
Large
B.
P>0.05
3 days
Small
C.
P<0.05
3 days
Large
D.
P<0.05
3 days
Small (but bigger than B)
Ｎｕｌｌ Ｖａｌｕｅ
e.g.,difference = 0 days
95% CI = Mean – 2 x SD / √sample size, Mean + 2 x SD / √sample size 31
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The effect of Creatinine and Diastolic BP are both not significant (P > 0.05), however with 95% CI, you may know creatinine may be associated with calcification, because CI is too wide and OR=3.96 is meaningfully large, thus the p‐value may become less than 0.05 with enrolling more patients. 33