實證統計 楊宗翰 12/6, 2008
Reporting guidelines <ul><li>RCT – CONSORT </li></ul><ul><li>Cohort, Case-Control, Cross-sectional studies – STROBE </li><...
Contents <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </l...
Why statistics? <ul><li>Describe </li></ul><ul><li>Compare </li></ul><ul><ul><li>Difference </li></ul></ul><ul><ul><li>Ass...
Type of Data <ul><li>類別型資料  </li></ul><ul><ul><li>名字型類別 </li></ul></ul><ul><ul><li>順序型類別 </li></ul></ul><ul><li>數值資料  </li...
Characteristics of Data <ul><li>Shape & distribution </li></ul><ul><li>描述資料的方式不同 </li></ul><ul><li>Statistical tests: </li...
Characteristics of Data <ul><li>描述資料 </li></ul><ul><ul><li>Location: mean, median, … </li></ul></ul><ul><ul><li>Spread: st...
Baseline Characteristics
Describe Data <ul><li>描述兩組或多組資料 </li></ul><ul><ul><li>Location: mean, median, … </li></ul></ul><ul><ul><li>Spread: standar...
 
 
Describe Your Data II
Ratio and Risk <ul><li>Percentage </li></ul><ul><li>Relative risk (RR) = [a/(a+b)] / [c/(c+d)] </li></ul><ul><li>Odds rati...
A study with total case = 200 <ul><li>RR = 4 =  (40/100)/(10/100) </li></ul><ul><li>OR = 6 =  (40/60)/(10/90) </li></ul><u...
 
Is the difference significant? <ul><li>Clinically </li></ul><ul><li>Statistically </li></ul>
Contents <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </l...
What is p-value? <ul><li>為何要統計? </li></ul><ul><li>如何看待統計的結果? </li></ul>
假設檢定與  p- 值 <ul><li>H0 (null hypothesis) </li></ul><ul><ul><li>A與  B  對  RA  療效沒有差異。 </li></ul></ul><ul><ul><li>Effect of ...
Errors <ul><li>Type I error (alpha) = c </li></ul><ul><li>Type II error (beta) = b </li></ul><ul><li>Power = 1 – beta = d ...
Confidence Interval (C.I.) <ul><li>95% Confidence interval </li></ul><ul><ul><li>此區間包含真正母群體參數的機率是  95% </li></ul></ul>
P vs CI <ul><li>Why P-value < 0.05 </li></ul><ul><li>Treatment A v.s. treatment B in AMI </li></ul><ul><ul><li>P value = 0...
Contents <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </l...
Statistical tests <ul><li>適用於某種類型與分佈形態的資料 </li></ul><ul><li>數學模型與假設 </li></ul><ul><li>數值型  v.s.  類別型資料 </li></ul><ul><ul><...
 
Statistical tests <ul><li>If the authors have used obscure statistical tests, why have they done so and have they referenc...
Statistical tests <ul><li>Correlation v.s. Regression </li></ul><ul><li>Causation </li></ul><ul><ul><li>Is there evidence ...
資料分析 <ul><li>Method > Statistical analysis </li></ul><ul><li>Sample size calculation </li></ul><ul><li>What statistical te...
Contents <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </l...
Critical Appraisal <ul><li>Valid - RAMbo </li></ul><ul><li>Impact - result </li></ul><ul><li>Practical </li></ul>
Impact <ul><li>S tudy statistics (p-values & confidence intervals) </li></ul>
Impact - precise <ul><li>Confidence Interval </li></ul>
Appraise - Impact <ul><li>統計差異 </li></ul><ul><ul><li>是否顯著? </li></ul></ul><ul><ul><li>差多少? </li></ul></ul><ul><li>臨床差異 </l...
Results - Treatment
Treatment effects <ul><li>Control event rate (CER)= a/(a+b) </li></ul><ul><li>Experimental event rate (EER)= c/(c+d) </li>...
Appraise - Impact CER = Control Event Rate, EER = Experimental Event Rate RRR = Relative Risk Reduction (CER-EER)/CER ARR ...
Impact – size (loss 13.7%) <ul><li>ITT: EER = 0/116, CER = 12/116 (10%)  NNT=10 </li></ul><ul><li>PP: EER = 0/100, CER = 1...
Surrogate end points  <ul><li>一種簡單可直接測量的變數或方法,來代表或預測某些很少發生或是需要很麻煩才能得到的結果。 </li></ul><ul><li>Reduce the sample size, durati...
Results - Diagnosis
測量方法的特性 <ul><li>敏感度:有某個情況而測驗又能正確地區分那些有這個情況的病人比例(或 % )。  </li></ul><ul><li>專一性:沒有某個情況而測驗又能正確地區分那些沒有這個情況的病人比例(或 % )。  </li><...
Calculate the effects <ul><li>Sensitivity = a/(a+c) </li></ul><ul><li>Specificity = d/(b+d) </li></ul><ul><li>Predictive v...
Diagnosis  診斷 敏感度  (Sensitivity) 特異度  (Specificity)  陽性預測值  (Positive predictive value) 陰性預測值  (Negative predictive value)...
Diagnosis  診斷 盛行率  Prevalence 800 200 檢查陰性結果 100 900 檢查陽性結果 沒病 有病
Diagnosis  診斷 <ul><li>Positive Likelihood Ratio ( 陽性相似比 )   LR + </li></ul><ul><ul><li>True positive rate / False positive...
 
Calculation <ul><li>Pre-test odds = prevalence / (1 - prevalence)  </li></ul><ul><ul><li>0.25 / 0.75 = 0.3333 </li></ul></...
ROC curves
Receiver operator characteristic (ROC) curve <ul><li>A graph to display test performance at series of  cutoff points </li>...
Results – Meta Analysis
Systematic Review <ul><li>Question – PICO </li></ul><ul><li>Review process </li></ul><ul><ul><li>Inclusion </li></ul></ul>...
Heterogeneity <ul><li>Clinical </li></ul><ul><li>Statistical </li></ul><ul><ul><li>Cochrane Q (p-value), Cochrane Q/df </l...
Forest Plot (meta analysis) <ul><li>The  RR  +  95% CI  ==  solid square  +   line. T he  size  of the  solid square,  and...
Funnel Plot - Publication Bias
Results - Cohort
Regression <ul><li>Adjustment </li></ul>
Survival Analysis
Kaplan-Meier Survival Curve
Summary & Discussion <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistic...
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20081206 Biostatistics

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20081206 Biostatistics

  1. 1. 實證統計 楊宗翰 12/6, 2008
  2. 2. Reporting guidelines <ul><li>RCT – CONSORT </li></ul><ul><li>Cohort, Case-Control, Cross-sectional studies – STROBE </li></ul><ul><li>Systematic Review – QUOROM </li></ul><ul><li>Diagnostic Accuracy - STARD </li></ul>
  3. 3. Contents <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </li></ul><ul><li>Impact </li></ul><ul><ul><li>Treatment </li></ul></ul><ul><ul><li>Diagnosis </li></ul></ul><ul><ul><li>Systematic Review (meta analysis) </li></ul></ul><ul><ul><li>Cohort study (regression & survival) </li></ul></ul><ul><li>練習 </li></ul>
  4. 4. Why statistics? <ul><li>Describe </li></ul><ul><li>Compare </li></ul><ul><ul><li>Difference </li></ul></ul><ul><ul><li>Association </li></ul></ul><ul><ul><ul><li>Causal relationship </li></ul></ul></ul>
  5. 5. Type of Data <ul><li>類別型資料 </li></ul><ul><ul><li>名字型類別 </li></ul></ul><ul><ul><li>順序型類別 </li></ul></ul><ul><li>數值資料 </li></ul><ul><ul><li>連續型數值資料 </li></ul></ul><ul><ul><li>離散型資料 </li></ul></ul>
  6. 6. Characteristics of Data <ul><li>Shape & distribution </li></ul><ul><li>描述資料的方式不同 </li></ul><ul><li>Statistical tests: </li></ul><ul><ul><li>數學模型與假設 </li></ul></ul><ul><ul><li>適用於某種類型與分佈形態的資料 </li></ul></ul>
  7. 7. Characteristics of Data <ul><li>描述資料 </li></ul><ul><ul><li>Location: mean, median, … </li></ul></ul><ul><ul><li>Spread: standard deviation, range, … </li></ul></ul><ul><ul><li>95% Confidence interval </li></ul></ul><ul><ul><ul><li>此區間包含真正母群體參數的機率是 95% </li></ul></ul></ul><ul><li>Median & range: </li></ul><ul><ul><li>樣本數小,分佈明顯地偏斜,或有極端值 </li></ul></ul><ul><ul><li>資料可能不精確 </li></ul></ul><ul><ul><li>順序型資料 </li></ul></ul>
  8. 8. Baseline Characteristics
  9. 9. Describe Data <ul><li>描述兩組或多組資料 </li></ul><ul><ul><li>Location: mean, median, … </li></ul></ul><ul><ul><li>Spread: standard deviation, range, … </li></ul></ul><ul><li>描述配對的資料 </li></ul><ul><ul><li>差值的 location & spread </li></ul></ul><ul><li>沒有差異 = 0 </li></ul>
  10. 12. Describe Your Data II
  11. 13. Ratio and Risk <ul><li>Percentage </li></ul><ul><li>Relative risk (RR) = [a/(a+b)] / [c/(c+d)] </li></ul><ul><li>Odds ratio (OR) = (a/b) / (c/d) </li></ul><ul><li>OR ~ RR ? </li></ul>d c No b a Yes No Yes Exposure Outcome (Disease)
  12. 14. A study with total case = 200 <ul><li>RR = 4 = (40/100)/(10/100) </li></ul><ul><li>OR = 6 = (40/60)/(10/90) </li></ul><ul><li>沒有差異 = 1 </li></ul><ul><li>RR = ? (2.67) = (80/120)/(20/80) </li></ul><ul><li>OR = 6 = (80/40)/(20/60) </li></ul>60 20 No 40 80 Yes No Yes Smoke Lung Cancer 90 10 No 60 40 Yes No Yes Smoke Lung Cancer
  13. 16. Is the difference significant? <ul><li>Clinically </li></ul><ul><li>Statistically </li></ul>
  14. 17. Contents <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </li></ul><ul><li>Impact </li></ul><ul><ul><li>Treatment </li></ul></ul><ul><ul><li>Diagnosis </li></ul></ul><ul><ul><li>Systematic Review (meta analysis) </li></ul></ul><ul><ul><li>Cohort study (regression & survival) </li></ul></ul><ul><li>練習 </li></ul>
  15. 18. What is p-value? <ul><li>為何要統計? </li></ul><ul><li>如何看待統計的結果? </li></ul>
  16. 19. 假設檢定與 p- 值 <ul><li>H0 (null hypothesis) </li></ul><ul><ul><li>A與 B 對 RA 療效沒有差異。 </li></ul></ul><ul><ul><li>Effect of treatment A = Effect of treatment B </li></ul></ul><ul><li>H1 (alternative hypothesis) </li></ul><ul><ul><li>A與 B 對 RA 療效有差異。 </li></ul></ul><ul><li>p- 值 </li></ul><ul><ul><li>H0 為真的機會 </li></ul></ul><ul><ul><li>A 與 B 對 RA 療效沒有差異的機會。 </li></ul></ul><ul><ul><li>Alpha = 0.05 (機會很小) </li></ul></ul>
  17. 20. Errors <ul><li>Type I error (alpha) = c </li></ul><ul><li>Type II error (beta) = b </li></ul><ul><li>Power = 1 – beta = d </li></ul>d c Reject H0 b a Accept H0 H1 H0 Test Result
  18. 21. Confidence Interval (C.I.) <ul><li>95% Confidence interval </li></ul><ul><ul><li>此區間包含真正母群體參數的機率是 95% </li></ul></ul>
  19. 22. P vs CI <ul><li>Why P-value < 0.05 </li></ul><ul><li>Treatment A v.s. treatment B in AMI </li></ul><ul><ul><li>P value = 0.841, 0.048, 0.001 </li></ul></ul><ul><ul><li>95% C.I. of decrease in mortality rate </li></ul></ul><ul><ul><ul><li>-1.49 to 1.20 </li></ul></ul></ul><ul><ul><ul><li>-3.20 to -0.22 </li></ul></ul></ul><ul><ul><ul><li>-1.10 to -0.56 </li></ul></ul></ul>
  20. 23. Contents <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </li></ul><ul><li>Impact </li></ul><ul><ul><li>Treatment </li></ul></ul><ul><ul><li>Diagnosis </li></ul></ul><ul><ul><li>Systematic Review (meta analysis) </li></ul></ul><ul><ul><li>Cohort study (regression & survival) </li></ul></ul><ul><li>練習 </li></ul>
  21. 24. Statistical tests <ul><li>適用於某種類型與分佈形態的資料 </li></ul><ul><li>數學模型與假設 </li></ul><ul><li>數值型 v.s. 類別型資料 </li></ul><ul><ul><li>t test, F test v.s. Chi-square </li></ul></ul><ul><li>Independent v.s. paired data </li></ul><ul><ul><li>2-sample t test v.s. Pair t test </li></ul></ul><ul><li>Parametric v.s. non-parametric tests </li></ul><ul><ul><li>2-sample t test v.s. Mann Whitney test </li></ul></ul>
  22. 26. Statistical tests <ul><li>If the authors have used obscure statistical tests, why have they done so and have they referenced them? </li></ul><ul><li>Are the data analyzed according to the original protocol? </li></ul><ul><li>Were paired tests performed on paired data? </li></ul><ul><li>Was a 2 tailed test performed whenever the effect of an intervention could conceivably be a negative one? </li></ul><ul><li>Were &quot;outliers&quot; analyzed with both common sense and appropriate statistical adjustments? </li></ul>
  23. 27. Statistical tests <ul><li>Correlation v.s. Regression </li></ul><ul><li>Causation </li></ul><ul><ul><li>Is there evidence from true experiments in humans? </li></ul></ul><ul><ul><li>Is the association strong? </li></ul></ul><ul><ul><li>Is the association consistent from study to study? </li></ul></ul><ul><ul><li>Is the temporal relation appropriate? </li></ul></ul><ul><ul><li>Is there a dose-response gradient? </li></ul></ul><ul><ul><li>Does the association make epidemiological sense? </li></ul></ul><ul><ul><li>Does the association make biological sense? </li></ul></ul><ul><ul><li>Is the association specific? </li></ul></ul><ul><ul><li>Is the association analogous to a previously proved causal association? </li></ul></ul>
  24. 28. 資料分析 <ul><li>Method > Statistical analysis </li></ul><ul><li>Sample size calculation </li></ul><ul><li>What statistical tests </li></ul><ul><ul><li>Intention-to-treat principle </li></ul></ul><ul><ul><li>the last observation carried forward (LOCF) approach for missing data </li></ul></ul><ul><ul><li>Two-sided significant level of 0.05 </li></ul></ul>
  25. 29. Contents <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </li></ul><ul><li>Impact </li></ul><ul><ul><li>Treatment </li></ul></ul><ul><ul><li>Diagnosis </li></ul></ul><ul><ul><li>Systematic Review (meta analysis) </li></ul></ul><ul><ul><li>Cohort study (regression & survival) </li></ul></ul><ul><li>練習 </li></ul>
  26. 30. Critical Appraisal <ul><li>Valid - RAMbo </li></ul><ul><li>Impact - result </li></ul><ul><li>Practical </li></ul>
  27. 31. Impact <ul><li>S tudy statistics (p-values & confidence intervals) </li></ul>
  28. 32. Impact - precise <ul><li>Confidence Interval </li></ul>
  29. 33. Appraise - Impact <ul><li>統計差異 </li></ul><ul><ul><li>是否顯著? </li></ul></ul><ul><ul><li>差多少? </li></ul></ul><ul><li>臨床差異 </li></ul><ul><ul><li>血壓高低 </li></ul></ul><ul><ul><li>增加生活品質 </li></ul></ul><ul><ul><li>減少住院天數 </li></ul></ul><ul><ul><li>延長壽命 </li></ul></ul>
  30. 34. Results - Treatment
  31. 35. Treatment effects <ul><li>Control event rate (CER)= a/(a+b) </li></ul><ul><li>Experimental event rate (EER)= c/(c+d) </li></ul><ul><li>Relative risk reduction (RRR)= (CER—EER)/CER </li></ul><ul><li>Absolute risk reduction (ARR)= CER—EER </li></ul><ul><li>Number needed to treat (NNT)=1/ARR=1/(CER—EER); Number needed to harm (NNH) </li></ul>d c Control b a Exp No Yes Group Outcome
  32. 36. Appraise - Impact CER = Control Event Rate, EER = Experimental Event Rate RRR = Relative Risk Reduction (CER-EER)/CER ARR = Absolute Risk Reduction (CER-EER) NNT/NNH = Number Needed to Treat/Harm (1/ARR) 5000 (1/0.02%) 0.02% (0.04-0.02)% 50% (0.04-0.02)/0.04 0.02% 0.04% B 50 (1/2%) 2% (4-2)% 50% (4-2)/4 2% 4% A NNT 益一需治數 ARR 絕對風險降低 RRR 相對風險 降低 EER 實驗組發生率 CER 對照組發生率
  33. 37. Impact – size (loss 13.7%) <ul><li>ITT: EER = 0/116, CER = 12/116 (10%) NNT=10 </li></ul><ul><li>PP: EER = 0/100, CER = 12/100 (12%) NNT=8.3 </li></ul><ul><ul><li>H1: EER = 16 /116 ( 14% ), CER = 12/116 (10%); NN H = 25 </li></ul></ul><ul><ul><li>H2: EER = 16 /116 (14%), CER = 28 /116 (24%); NN T = 10 </li></ul></ul><ul><ul><li>H3: EER = 0/116, CER = 28 /116 (24%); NNT=5 </li></ul></ul><ul><ul><li>ITT for outcome is improving ( 假設所有 missing 的皆發生壞事件 ) </li></ul></ul><ul><li>RR = EER/CER = 0.0/0.1 = 0% </li></ul><ul><li>RRR = (CER – EER)/CER = 100% </li></ul><ul><li>ARR = CER – EER = 10% - 0 = 10% </li></ul><ul><li>NNT = 1/ARR = 10 </li></ul>
  34. 38. Surrogate end points <ul><li>一種簡單可直接測量的變數或方法,來代表或預測某些很少發生或是需要很麻煩才能得到的結果。 </li></ul><ul><li>Reduce the sample size, duration, and cost, of clinical trials </li></ul><ul><li>Allow treatments to be assessed in situations where the use of primary outcomes would be excessively invasive or unethical. </li></ul><ul><li>Commonly used surrogate end points include: </li></ul><ul><ul><li>pharmacokinetic measurements (concentration-time curves of a drug or its active metabolite in the bloodstream); </li></ul></ul><ul><ul><li>laboratory measures such as the MIC of an antimicrobial against a bacterial culture on agar; </li></ul></ul><ul><ul><li>macroscopic appearance of tissues (gastric erosion seen at endoscopy); </li></ul></ul><ul><ul><li>change in levels of serum markers of disease (prostate specific antigen); </li></ul></ul><ul><ul><li>radiological appearance (shadowing on a chest x ray film). </li></ul></ul>
  35. 39. Results - Diagnosis
  36. 40. 測量方法的特性 <ul><li>敏感度:有某個情況而測驗又能正確地區分那些有這個情況的病人比例(或 % )。 </li></ul><ul><li>專一性:沒有某個情況而測驗又能正確地區分那些沒有這個情況的病人比例(或 % )。 </li></ul><ul><li>陽性預測率( PPV ):測驗陽性的病人中,確實有這個情況的病人比例(或 % )。 </li></ul><ul><li>陰性預測率( NPV ):測驗陰性的病人中,確實沒有這個情況的病人比例(或 % )。 </li></ul>
  37. 41. Calculate the effects <ul><li>Sensitivity = a/(a+c) </li></ul><ul><li>Specificity = d/(b+d) </li></ul><ul><li>Predictive value </li></ul><ul><ul><li>PPV = a/(a+b); NPV = d/(c+d) </li></ul></ul><ul><li>Accuracy = (a+d)/(a+b+c+d) </li></ul><ul><li>Likelihood ratio </li></ul><ul><ul><li>PLR = sen / (1 – spec) </li></ul></ul><ul><ul><li>NLR = (1 - sen) / spec </li></ul></ul>d c Negative b a Positive No Yes Test Disease
  38. 42. Diagnosis 診斷 敏感度 (Sensitivity) 特異度 (Specificity) 陽性預測值 (Positive predictive value) 陰性預測值 (Negative predictive value) 800 200 陰性結果 100 900 陽性結果 沒病 有病
  39. 43. Diagnosis 診斷 盛行率 Prevalence 800 200 檢查陰性結果 100 900 檢查陽性結果 沒病 有病
  40. 44. Diagnosis 診斷 <ul><li>Positive Likelihood Ratio ( 陽性相似比 ) LR + </li></ul><ul><ul><li>True positive rate / False positive rate </li></ul></ul><ul><ul><li>Sensitivity / ( 1 - Specificity ) </li></ul></ul><ul><ul><li>The amount by which the pretest probability is increased in patients with a positive test </li></ul></ul><ul><ul><li>LR+ ≧4 valuable, LR+ ≧10 good </li></ul></ul><ul><li>Negative Likelihood Ratio ( 陰陽性相似比 ) LR - </li></ul><ul><ul><li>False negative rate / True negative rate </li></ul></ul><ul><ul><li>( 1 - Sensitivity) / Specificity </li></ul></ul><ul><ul><li>The amount by which the pretest probability of disease is reduced in patients with a negative test </li></ul></ul><ul><ul><li>LR- ≦0.6 useful, LR- ≦0.1 good </li></ul></ul>
  41. 46. Calculation <ul><li>Pre-test odds = prevalence / (1 - prevalence) </li></ul><ul><ul><li>0.25 / 0.75 = 0.3333 </li></ul></ul><ul><li>Post-test odds </li></ul><ul><ul><li>pre-test odds X likelihood ratio </li></ul></ul><ul><ul><li>0.3333 X 4.8 = 1.5998 </li></ul></ul><ul><li>Post-test probability </li></ul><ul><ul><li>post-test odds/(post-test odds + 1) </li></ul></ul><ul><ul><li>1.5998 / (1.5998 + 1) = 0.6154 </li></ul></ul><ul><li>Multiple tests </li></ul><ul><ul><li>Pre-test odds x LR1 + (test 1+) x LR2 - (test 2 -) x LR …. = Post-test odds </li></ul></ul>
  42. 47. ROC curves
  43. 48. Receiver operator characteristic (ROC) curve <ul><li>A graph to display test performance at series of cutoff points </li></ul><ul><li>A curve plotting the true positive rate on the vertical axis vs. the false positive rate (1 - specificity) on the horizontal axis </li></ul><ul><li>If the area under the ROC curve is 0.5 , the model has no discriminatory power </li></ul><ul><li>If the area is 1.0 , the model discriminates perfectly </li></ul><ul><li>AUROC > 0.8 is good, > 0.9 is excellent </li></ul>
  44. 49. Results – Meta Analysis
  45. 50. Systematic Review <ul><li>Question – PICO </li></ul><ul><li>Review process </li></ul><ul><ul><li>Inclusion </li></ul></ul><ul><ul><li>Exclusion </li></ul></ul><ul><ul><li>Review RCT / Cohort / CS / Case series … </li></ul></ul>
  46. 51. Heterogeneity <ul><li>Clinical </li></ul><ul><li>Statistical </li></ul><ul><ul><li>Cochrane Q (p-value), Cochrane Q/df </li></ul></ul><ul><ul><li>I 2 </li></ul></ul>
  47. 52. Forest Plot (meta analysis) <ul><li>The RR + 95% CI == solid square + line. T he size of the solid square, and the length of the line </li></ul><ul><li>Diamond -shaped symbols == the summary estimator of overall effect of all studies </li></ul><ul><li>Cross 1 or 0 </li></ul><ul><li>Heterogeneity (‘non-combinability’) </li></ul><ul><ul><li>visual examination; Cochran Q (heterogeneity chi-square), I 2 statistic. </li></ul></ul>    
  48. 53. Funnel Plot - Publication Bias
  49. 54. Results - Cohort
  50. 55. Regression <ul><li>Adjustment </li></ul>
  51. 56. Survival Analysis
  52. 57. Kaplan-Meier Survival Curve
  53. 58. Summary & Discussion <ul><li>Why statistics? </li></ul><ul><li>P value vs. confidence interval </li></ul><ul><li>Statistical tests </li></ul><ul><li>Impact </li></ul><ul><ul><li>Treatment </li></ul></ul><ul><ul><li>Diagnosis </li></ul></ul><ul><ul><li>Systematic Review (meta analysis) </li></ul></ul><ul><ul><li>Cohort study (regression & survival) </li></ul></ul><ul><li>練習 </li></ul>

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