The Bahrain Branch of the UK Cochrane Centre In Collaboration with Reyada Training & Management Consultancy, Dubai-U

1. http://bahrain.cochrane.org http://www.rt.ae Cochrane Collaboration and Systematic Review Workshop, 20-21 February 2007, Dubai - UAE The Bahrain Branch of the UK Cochrane Centre In Collaboration with Reyada Training & Management Consultancy, Dubai-UAE W04 Dr. Zbys Fedorowicz, Dr. Dunia Al Hashimi, Dr. Ahmed Al Asfoor

2. Statistical Concepts

3. 1/SE “funnel” ofunbiasedstudies region ofp>0.05 0 non-sig.missingstudies effectmagnitude Basic Concepts • Statisticsis the methodology of collecting, organizing, analyzing and interpreting data • Descriptive statistics: presentation of data in graphs and tables, calculation of numerical summaries • Inferential statistics: methodology for arriving or making decisions about a population by reasoning from the evidence of observed numerical data from a sample of the population

4. Test of hypothesis Example • A clinical trial for prevention of infant hypocalcaemia in which pregnant women receiving vitamin D supplement were compared with untreated women. The infant’s plasma calcium concentration measured six days after birth was of principal interest

5. NullHypothesis AlternativeHypothesis • Have to start with a hypothesis • Usually we start with “No effect or difference” • May end up with “There is an effect or a difference” • Accept / Reject considering the role of chance

6. The p-value The P-value is the probability of the observed data or more extreme outcome would have occurred by chance alone if the null hypothesis (null value) is true Small p-values mean the null value is unlikely given our data. Significant result Small P-values Non-significant result Large P-values

7. The p-value Infant 6th day plasma calcium (mg per 100ml) mean sd Vitamin D (n=233) 9.36 1.15 Control (n=394) 9.01 1.33 Could the difference (=0.35) between the two samples be due to sampling variation, or are they statistically significant (Very unlikely to be due to chance alone) ? P-value< 0001 Under the null hypothesis the chances of getting such a difference are less than 1 in 1000

8. Estimation and confidence limits • Main purpose of a clinical trial should be to estimate the magnitude of improvement of one treatment over another • Significance tests give the strength of evidence for one treatment being better they do not tell how much better • Significance tests P-value (not an estimate of any quantity; tell nothing about the size of a difference; tell nothing about the direction of a difference) • Statistical estimation methods – confidence intervals

9. 95% CI X = TRUE VALUE (--------------------X-----------------) (-------- X-------------------------) (---------------------X----------------) X (-----------------------------------) (-----------------X----------------) (----------------------X----------------) (----X---------------------------------) 95% CI should contain true value ~ 19/20 times

10. 95% CI Infant 6th day plasma calcium (mg per 100ml) mean sd Vitamin D (n=233) 9.36 1.15 Control (n=394) 9.01 1.33 Could the difference (=0.35) between the two samples be due to sampling variation, or are they statistically significant (Very unlikely to be due to chance alone) ? 95% CI for the difference in means (0.15, 0.55) There are 1 in 20 chances that the true diff is outside these limits

11. Types of data for outcome • Dichotomous (or binary) data, where each individual’s outcome is one of only two possible categorical responses; • Continuous data, where each individual’s outcome is a measurement of a numerical quantity; • Ordinal data (including measurement scales), where the outcome is one of several ordered categories, or generated by scoring and summing categorical responses;

12. Types of data for outcome • Counts and rates calculated from counting the number of events that each individual experiences; • Time-to-event (typically survival) data that analyze the time until an event occurs, but where not all individuals in the study experience the event (censored data).

13. Effect measures Dichotomous outcome Example: Dead or alive; clinical improvement or no clinical improvement • Risk ratio (RR) (also called the relative risk) • Odds ratio (OR) • Risk difference (RD) (also called the absolute risk reduction, ARR) • Relative risk reduction (RRR) • Number needed to treat (NNT)

14. Risk and odds Riskis the probability with which a health outcome (usually and adverse effect) will occur • Risk = 0.1 --- 10 out of 100 will have the event Oddsis the ratio of the number of people with the event to the number without • Odds are 1:10, or 0.1 --- 1 person will have the event for every 10 who do not

15. number of events Risk = total number of observations risk in Exp group (EER) Risk Ratio (RR) = risk in control group (CER) ? = 0.15/ 0.20 = 0.75 Event rates a b c d Risk in Exp group? Risk in Control group? 15/100 = 0.15 20/100 = 0.20 Experimental Event Rate (EER) Control Event Rate (CER)

16. RR = 0.75 Probability of an event with treatment is three-quarters of that without the treatment RR = 1 Probability of an event with treatment is the same as that without the treatment RR = 1.3 Events with treatments are 30% more likely than events without the treatment

17. 80 80 85 80 20 20 15 20 IN ABSOLUTE TERMS  BY 0.25 OR 25 % EER = 0.15 = 0.75 RR = CER = 0.20  BY 0.3 OR 30 % EER = 0.20 EER = 0.20 RR = RR = = 1.0 = 1.3 CER = 0.20 CER = 0.15 a b c d a+b c+d IN RELATIVE TERMS  BY 0.20 – 0.15 = 0.05 OR 5 %  BY 0.15 – 0.20 = - 0.05 OR 5 %

18. Event rates - Odds Ratio (OR) number of events Odds = number without the event odds in Exp group (EER) Odds Ratio (OR) = odds in control group (CER) ? = 0.18 / 0.25 = 0.72 a b c d a+b c+d Odds in Exp group? Odds in Control group? 15/85 = 0.18 20/80 = 0.25 Experimental Event Rate (EER) Control Event Rate (CER)

19. Health care interventions are intended either to reduce the risk of occurrence of an adverse outcome or increase the chance of a good outcome • A trial in which the experimental intervention reduces the occurrences of an adverse event will have an odds ratio and risk ratio lessthan one and a negativerisk difference • A trial in which the experimental intervention increases the occurrences of a good outcome will have an odds ratio and risk ratio greater than one and a positiverisk difference

20. Trial- Treatment of MI • New drug for acute myocardial infarction to reduce mortality • 40% mortality rate at 30 days among untreated

21. Trial- Treatment of MI • New drug for acute myocardial infarction to reduce mortality • 40% mortality rate at 30 days among untreated • 30% mortality among treated How would you describe the effect of the new drug? RR = 30 / 40 = 0.75 ARD = 40 – 30 = 10% RRR = 100 ( 1 – RR ) = 25%

22. Number needed to treat (NNT) • In considering the consequences of treating OR not treating, another sure of risk is the NNT • NNT is the number of patients who would have to receive the treatment for 1 of them to benefit

23. Concept • If a disease has a mortality rate of 100% without treatment. • Therapy reduces the mortality to 50% • How many people would you need to treat to prevent one death? • Treating 100 patients with otherwise fatal disease resulted in 50 survivors • 1 out of every 2 treated • Since all were destined to die • THE NNT TO PREVENT 1 DEATH IS 2 • NNT = 1 / ARD

24. Formulas for commonly used measures of therapeutic effect

25. Effect measures Continuous outcome Example: weight, heart rate • The mean difference • The standardized mean difference • Used in meta analysis when the trials assess the same outcome, but measure it in a variety of ways (for example, all trials measure depression but they use different psychometric scales).

26. Effect measures Time-to-event (survival) outcomes • Sometimes analyzed as dichotomous data • Appropriate measure is the hazard ratio • Interpreted in a similar way to a risk ratio • Describes how many times more (or less) likely a participant is to suffer the event at a particular point in time if they receive the experimental rather than the control intervention