An Idiots Guide to Statistics Curriculum 3.6 Daisy de Ferranti Stephanie de Giorgio Lindo Van der Merwe

Overview Why bore you with Statistics Definitions How to work through the stats questions

Why bore you with Statistics AKT- Definitions, interpretation of terms, 2 by 2 table (and forest plot for statisticians!)

Present Absent Positive a b Negative c d

Present Absent Positive True positive False positive Negative False negative True negative

Definitions Sensitivity: (True positive rate) How good is this test at picking up people who have the condition? a/a+c

Specificity True negative rate How good is this test at correctly excuding people without the condition d/b+d

Positive Predictive value Post test probability of a positive test If a person tests positive, what is the probability that he has the condition a/a+b

Negative predictive value Post test probability of a negative test If a person tests negative what is the probabilty that he does not have the condition d/c+d

How to remember this! SnNOUT – with high sensitivity a negative result rules OUT the diagnosis SpPin – with high specificity, a positive result rules IN the diagnosis

An example Gastric cancer Blood result Present Absent Positive 20 30 Negative 5 45

Sensitivity 20/25 = 0.8 Specificity 45/75 = 0.6 PPV 20/50 = 0.4 NPV 45/50 = 0.9

Accuracy What proportion of all tests have given the correct result (ie true positives and true negatives as a proportion of all the results) a+d/a+b+c+d

Likelihood ratio of a positive test How much more likely is positive test to be found in a person with, as opposed to without, the condition Sensitivity/1-specificity

Interventions Dead Alive Total no Control 404 a 921 b 1324 a+b Surgical 350 c 974 d 1325 c+d

Risk Chance of being dead in control group X Chance of being dead in surgical group Y

Relative Risk RR of death is the risk in surgical pts compared with controls. y/x

Relative risk reduction Amount by which the risk of death is reduced by surgery

Another practical example – treatment of candida Improved Not improved Total no Antifungal 80 20 100 Placebo 60 40

Risk in placebo group = 40/100=0.4=40% Risk in treatment group = 20/100=0.2=20% Absolute risk reduction (ARR) = 80/100 – 60/100 = 20% Relative risk reduction = Risk in placebo (40)– risk in treatment(20) = 0.5 Risk in placebo (40)

Glossary Index

Hierarchy of Evidence Systematic review & meta-analysis RCT Cohort studies Case-control studies Cross-sectional surveys Case reports

Types of Study Case control: Retrospective Group of cases with condition & group of controls without are studied to determine relative frequency of particular exposures of interest in 2 groups Concerned with aetiology of disease rather than Rx Cohort: Prospective Two groups of people are selected on basis of differences in their exposure to particular agent & followed up to establish how many in each group develop a particular disease Follow up period generally years Concerned with aetiology of disease

Types of Study 1. Case reports: Describes medical hx of single pt in form of story. 2. Cross-sectional surveys: Population or sample of population examined to determine prevalence of certain condition

Types of Study 5. RCT Participants in trial are randomly allocated to either one intervention (ie drug) or another (ie placebo) Both groups followed up for specified time & analysed in terms of specific outcomes defined at onset (ie death, MI) Often short follow up due to costs & pressure to produce timely evidence 6. Systematic Reviews & Meta-analysis Systematic review: Summary of medical literature that uses explicit methods to perform a thorough search & critical appraisal of individual studies Meta-analysis: A systematic review that uses quantitative methods to summarise results – pooling all information from number of different (but similar) studies

Statistics which describe Data Mean Median Mode Standard Deviation

Mean Sum of all values, divided by the number of values Used in “normal distribution” – spread of data is fairly similar on each side of mid point

Median It is the point which has half the values above & half below Used to represent average when data not symmetrical - “skewed distribution” Mean=median in symmetrical distribution but not in skew distribution Mode Most common set of events

Standard Deviation Good news – not necessary to know how to calculate the SD! Used for data which is “normally distributed” SD indicates how much a set of values is spread around the mean +/- 1 SD (range of one SD above & below the mean) includes 68.2% of the values +/- 2 SD includes 95.4% of values +/- 3 SD includes 99.7%

Statistics which test confidence P value Confidence interval

P value Test of probability ie any observed difference having happened by chance Used to determine whether a hypothesis is true “Null hypothesis” – no difference between two groups/treatments P value <0.05 “statistically significant” ie unlikely to have happened by chance, hence important The lower the p value, the less likely the difference happened by chance & thus the higher the significance Significant p rejects Null hypothesis

Confidence interval When is it used? What does it mean? Typically when, instead of simply wanting mean value of sample, we want a range that is likely to contain the “true population value” “True value” is mean value that we would get if we had data for the whole population What does it mean? CI gives the range in which the true value is likely to be (usually with level of 95% certainty) Provides same information as p value, but more useful Size of CI related to sample size of study – larger studies have narrower CI If CI crosses 0 – Null hypothesis true

Forest Plot/”blobbogram”

Forest Plot Allows readers to see information from individual studies that went into the meta-analysis at a glance Results of component studies are shown as squares centred on point estimate of result of each study Horizontal line runs through to show its CI Diamond symbol represents the overall estimate from meta-analysis and its CI Significance is achieved if the diamond is clear of the “line of no effect”

Interpretation i. Wide CI, crosses 0 ii. Does not cross 0, intervention works but weak evidence iii. Narrow CI, crosses 0, intervention no benefit iv. Narrow CI, intervention works v. Intervention detrimental vi. Meta-analysis: intervention works

Key definitions Incidence: proportion of a defined group developing a disease within a stated period Prevalence: proportion of a defined group having a disease at any one time Single blinded: subjects did not know which treatment they were receiving Double blinded: neither investigators nor subjects knew who was receiving which treatment Unblinded: all participants were aware of who received which intervention Power: ability of a study to minimise uncertainties that arise because of chance variation between samples - ie larger samples Type II error: common – accept null when alternative is true Type I error: less common – accept alternative when null is true

Enough of the theory – here’s the practical bit!! What do we need to be able to do? 1. Interpret drug rep data 2. Explain risk/benefits to our patients 3. Understand evidenced based medicine

Survival analysis and risk reduction Use of ramipril in preventing stroke: double blind randomised trial. BMJ 324:699-702 To determine the effect of ramipril on secondary prevention of stroke. 267 hospitals in 19 countries 9297 patients with vascular disease or diabetes followed for 4.5 yrs (HOPE study)

Outcome: stroke, TIA and cognitive function measured Outcome: stroke, TIA and cognitive function measured. Blood pressure recorded at entry to study, after 2 years and at end. Results: Reduction in BP modest Relative risk of stroke reduced by 31% in ramipril group compared to placebo, relative risk of fatal stroke reduced by 61%

Summary of results Stroke No-stroke Total Ramipril 156 (Fatal 17) 4479 4635 Placebo 226 (Fatal 44) 4426 4652

Risk of stroke in ramipril group 156/4635= 0.036 = 3.36% Risk of stroke in placebo group 226/4652= 0.048 = 4.48% Relative risk reduction = (4.86 – 3.36)/4.86 = 0.31 = 31%

Absolute risk reduction (ARR) Risk in placebo – risk in rampril = 4.86 – 3.36 = 1.5% NNT = 100 = 100 = 67 ARR 1.5

For fatal stroke Risk in ramipril group = 17/4635= 0.0036 Risk in placebo group - 44/4652 = 0.0094 RRR = 0.0094 - 0.0036 = 0.617 = 61% 0.0094

Rampril reduced risk of stroke in high risk patients by 31%, which seems good. However, have to treat 67 people for 4 ½ years in order to benefit 1 patient by preventing 1 stroke

Odds ratios and CI Systematic r/v of long term anticoagulation or antiplatelet treatment in pts with atrial fibrillation BMJ 322:321-326 Objective - to examine benefits/risks of warfarin compared to aspirin/indomethacin Methods - meta-analysis of RCT. Odds ratios (95% CI) calculated to estimate treatment effects

Results for one of the trials Odds of vascular death in patients on warfarin number of times an event happens = 16 = 0.088 number of times it does not happen 197-16 Odds of vascular death in aspirin pts = 14 = 0.080 188 - 14 Odds ratio = odds in warfarin pts = 0.088 = 1.10 odds in aspirin pts 0.080 Odds ratio of >1 indicates that rate of vasc death increased in warfarin pts over those in aspirin pts.

If the confidence interval for the Odds Ratio containes 1 ie no difference, then the difference in results is NOT statistically significant Seen by CI plot line crossing the line at 1. Overall the study did not show any benefit of long term anticoagulation and an increased risk of bleeding

In summary Important to understand for career, not just for exam. Try to understand basic concepts well as can then apply to most questions.