Basic statistics www bradfordvts co uk EBM

Basic statistics www. bradfordvts. co. uk

EBM SKILLS - STATISTICS • CHANCE - p = 1 in 20 (0. 05). • > 1 in 20 (0. 051) = not significant • < 1 in 20 (0. 049) = statistically significant • CONFIDENCE INTERVALS • what is the range of values between which we could be 95% certain that this result would lie if this intervention was applied to the general population

EBM SKILLS - A BASIC INTRODUCTION CHANCE, BIAS, CONFOUNDING VARIABLES

TYPES OF STUDY - HYPOTHESIS FORMING • CASE REPORTS / CASE SERIES • CROSS SECTIONAL / PREVALENCE STUDIES measure personal factors & disease states - hypothesis FORMING - cannot indicate cause & effect • CORRELATIONAL / ECOLOGICAL / GEOGRAPHIC STUDIES. prevalence &/or incidence measurement in one population c/w another pop.

TYPES OF STUDY - HYPOTHESIS TESTING CASE CONTROL STUDIES

CASE CONTROL EXAMPLE -SMOKING & LUNG CANCER DISEASE Cases Controls EXPOSURE Yes a b EXPOSURE No c d Odds Ratio = ad/bc (1 = no association, > 1 = possible association, < 1 = protective effect) DISEASE Cases Controls EXPOSURE (smoking) Yes No (lung cancer) 56 7 230 246 The odds ratio would therefore be 56 x 246 = 13776 = 8. 6. 7 x 230 1610

TYPES OF STUDY - HYPOTHESIS TESTING • COHORT STUDIES

COHORT STUDIES OUTCOME Exposed Not exposed Yes a c No b d Attributable risk (absolute risk or risk difference) "What is the incidence of disease attributable to exposure" Answer = a - c. Relative risk "How many times are exposed persons more likely to develop the disease, relative to non-exposed persons? " i. e. the incidence in the exposed divided by the incidence in the nonexposed. This is expressed as a divided by a+b c c+d .

COHORT STUDY EXAMPLE Deep vein thromboses (DVT) in oral contraceptive users. (Hypothetical results). OUTCOME (DVT) Exposed ( on oral contraceptive ) Not exposed (not on o. c. ) 10009 Yes 41 7 No 9996 These results would give an attributable risk of 34 and a relative risk of 6 - significantly large enough numbers to indicate the possibility of a real association between exposure and outcome. However, the possibility of biases very often arises.

RANDOMISED CONTROLLED TRIALS

RANDOMISED CONTROLLED TRIALS OUTCOME Yes No Comparison intervention a b Experimental intervention c d Relative risk reduction: “ How many fewer patients will get the outcome measured if they get active treatment versus comparison intervention” a /a+b - c/c+d a/a+b Absolute risk reduction: “What is the size of this effect in the population” a/a+b - c/c+d

RCT EXAMPLE - 4 S STUDY • STABLE ANGINA OR MYOCARDIAL INFARCTION MORE THAN 6 MONTHS PREVIOUSLY • SERUM CHOLESTEROL > 6. 2 mmol/l • EXCLUDED PATIENTS WITH ARYHTHMIAS AND HEART FAILURE • ALL PATIENTS GIVEN 8 WEEKS OF DIETARY THERAPY • IF CHOLESTEROL STILL RAISED (>5. 5) RANDOMISED TO RECEIVE SIMVASTATIN (20 mg > 40 mg) OR PLACEBO • OUTCOME DEATH OR MYOCARDIAL INFARCTION (LENGTH OF TREATMENT 5. 4 YEARS ) WERE THE OUTCOMES

RCT EXAMPLE - 4 S STUDY OUTCOME (death) Yes No 256 1967 Comparison intervention (placebo) 2223 Experimental intervention (simvastatin) 182 2221 2039 The ARR is (256/2223) - (182/2221) = 0. 115 - 0. 082 = 0. 033. The RRR is 0. 033/0. 115 = 0. 29 or expressed as a percentage 29%. 1/ARR = NUMBER NEEDED TO TREAT. 1/0. 033 = 30. i. e. if we treat 30 patients with IHD with simvastatin as per 4 S study, in 5. 4 years we will have prevented 1 death.

NNT EXAMPLES Intervention Outcome NNT

Why are RCTs the “gold standard” Breast cancer mortality in studies of screening with mammography; women aged 50 and over (55 in Malmo study, 45 in UK)

SCREENING - WILSON & JUNGEN (WHO, 1968) • IS THE DISORDER COMMON / IMPORTANT • ARE THERE TREATMENTS FOR THE DISORDER • IS THERE A KNOWN NATURAL HISTORY & “WINDOW OF OPPORTUNITY” WHERE SCREENING CAN DETECT DISEASE EARLY WITH IMPROVED CHANCE OF CURE • IS THE TEST ACCEPTABLE TO PATIENTS • SENSITIVE AND SPECIFIC • GENERALISABLE • CHEAP / COST EFFECTIVE • APPLY TO GROUP AT HIGH RISK

SCREENING DISEASE PRESENT ABSENT TEST POSITIVE A B NEGATIVE C D Sensitivity = a/a+c; Specificity = d/b+d; positive predicitive value = a/a+b; negative predicitve value = d/c+d.

Value of exercise ECG in coronary artery stenosis DISEASE PRESENT POSITIVE 137 11 NEGATIVE TEST ABSENT 90 112 Sensitivity = a/a+c = 60%; Specificity = d/b+d = 91%; positive predicitive value = a/a+b = 93%; negative predicitve value = d/c+d = 55%.

Sensitivities and Specificities for different tests Alcohol dependency or abuse (as defined by extensive investigations in medical and orthopaedic in patients) GGT MCV LFTs “Yes” to 1 or > of CAGE ? s “Yes” to 3 or > of CAGE ? s SENS 54% 63% 37% 85% 51% SPEC 76% 64% 81% 100%

MAKING SENSE OF THE EVIDENCE - ARE THESE RESULTS VALID i. e. should I believe them? • • Randomised (where appropriate)? Drop outs and withdrawals? Followup complete? Analysed in the groups to which randomised? “Intention to treat”.

MAKING SENSE OF THE EVIDENCE- ARE THESE RESULTS USEFUL? i. e. should I be impressed by them, are they relevant to my patients (GENERALISABLE) • How large was the treatment effect? • How precise was the estimate of treatment effect • Were all important clinical outcomes considered? • Do benefits outweigh risks?