# Basic statistics.

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Basic statistics

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) (lung cancer) EXPOSURE Yes (smoking) No The odds ratio would therefore be 56 x 246 = = 8.6. 7 x

TYPES OF STUDY - HYPOTHESIS TESTING
COHORT STUDIES

This is expressed as a divided by c .
COHORT STUDIES OUTCOME Yes No Exposed a b Not exposed c 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 non-exposed. This is expressed as a divided by c a+b c+d

Exposed ( on oral contraceptive ) 41 9996
COHORT STUDY EXAMPLE Deep vein thromboses (DVT) in oral contraceptive users. (Hypothetical results). OUTCOME (DVT) Yes No Exposed ( on oral contraceptive ) Not exposed (not on o.c.) 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 - 4S STUDY STABLE ANGINA OR MYOCARDIAL INFARCTION MORE THAN 6 MONTHS PREVIOUSLY SERUM CHOLESTEROL > 6.2mmol/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 (20mg > 40mg) OR PLACEBO OUTCOME DEATH OR MYOCARDIAL INFARCTION (LENGTH OF TREATMENT 5.4 YEARS ) WERE THE OUTCOMES

1/ARR = NUMBER NEEDED TO TREAT.
RCT EXAMPLE - 4S STUDY OUTCOME (death) Yes No Comparison intervention (placebo) Experimental intervention (simvastatin) The ARR is (256/2223) - (182/2221) = = 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 4S 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

DISEASE PRESENT ABSENT SCREENING 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 ABSENT TEST POSITIVE NEGATIVE 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) SENS SPEC GGT % % MCV % % LFTs % % “Yes” to 1 or > of CAGE ?s 85% % “Yes” to 3 or > of CAGE ?s 51% %

MAKING SENSE OF THE EVIDENCE - ARE THESE RESULTS VALID - i. e
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
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?