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

COFFEE DRINKING LUNG CANCER

SMOKING

STUDY

CONFOUNDING VARIABLE

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

Controls

Population

CasesYes

No

Yes

No

Exposure to Risk Factor

TIME

STUDY

CASE CONTROL EXAMPLE -SMOKING & LUNG CANCER

DISEASECases Controls

EXPOSURE Yes a bEXPOSURE No c d

Odds Ratio = ad/bc (1 = no association, > 1 = possible association, < 1 = protective effect)

DISEASECases Controls

(lung cancer)EXPOSURE Yes 56 230(smoking) No 7 246

The odds ratio would therefore be 56 x 246 = 13776 = 8.6. 7 x 230 1610

TYPES OF STUDY - HYPOTHESIS TESTING

• COHORT STUDIES

Population

Sample

Yes

No

Yes

No

Time

Exposed

Not exposed

COHORT STUDIES OUTCOME

Yes NoExposed 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

COHORT STUDY EXAMPLE

Deep vein thromboses (DVT) in oral contraceptive users. (Hypothetical results).

OUTCOME (DVT)

Yes NoExposed ( on oral contraceptive ) 41 9996

Not exposed (not on o.c.) 7 10009

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

Population Sample Time

Improved

Not improved

Not improved

Improved

Experimental intervention

Comparisonintervention

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

RCT EXAMPLE - 4S STUDY

OUTCOME (death) Yes No

Comparison intervention (placebo) 256 1967 2223

Experimental intervention (simvastatin) 182 2039 2221

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 4S study, in 5.4

years we will have prevented 1 death.

NNT EXAMPLES

Intervention Outcome NNTStreptokinase + asprirn v. placebo

(ISIS 2)prevent 1 deathat 5 weeks

20

tPA v. streptokinase(GUSTO trial)

save 1 life withtPA usage

100

Simvastatin v. placebo in IHD(4S study)

prevent 1event in 5y

15

Treating hypertension in the over-60s

prevent 1 eventin 5y

18

Aspirin v. placebo in healthyadults

prevent MI ordeath in 1 year

500

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)

Relative risk

0.1 0.2 0.5 1.0 2.0

Reduced RR Increased RR

Randomised Trials

Geographical study

Case control studies

HIP

Two County

Malmo

Edinburgh

Stockholm

UK

BCDDP

Nijmegen

Utrecht

Florence

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

PRESENTABSENT

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 137 11

NEGATIVE 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)

SENS SPEC

GGT 54% 76%

MCV 63% 64%

LFTs 37% 81%

“Yes” to 1 or > of CAGE ?s 85% 81%

“Yes” to 3 or > of CAGE ?s 51% 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?