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Promoting a knowledge based NHS www.southeastlibrarysearch.nhs.uk Promoting a knowledge based NHS www.southeastlibrarysearch.nhs.uk

Introduction to Medical Statistics

Mark Kerr Clinical Librarian, EKHUFT

CLIST July 30th 2014

Promoting a knowledge based NHS www.southeastlibrarysearch.nhs.uk


Learning objectives

By the end of this session you will:

• understand how statistics represent medical

research

• interpret statistical tables in research papers

• describe common medical statistical concepts

• identify statistical inadequacies in research

• Interpret statistical diagrams


The different types of statistics

Descriptive statistics - summarise the population and the results

Statistics for validity – describe the reliability of the study and how the results are applicable to others

Statistics to demonstrate difference (statistics for probability) – describe the results as comparisons between groups under study


Descriptive statistics


Descriptive statistics

Summarise the population and the results

1) Numerical – where a value can fall at any point in a range (e.g. weight)

2) Categorical – where a value is selected from specific options (e.g. gender) – can be ‘nominal’ or ‘ordinal’

Some measurements can fall into either – BMI (e.g. 28, or ‘overweight’)

Different techniques are used to summarise each type of data.


Classification of Types of Data


Normal vs skewed data The type of data distribution matters when it comes to

summarising and (later) statistical testing

www.southalabama.edu/coe/bset/johnson/lectures/lec15.htm

Data distributions

http://www.southalabama.edu/coe/bset/johnson/lectures/lec15.htm


‘Averaging’ values - mean

Used to calculate the average where the data are ‘normally distributed’, ie a point is equally likely to appear above or below the mean:

To calculate the mean: – Add up all the values – Divide by the total number of values

1 + 1 + 2 + 3 + 4 + 5 +5 + 6 + 7 + 9 = 43 43 / 10 = 4.3 = Mean Susceptible to extreme outliers

1 1 2 3 4 5 5 6 7 9


‘Averaging’ data - median

1 1 2 2 2 2 2 2 3 3 3 3 4 4 4 5 6 6 7 9 15

Median is used for skewed data where values are not evenly

distributed around a central value.

To calculate the median, line up all the values and find the

centre value. If there is an even number of values, take the

mean of the 2 centre values.

Less susceptible to outliers…


‘Averaging’ data - mode

1 1 2 2 2 2 2 2 3 3 3 3 4 4 4 5 6 6 7 9 15

Mode is often used for categorical data where values

cannot be added up. You identify the most frequent

value. Here it would be 2.

You have 30 seconds to calculate/guesstimate the mean, mode and median


What is the difference?

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fre

qu

en

cy

Length of Stay

Median

= 3

Mean

= 4.1

Mode

= 2


Summarising numerical results

We summarise numerical results by reporting:

Mean

Median

Standard Deviation

Inter-Quartile Range

1 1 2 3 4 5 5 6 7 9

3 3 4 4 4 5 5 5 5 7

AVERAGE

SPREAD


Inter-quartile range

1 1 2 2 2 2 2 2 3 3 3 3 4 4 4 5 6 6 7 9 15

The inter-quartile range (IQR) is the middle 50% of the values.

2 2 2 3 3 3 3 4 4 4 5


0

2

4

6

8

10

12

60 65 70 75 80 85 90 95 100

The standard deviation measures how widely the set of values is spread around the mean

Mean (SD)

80 kg (10 kg)

Standard deviation


0

2

4

6

8

10

12

60 65 70 75 80 85 90 95 100

The standard deviation measures how widely the set of values is spread around the mean

Mean (SD)

80 kg (5 kg)

Standard deviation


Standard deviation

0

2

4

6

8

10

12

60 65 70 75 80 85 90 95 100

68.2% of results are between +1 and -1

standard deviations from the mean

Mean (SD)

80 kg (5 kg)

68.2%

95.4 % of results are between

2 standard deviations from the

mean

99.7 % of results are between

3 standard deviations from the

mean


Statistical Validity

“Validity – the extent to which a

test measures what it is supposed

to measure.” (Gosall 2009)


Statistical Validity

The degree to which an observed result, such as a

difference between two measurements, can be relied upon

and not attributed to random error in sampling and

measurement

Sample Size – enough to detect true difference

Power – ability to detect a true difference

P – probability of results if null hypothesis is true

CI – the degree of uncertainty around an estimate


To calculate the sample size, you need to know:

The minimum clinically important difference

The frequency (prevalence) and spread of data we might expect - usually from previous studies

Type of study design (superiority, non-inferiority, equivalence)

Type of primary outcome (dichotomous/continuous)

General aim is to achieve valid outcome with smallest possible sample, for cost and practicality

Sample Size


The evidence: a statement on sample size calculation

and the expected sample – and the proof in the results

that this was achieved:

CLOTS Trial: Lancet. 2009 June 6; 373(9679): 1958–1965.

Sample Size – the evidence


The p value gives a measure of how likely it is that any differences between control and experimental groups are due to chance alone. P values range from 0 (impossible to happen by chance) to 1 (the event will certainly happen).

p=0.001 unlikely result happened by chance: 1 in 1000 Strong evidence

p=0.05 fairly unlikely result happened by chance: 1 in 20 Weak evidence, within a whisker of non-significance

p=0.5 equally likely the result happened by chance: 1 in 2 Still some indication of benefit?

p=0.75 very likely the result happened by chance: 3 in 4 No useful result?

Results where p is less than 0.05 are said to be “significant.” This is just an arbitrary figure, in 1 in 20 cases, the results could be due to chance.

P (Probability) Value


P Values – just a first step From: http://theconversation.com/the-problem-with-p-values-how-significant-are-they-really-20029


Type 1 error = concluding a relationship exists between two

variables, when in fact there is no relationship, leading us to

reject the null hypothesis when it is actually true

A study has avoided Type 1 error if P<0.05

Type I or ά Error

Type II or β Error Type 2 error = concluding a relationship doesn’t exist

between two variables, when in fact there is a relationship,

i.e. a high (poor) P value when the null hypothesis was

correct

A study has avoided Type II error if Power>80%


Used in the same way as p values in assessing the effects of chance but gives more information.

Any result obtained in a sample of patients only gives an estimate of the result which would be obtained in the whole population.

The real value will not be known, but the confidence interval shows the size of the likely variation from the true figure.

A 95% CI means a 95% chance that the ‘true’ result lies within the range specified. (Equivalent to a p value of 0.05).

The larger the trial the narrower the confidence interval, and therefore the more likely the result is to be definitive.

If the CI includes the point of zero effect (i.e. 0 for a difference, 1 for a ratio) it can mean either that there is no significant difference between the treatments and/or that the sample size was too small to allow us to be confident where the true result lies.

95% CI (Confidence Interval)


Not about you recalculating statistics

Not about you accessing raw research data

Look for evidence in the study that potential errors have

been considered and managed

Achieving the sample, good power, adequate P & CI values

are just an indication that SOME errors have been avoided.

P-value cannot compensate for systematic error (bias) in a

trial. If the bias is large, the p-value is likely invalid and

irrelevant.

It’s all about evidence...


The quick statistical validity check

WHAT

– What was the sample size?

– Did randomisation work?

– Did they recruit to that number and

record/report outcomes data for them?

– What was the primary outcome?

– Was the primary outcome reported with a

‘good’ P value?

WHERE

– Statistical Analysis

– Baseline characteristics

– Consort Diagram

– Outcomes table

– Abstract/Methods

– Outcomes table


Statistics for probability (measures of effect)


Definitions

• Risk: the number of participants having the event in a group divided by the total number of participants

• Odds: the number of participants having the event divided by the number of participants not having the event

• Risk ratio (relative risk): the risk of the event in the intervention group divided by the risk of the event in the control group

• Odds ratio: the odds of the event in the intervention group divided by the odds of the event in the control group

• Risk difference: the absolute change in risk that is attributable to the experimental intervention

• Number needed to treat (NNT): the number of people you would have to treat with the experimental intervention (compared with the control) to prevent one event (in a specific time period).

(EER = Experimental Event Rate, CER = Control Event Rate)


Counting the number of events

When measuring

an event rate we

count how many

people experience

the event…

… and divide that

number by the total

number of people in

the group

Ratio

Proportion

(Event) Rate

Percentage

Prevalence


So...

If we wanted to compare two groups for the

number of people who fell over in a group,

we would simply count the number of

people who fell over in Group A and count

the number of people who fell over in

Group B. The number of people falling

over could be expressed as a simple

count, but to make comparison easier it is

usually expressed as a %.


The 2x2 Matrix: Risk & Relative Risk

In treatment group

Risk = a ÷ (a+b)

In control group

Risk = c ÷ (c+d)

RR = (a ÷ (a+b)) ÷ (c ÷ (c+d))

Relative Risk compares

the event rates between

two groups


Absolute or relative difference

Difference can be Absolute or Relative

Absolute Difference: X – Y where X and Y are averages or proportions

or

Relative Difference: X ÷ Y where X and Y are proportions


Absolute or relative difference

If 60 out of 100 people in Group B suffer a fall,

and 20 out of 100 people in Group A suffer a

fall

the absolute difference = 60-20 = 40

people who fall

the relative difference = 60 ÷ 20 = 3

(or you are 3 times more likely to suffer a

fall in Group B)


Event rates (proportions)

2x2 table Disease/

outcome

Disease/

outcome

Total

Yes No

Risk factor

/ Exposure

a b a + b

No risk factor

/ Control

c d c + d

• Exposure Event Rate = a ÷ (a + b)

• Control Event Rate = c ÷ (c + d)


Event rates (proportions)

2x2 table Falls Falls Total

Yes No

Vitamin D

(Group A)

20 80 100

No Vitamin D

(Group B)

60 40 100

• Exposure Event Rate = 20 ÷ (20 + 80) = 20%

• Control Event Rate = 60 ÷ (60 + 40) = 60%


Relative risk

Pfeifer M, Begerow B, Minne HW, et al. Effects of a short-term vitamin D and calcium supplementation on body sway and secondary hyperparathyroidism in elderly women. Bone Miner Res 2000;15:1113-8.

% of people who fell

Risk ratio Vitamin D

and calcium

Calcium

alone

16% 28% 0.57


Relative risk

Vitamin D

and calcium Calcium

alone

% of people who fell 16% 28%

Relative Risk (RR)

= Exposure Event Rate ÷ Control Event Rate

= 16% ÷ 28%

= 0.57 or 57%


Relative risk reduction

Relative Risk Reduction (RRR)

= 1 – Relative Risk

= 1 – 0.57

= 0.43 or 43%

Vitamin D

and calcium Calcium

alone



Odds ratios

Odds are worked out differently to risks.

No. of people who experience outcome

÷

No. of people who don’t experience outcome

An odds ratio compares the odds of Group A experiencing an event compared to the odds of Group B experiencing an event.


The 2x2 Matrix: Odds & Odds Ratio


Odds ratios

So, using the same falls example:

If 11 out of 70 people fell in Group A, the odds of falling in that group are 11 ÷ 59 = 0.19

If 19 out of 67 people fell in Group B, the odds of falling in that group are 19 ÷ 48 = 0.40

Odds ratio = 0.19 ÷ 0.40 = 0.48


Odds ratio

OR is particularly useful because as an effect-size

statistic, it gives clear and direct information to

clinicians about which treatment approach has the

best odds of benefiting the patient.

Also used in cross-sectional studies and case-

control studies, where exposure or not exposure

replaces treatment and control, and outcome is

presence or absence of disease.


Odds versus risk

• If 50 in every 100 children are boys then:

– Risk of having a boy = 50/100 = 0.5

– Odds of having a boy = 50/50 = 1

• If 1 in 100 patients suffers a side-effect then:

– Risk of having a side-effect = 1/100 = 0.01

– Odds of having a side-effect = 1/99 = 0.01


Odds versus risk

Risk can be stated as “6 people die out of every 10

who are exposed”

Risks are a consequence of a risk leading to an

outcome, whereas odds compare two groups,

and can be reversed

Odds can be stated as “for every 4 people who

recover, 6 people do not” (or for 6 who don’t, 4

do).


Success/Failure

Measure No Effect Total Success

Absolute Risk Reduction Zero Initial Risk

Risk Ratio/Relative Risk 1 (or 100%) 0

Odds Ratio* 1 0 (or ∞)

Number Needed to Treat ∞ 1


SAFE Study

http://www.nejm.org/doi/pdf/10.1056/NEJMoa040232

NEJM Correspondence

http://www.nejm.org/doi/full/10.1056/NEJM200410283511818

Journal Club Commentaries

http://www.biomedcentral.com/content/pdf/cc3006.pdf


SAFE Study - albumin/saline a

c d

b

Outcome

YES NO

Treatment

Control

http://www.nejm.org/doi/pdf/10.1056/NEJMoa040232

http://www.nejm.org/doi/full/10.1056/NEJM200410283511818




ODDS & RISK EXERCISES RISK

• 133 women take an antibiotic for treatment of UTI

• 14 still have UTI after 6 weeks

• Q1: What is the risk of remaining infected?

ODDS

• Q2: For these 133 women, what is the risk of having the event (still infected) divided by the risk of not having it (cured)?

COMPARING ODDS & RISK

• Q3: Both are similar, due to small result. But if you include the 148 women in this trial receiving placebo, of whom 128 still had UTI after 6 weeks. In this group what is the risk of staying infected?

• Q4: What are the odds?

• Odds and Risk are never identical, although similar at low values. But depending on presentation can seem much more powerful (especially in a newspaper headline)


The Answers •[1] 14/133 = approx 0.1

•[2] 14/119 = still approx 0.1; more formally, it is 14/133 (risk of having the event) divided by 119/133 (risk of not having the event), still 14/119 or 0.1

•[3] 128 (number with event – still infected)/148 (total number in the group)

•= 0.86

•[4] 128 (still infected)/20 (number cured) = 6.4 – very different).


Relative risk or risk ratio (RR) Risk of event in one group divided by risk of the event in other group.

RR = no. with event in treatment group / no. with event in control group

no. in treatment group no. in control group

= (14/133) / (128/148)

= 0.1 / 0.86

= 0.12

RR =1 Intervention has identical effect to control

RR <1 Intervention reduces chances of having the event

RR >1 Intervention increases the chances of having the event

RR = 0 No events in treated group = 100% perfect treatment!

Comparing two groups

Event No Event Total

Intervention 14 119 133

Control 128 20 148


Odds ratio (OR) Odds in the treated group / odds in the control group

OR = no. with event in treatment group / no. with event in control group

no. without event in treatment group no. without event in control group

= (14/119) / (128/20)

= 0.118 / 6.40

= 0.018

OR =1 Intervention has identical effect to control

OR <1 Intervention reduces chances of having the event

OR >1 Intervention increases the chances of having the event

OR = 0 No events in treated group = 100% perfect treatment!

Comparing two groups

Event No Event Total

Intervention 14 119 133

Control 128 20 148


Absolute risk reduction and

Number needed to treat

Absolute Risk Reduction (ARR) or Risk Difference

= Control Event Rate (CER) – Experimental Event Rate (EER)

= 28% – 16% = 12%

Or

= Relative Risk Reduction (RRR) x Control Event Rate (CER)

= 1 – (0.16 / 0.28) = 0.43

= 0.43 x 0.28

= 0.12 (1%)

Vitamin D

and calcium Calcium

alone



Number needed to treat

Absolute Risk Reduction: CER – EER

or

Absolute Risk Reduction: RRR x CER

Number Needed to Treat: 1 ÷ ARR (or 100 ÷ ARR, if

ARR expressed as a percentage)

[Number of people to treat with an intervention to prevent one outcome]


Number Needed To Treat

• A measure of the relative efficacy / risk of a

treatment

• How many patients need to be exposed to a risk

factor (i.e. a treatment) over a specific period for

one extra patient to be show benefit/harm who

would not otherwise have shown benefit/harm.

• 1÷Absolute Risk Reduction or 1÷Risk Difference

• Consider also NNH (harm), NNV (vaccinate)


Examples

• When dose-adjusted warfarin was compared to

aspirin, the absolute risk reduction of stroke was

0.6% in warfarinized patients (NNT 167)

• Tamoxifen vs Placebo for BrCa: – NNT 112 (5 yrs treatment);

– NNH (Venous Thromboembolic Events) = 137,

– NNH (Mortality) = 256 (so need to identify/control for high

risk of BrCa against high risk of adverse events)

• Cochrane (2010): Vaccines for Influenza in healthy

adults – NNV = 33 (matched vaccines) to 100

(unmatched)


• 4 out of 55 or 7.3% died on Streptomycin = EER

• 14 out of 52 or 26.9% died on placebo = CER

ARR = CER–EER = 26.9% – 7. 3% = 19.6% (or 0.196) NNT = 1/0.196 = 6

6 patients with TB would need to be treated with streptomycin to prevent 1 additional person dying

• RR of dying on streptomycin compared to placebo was 0.27

• Tx with streptomycin showed 73% reduction in the risk of death compared with placebo.

• Antibiotic treatment prevented approximately three quarters of the deaths that would have occurred on placebo.

4 51

14 38

BMJ 30.12.1948 769-80

http://www.tbonline.info/galleries/image/37/

http://www.tbonline.info/galleries/image/37/


Reading Statistical Diagrams

Forest Plots, Survival Curves, Life

Expectancy Curves and ROC Curves


Reading Statistical Diagrams

You’re appraising, not recalculating

First test significance, then what or how much

Read the words & numbers, not just the pictures!


Line width shows

the CI, box size

reflects the size of

the group

3 sub-group

analyses, each pair

adds up to ‘All’

figures

Summary diamond

shows overall total

Line of zero

effect or unity

Effectiveness of thigh-length graduated compression stockings to reduce the risk of deep vein thrombosis after stroke (CLOTS trial 1): a multicentre, randomised controlled trial

CLOTS Trial: Lancet. 2009 June 6; 373(9679): 1958–1965.

Not all Forest Plots are meta-analyses


Use of weaning protocols for reducing duration of mechanical ventilation in critically ill adult patients:Cochrane systematic review and meta-analysis BMJ 2011;342:c7237

Odds Ratio Diagram – Forest Plot


Not all Forest Plots are Odds Ratios

BMJ 2011;342:c7237


Heterogeneity Occurs where the results of different studies vary from each other more

than might be expected by chance. Visually, on a Forest Plot, where the CI

lines do NOT overlap. Significant heterogeneity would rule out meta-

analysis, alternatives would include sub-group or sensitivity analysis.

Χ2 = variation in results above that

expected by chance – relates to DF

(“n of studies -1” = ‘perfect’), much

higher suggests heterogeneity’

Low P value for Χ2 may indicate

heterogeneity

High I2 indicates heterogeneity

If Z Statistic > 2.2, then

heterogeneity is present; Z should

have an associated P value


The survival curve is a graphical display of the Kaplan-Meier

estimate that an event will occur

Does not presume normal distribution

Log Rank test compares rates in 2 groups

Measures time to an event following treatment (‘survival’),

but may be non-mortality – revision of arthroscopy, time in

remission before relapse, or positive (pregnancy, discharge)

If sample large enough, the estimate approaches the true

survival function for the population

Allows inclusion of patients starting & leaving studies at

different time intervals

Survival Curves


Dropouts/mortality NOT due to target cause, but lost to

follow-up, withdrawal from study

Marked on curve but doesn’t affect analysis

Assumes loss to follow-up is independent of their prognosis

For each event survival curve drops - denominator changes,

but plot stays the same, marked by ticks

Censored Data

Gijbels Irène. Censored data.

WIREs Comp Stat 2010, 2: 178-188


A gap in the horizontal direction =

“the median (50%) survival time is

much larger (about 200 days larger)

in the patients without cachexia”.

A gap in the vertical direction =

“at 500 days, the probability of survival

is about 45% in the patients without

cachexia and only 25% in the patients

with cachexia”.

Comparing/Describing Survival


Vertical axis = estimated probability of survival for a hypothetical cohort, not actual % surviving.

Precision depends on the number of observations: estimates at left-hand side are more precise than right-hand side (because of smaller numbers due to deaths and dropouts).

Curves may give the impression that a given event occurs more frequently early than late, because of high survival rate and large number people at beginning.

Rule of thumb is to truncate the x axis at the point where you only have 10 survivors, or 10% of the original cohort, whichever is higher, as reliability of curve diminishes as population survival reduces

Survival Curves

Cumulative morbidity plots are often better than survival plots when overall survival is high


Hazard is a measure of how rapidly the event occurs. The hazard ratio compares the hazards in two groups.

If a hazard ratio is, say, 4.17, the estimated relative risk of the event in group 2 is 4.17 higher than in group 1.

The hazard ratio is significant if the confidence interval does not include the value 1.

Note: calculating the hazard ratio assumes the ratio is consistent over time - if the survival curves cross, the hazard ratio should be ignored.

Hazard Ratios


Relative survival for Merkel cell carcinoma by extent of disease at time

of diagnosis. Percent relative survival was calculated for cases in the

National Cancer Database using age- and sex-matched control data from

the Centers for Disease Control and Prevention

http://hematology.wustl.edu/conferences/presentations/Rokkam20091211.ppt

Survival Curves


Studenski S, Perera S, Patel K, Rosano C, Faulkner K, Inzitari M, et al. Gait speed and survival in older adults. JAMA 2011;305:50-8.

Life Expectancy Curve


Diagnostic Test Study Statistics

How good is the screening/diagnostic

test at predicting/confirming the

outcome of the Gold Standard test?


Test & Disease probability

Zone of uncertainty Treatment zone Discharge zone

0% chance

of disease

100% chance

of disease

Before doing the test,

probability of disease (pre-test

probability) is in this zone

After doing the test, we want the probability of disease

(post-test probability) to be in one of these two zones

GS

-ve

GS

+ve

Test-discharge

threshold Test-treatment

threshold


Key Screening Questions

• Is the test useful?

– Was it researched in a population relevant to the individual or population in whish it will be used?

• Is the test reliable?

– Can it be repeated and the effects reproduced using the same of different observers?

• Is the test valid?

– Does it measure what it sets out to measure and is the result true, when compared with the gold standard?


Biases to avoid – or identify

• Spectrum bias

– Tested on ‘healthy’ as well as ‘ill’ subjects

• Verification/Ascertainment bias

– ALL patients get BOTH tests

• Review bias

– Proper blinding to avoid influencing test results

• Lead time bias

– Earlier test without change in outcome


Lead time bias

http://en.wikipedia.org/wiki/Lead_time_bias

Where an earlier test implies longer survival, but actually there is no difference in

clinical outcome, so what seems like an effective early test (breast screening, genetic

test for Huntingtons) causes no real benefit, and may cause harm (anxiety etc).

http://en.wikipedia.org/wiki/Lead_time_bias


Sensitivity

Disease No

Disease

Test Result

Positive

Negative

TP FP

FN TN

Gold Standard

Sensitivity

TP/TP+FN

Sensitivity: The capacity of the test to correctly identify diseased

individuals in a population; “TRUE POSITIVES”.


Specificity

Disease No

Disease

Positive

Negative

TP FP

FN TN Test Result

Gold Standard

Specificity

TN/FP+TN

Specificity: The capacity of the test to correctly exclude individuals

who are free of the disease; “TRUE NEGATIVES”.


Example

Disease No

Disease

Positive

Negative

75

25

20

180

100 200 300

95

205

Sensitivity = 75/100 = 75% Specificity = 180/200 = 90%

Test Result

Gold Standard


Accuracy of the test

(a+d)/(a+b+c+d)

Disease No

Disease

Positive

Negative

a

c

b

d

Test Result

Gold Standard


Likelihood ratios • Reflects the degree of confidence that a person

who scores in the positive range does have the

disorder, or in the negative range does not have

the disorder

• LR+ = sensitivity/1-specificity

• LR- = 1-sensitivity/specificity

• The higher the LR+ the more useful the indicator

for identifying people with the disorder

• The higher the LR-, the more useful the indicator

for identifying people without the disorder


Worked example: Prevalence of 30%, Sensitivity of 50%, Specificity of 90%

30

70

15

7

100

22 people test positive……….

of whom 15 have the disease

So, chance of disease is 15/22 about 70%

Disease +ve

Disease -ve

Testing +ve

Sensitivity

= 50%

False

positive

rate = 10%


Positive Predictive Value

Disease No

Disease

Positive

Negative

TP FP

FN TN Test Result

Gold Standard

PPV=TP/TP+FP

PPV: the probability of the disease being present, among those with positive

diagnostic test results


Negative Predictive Value

Disease No

Disease

Positive

Negative

TP FP

FN TN Test Result

Gold Standard

NPV=TN/TN+FN

NPV: the probability of the disease being absent, among those with negative

diagnostic test results


Example

5000 pregnant women underwent a test for blood

glucose at 24 weeks, following a glucose load. 243

women were found to have a blood glucose greater

than 6.8 mmol/L and were referred for an OGTT. 186

were found to have gestational diabetes. Four women

who initially had tested negative were diagnosed as

having diabetes later in their pregnancy.


The 2x2 Table

Diabetes No diabetes Total

Positive 186 57 243

Negative 4 4753 4757

Total 190 4810 5000

Diagnostic calculator: http://ktclearinghouse.ca/cebm/toolbox/statscalc

http://ktclearinghouse.ca/cebm/toolbox/statscalc


The Sums Prevalence

Sensitivity

Specificity

Positive predictive value

Negative predictive value

Likelihood ratio + test

Likelihood ratio - test

Accuracy

190/5000

186/190

4753/4810

186/243

4753/4757

(186/190)/(57/4810)

(4/190)/(4753/4810)

(186+4753)/5000

3.8%

97.9%

98.8%

76.5%

99.9%

82.6

.02

98.8%


The Fagan Nomogram:

If you know 2 of the 3

elements, then you can

calculate the third, and see

the results of changes

i.e. for a known prevalence,

you can adjust the

likelihood ratio to see how it

affects the post-test

probability

Prev = 3.8% (0.038)

LR+ = 82.6

LR- = 0.02


ROC Curves: Breath Test for Biomarkers of TB

Sensitivity: 71/2%

Specificity: 72%

Accuracy: 80%

Prevalence: 5%


• Each point on the ROC curve represents a sensitivity/specificity pair corresponding to a particular decision threshold.

• The area under the ROC curve is a measure of how well a parameter can distinguish between two diagnostic groups (diseased/normal).

• Not just ‘diagnosis’ but also ‘prediction’

ROC Curves


• Represents the trade off between the false negative

(sensitivity) and false positive (specificity) rates for every

possible combination.

• If the ROC curve rises rapidly towards the upper right-

hand corner of the graph, or if the value of area under

the curve is large, we can say the test performs well.

• Area = 1.0 = an ideal test, because it achieves both

100% sensitivity and 100% specificity (i.e. the curve hits

the top left corner, where both are 100%). Area = 0.5 =

‘bad test’, as it doesn’t show a clear benefit of the test.

ROC Curves


• LR is the likelihood that a given test result would be expected in a patient with the target disorder compared to the likelihood that that same result would be expected in a patient without the target disorder.

• More useful than sensitivity/specificity: – less likely to change with prevalence of disorder

– can calculate for several levels of symptom/sign/test

– can be used to combine results of multiple tests

– can be used to calculate post-test probability

Likelihood Ratios


• A good test should have a LR+ of at least 2.0 and a LR- of 0.5 or less. This would correspond to an AUC of roughly 0.75. A better test would have likelihood ratios of 5 and 0.2, respectively, and this corresponds to an AUC of around 0.92.

• 0.50 to 0.75 = fair

• 0.75 to 0.92 = good

• 0.92 to 0.97 = very good

• 0.97 to 1.00 = excellent

ROC Curves & Likelihood ratios


Clinical interpretation:

“maximum proportional

reduction in expected regret”

Measures the optimal cut-off

point, the ‘best’ trade-off

between sensitivity and

specificity

Calculated as

sensitivity+specificity>1

For a test to be useful, then

sensitivity + specificity > 1

(Youden Index > 0)

Statistics in Medicine 1996; 15: 969–86.

Youden Index


Key References, Help, Ideas… Feedback, comment, complaints and suggestions: [email protected]

KSS Searching and training Wiki

https://sites.google.com/site/healthliteraturesearchers/Home

KSS Resources for Appraisal & Statistics Workshops

https://sites.google.com/site/healthliteraturesearchers/staff-development-1/cpd-for-library-staff

EQUATOR NETWORK – toolkits for every study type (CONSORT, PRISMA, GRADE et al)

http://www.equator-network.org/toolkits/

Medical Calculators:

http://www.mdcalc.com/ ; http://ktclearinghouse.ca/cebm/toolbox ; www.medal.org

NIHS RDS Resource Packs – guides to Research, SPSS, Statistics etc

http://www.rds-eastmidlands.nihr.ac.uk/resources/cat_view/13-resource-packs.html

Statistics in medicine

Anaesthesia & Intensive Care Medicine, April 2012 13/4 181-88

Statistics for clinical trials and audit

Anaesthesia & Intensive Care Medicine, April 2012, 13/4 189–193

mailto:[email protected]

https://sites.google.com/site/healthliteraturesearchers/Home















http://www.mdcalc.com/

http://www.mdcalc.com/

http://ktclearinghouse.ca/cebm/toolbox

http://www.medal.org/








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