chris and abbie’s vital statistics. it’s actually quite dull!!! but......it is quite easy if you...

Chris and Abbie’s Vital Statistics

• It’s actually quite dull!!!

• But......It is quite easy if you think it through.

Arghhh Statistics...

• Some Definitions…

Arghhh Statistics...

• Risk:

Arghhh Statistics...

The probability that something will occur…In a particular group

• Risk Ratio:

Arghhh Statistics...

The probability that something will occur in one group

compared to another group.

• Odds:

Arghhh Statistics...

The chance of something occurring compared to it

not occurring…

• Odds Ratio…

Arghhh Statistics...

The ratio of the odds of something occurring in one

group compared to odds of it occurring in a different group

• Number needed to Treat…

Arghhh Statistics...

Number of people needed to treat to have one given outcome....= 1 ÷ Absolute Risk Reduction

Arghhh Statistics...

• An example…. Sausage Addicts!• A study over one year.

Eats Sausage Does not eat Sausage Totals

Heart Attack 25 12 37

No Heart Attack 1675 1788 3463

Total 1700 1800 3500

Risk

Sausage Fans Eats Sausage Does not eat Sausage Totals

Heart Attack 25 12 37

No Heart Attack 1675 1788 3463

Total 1700 1800 3500

• What is the risk of having a heart attack in the sausage eating group?

Risk in sausage group

Sausage Fans Eats Sausage Does not eat Sausage Totals

Heart Attack 25 12 37

No Heart Attack 1675 1788 3463

Total 1700 1800 3500

• Risk = Number of heart attack/total population

= 25/1700 = 0.0147 (1.47%)

Risk in non sausage group

• Risk = Number of heart attack/total population

Sausage Fans Eats Sausage Does not eat Sausage Totals

Heart Attack 25 12 37

No Heart Attack 1675 1788 3463

Total 1700 1800 3500

= 12/1800 = 0.00667 (0.67%)

Relative Risk

• Relative Risk in one group/risk in the other group.

Sausage Fans Eats Sausage Does not eat Sausage Totals

Heart Attack 25 12 37

No Heart Attack 1675 1788 3463

Total 1700 1800 3500

= 0.147/0.0067 = 2.19

Absolute Risk

Absolute risk =

(Risk in sausage eaters) – (Risk in non sausage eaters)

= (25/1700) - (12/1800) = 0.0080 (0.8%)

Sausage Fans Eats Sausage Does not eat Sausage Totals

Heart Attack 25 12 37

No Heart Attack 1675 1788 3463

Total 1700 1800 3500

Number needed to harm

• Number needed to harm = 1 ÷ Absolute risk reduction

= 1/0.008 = 125

i.e. if 100 people ate sausages for 1 year an additional 0.8 would have a heart attack. If 1000 people ate sausages for 1 year an additional 8 would have a heart attack. 1000/8 = 125....So 125 people are needed to eat sausages for 1 year to get one additional heart attack.

Odds of heart attack in sausage group

Heart attack ÷ no heart attack

Sausage Fans Eats Sausage Does not eat Sausage Totals

Heart Attack 25 12 37

No Heart Attack 1675 1788 3463

Total 1700 1800 3500

= 25/1675 = 0.0149.

i.e. For every person who does not have a heart attack 0.0149 of a person does have a heart

attack.

Odds of heart attack in non sausage group

Heart attack ÷ no heart attack

Sausage Fans Eats Sausage Does not eat Sausage Totals

Heart Attack 25 12 37

No Heart Attack 1675 1788 3463

Total 1700 1800 3500

12/1788 = 0.00671.

i.e. For every person who does not have a heart attack 0.00671 of a person does have a heart attack. (its less)

Odd Ratio

• Odds of Heart attack in sausage eaters: 0.0149• Odds of Heart attack in none sausage eaters: 0.00671

Odds ratio 0.00671/0.0149 = 2.22

So eating sausages doubles your odds of having a heart attack in one year...

Arghhh more stats….!

• And Now Abbie…..!

Sensitivity and Specificity

• Why Bother?

• If disease is present a truly accurate, test will always give a positive result

• If disease is not present, the test will always give a negative result.

Sensitivity…

• …

• the proportion of people with disease who have a positive test result

= true positive

(true positive + false negative)

Specificity

• …

• the proportion of people without disease who have a negative test result

= true negative

(true negative + false positive)

An example

Allergy test

Chocolate allergy

No chocolate allergy

Positive 35 5

Negative 1 40

Total 36 45

False negative

True positive False positive

True negative

Work it out…

• Sensitivity =

• Specificity =

35/36 = 0.97 (97%)

40/45 = 0.89 (89%)

Clinically…

PSA for prostate cancer Sensitivity is 46% Specificity is 91%

Ca125 for ovarian cancer Sensitivity is 72% Specificity is 78%

Predictions…

PPV : proportion of positive test results that are true positives

= number of true positives

No. of true positives + no. of false positives

Continued…

NPV : proportion of negative test results that are true negatives

= number of true negatives

No. of true negatives + no. of false negatives

An example

Allergy test

Chocolate allergy

No chocolate allergy

Positive 35 5

Negative 1 40

Total 36 45

False negative

True positive False positive

True negative

Worked example…

• PPV =

• NPV =

35/40 = 0.875 (88%)

40/41 = 0.975 (98%)

Papers…

• Meta analysis• Systematic review• Can anyone tell me the difference?

“Science is cumulative, with new ideas being based on previous knowledge and observation, and new advances in science should help us make sense of what we already know and have observed. But if we don't collect previous knowledge and observation in a systematic way, we are unlikely to make progress as quickly as we could.”

The Cochrane Collaboration open learning material http://www.cochrane-net.org/openlearning/html/mod1-2.htm

Meta-analysis

• Calculating the results of each study identified by the reviewer, and then to calculate an average of those results in a meta-analysis.

• Systematic reviews do not have to have a meta-analysis - there are times when it is not appropriate or possible and vice-versa

• We tend to use forest plots to present the results of a meta-analysis…

Forest Plots

• Forest plots show the information at a glance from the individual studies that went into the meta-analysis.

• It provides a simple visual representation of the amount of variation between the results of the studies, as well as an estimate of the overall result of all the studies together.

Can someone talk me through it?

Give papers out…

Paper to work on…

• Can you decipher the forest plot?

And again…

And now for some fun…

• CRITICAL APPRAISAL!

Critical Appraisal

Critical Appraisal

Critical Appraisal

Critical Appraisal

Critical Appraisal

Critical Appraisal Skills Programme (CASP)

The Answers…

The Answers…

The Answers…

  Rosuvastatin Placebo Total

Primary End point 44 91 135

No Primary Endpoint 3021 2939 5960

Total 3065 3030 6095

Results PercentRisk Rx 0.01436 1.435563Risk Placebo 0.03003 3.0033Relative Risk 0.478 47.79951Absolute risk 0.01568 1.567738NNT 63.7862