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Interpreting numbers ScotPHO training course March 2011 Dr Gerry McCartney Head of Public Health Observatory Division NHS Health Scotland [email protected]. Approaching numbers: some questions to ask. 68% of Doctors don’t listen to their patients. What is being counted? Definitions - PowerPoint PPT Presentation
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Interpreting numbersScotPHO training course
March 2011
Dr Gerry McCartney
Head of Public Health Observatory Division
NHS Health Scotland
Approaching numbers: some questions to ask
• What is being counted?– Definitions– Type of numbers - counts, means, etc.
• Who/where (population): what is the denominator?• When (time): what time period do they cover?• How (source): where did they come from?• Why were they produced: is there an agenda?
68% of Doctors don’t
listen to their patientsSMOKERS ON PILL DOUBLE STROKE RISK
Incidence and Prevalence
• Dealt with in more detail later in course• Incidence describes the number of new cases in the
population over a period of time• Prevalence describes the number of cases present in a
population at any one point in time
Framework for interpreting numbers
Could your interpretation be affected by either:
• Error• Chance• Confounding (the mixing of two effects) • Bias (systematic departure from truth – either deliberate
or unintentional)
Example: COPD (lung disease) variation
• Is COPD more common in Board A or Board B?• Errors (e.g. different definitions used in each Board)?• Chance (e.g. no confidence intervals used)?• Bias (e.g. are there systematic differences in how disease is
recorded)?• Confounding (e.g. are there mixed effects – such as age
structure)?
NHS Board A Cases per 1,000 population
NHS Board B Cases per 1,000 population
Anytown 230 Smalltown 190
Othertown 280 Seatown 210
Bigtown 159 Hilltown 149
Overall 223 Overall 183
Sources of error:
• Mistakes in data collection, data recording, data storage, data transmission
• Coding errors, transcription errors• Can be random or systematic
• Do the numbers add up?• Are the number plausible?
Chance and interpreting numbers
• Most figures report data for a sample from a larger population
• A different sample would give a different result• Year to year fluctuation can be due to chance • The size of the sample dictates the degree to which a
difference is likely to be due to chance• Confidence intervals and p-values give estimates of the
precision of a value– E.g. Relative risk of heart disease amongst diabetics is 7.4 (95% CI 6.5-
8.6) means that there is a less than 1 in 20 chance of the true value lying outwith the range 6.5 to 8.6
Bias – identification and interpretation
• Bias is a systematic alteration of figures away from the true value
Examples• Selection bias – critically appraise sampling strategy, loss to
follow-up, response rate• Information bias – completeness of data, calibration,
participant self-report, recall time • Publication bias – think about a funnel plot
Confounding: when separate effects are mixed together
• In this example, the effect of location is mixed with (confounded by) the effect of age
• The population of Western Isles is older so has higher rates of CHD admission
• Is CHD more common in Western Isles after taking age into account?
NHS Western Isles NHS Lothian
CHD admissions per 100,000 per year
350 200
Methods for dealing with confounding
Design•Randomisation (only for experimental studies)•Restriction (e.g. narrow the comparison groups by age, sex,
ethnicity, socioeconomic status)•Matching
Analysis• Stratification (i.e. compare sub-groups, but has dangers) • Standardisation*• Multivariate analysis*
*dealt with in more detail elsewhere
Standardisation: brief interpretation
•A method of “removing” the effect of other factors to allow a “fair” comparison
•The other factors are most commonly age and sex, but standardisation can be used for other factors
•Standardisation shows the rates you would get if the population had a “standard” age and sex structure
NHS Western Isles NHS Lothian
Crude CHD admissions per 100,000 per year
350 200
Directly age standardised CHD admissions per 100,000 per year
250 220
Standardised Mortality Ratios (SMRs):
• This is a comparison of mortality in a population with a ‘standard’ population taking account of age structure
• The standard population is allocated a value of 100 for whatever the mortality rate is
• The age and sex standardised mortality of the population of interest is then divided by that in the standard population to give a figure for comparison with the 100
• An SMR of 150 indicates that mortality is 50% higher after accounting for age and sex differences
Interpreting associations: does A cause B?
A B
A B
A
B
A B
C
?
Causal relationship
Confounding
Chance
Some quick notes on interpreting graphs:
• Beware of: ambiguity, distortion and distraction
Data Ambiguity
Data distortion (1)10
.110
.210
.310
.4
0 1 2 3 4 5 6 7
Data Distortion (2)
Data Distortion (3)
Data distortion (4)
0
200
400
600
800
1000
1200
1400
Financial year
Ra
te p
er
10
0'0
00
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on
Male
Female
General acute inpatient discharges with an alcohol-related diagnosis in any position, by gender, Scotland, 1982/3 - 2009/10
Data distortion (5)
0
200
400
600
800
1000
1200
1400
Financial year
Ra
te p
er
10
0'0
00
po
pu
lati
on
Male
Female
General acute inpatient discharges with an alcohol-related diagnosis in any position, by gender, Scotland, 1982/3 - 2009/10
Summary
• Always ask the questions: what, who, where, when, how and why
• Think about possible problems with data: errors, chance, bias and confounding
• Even when things are associated they may not be cause and effect
• Beware of the possibility of graphs creating distortions, distractions or ambiguity