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How to present and use statistics
Chris RobertsonDavid Young
Department of Statistics and Modelling Science, University of Strathclyde
Health Protection ScotlandRoyal Hospital for Sick Children,
Yorkhill NHS Trust
YORKHILL HOSPITAL
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Outline
o Introductiono What is statisticso Hypotheseso Statistics in Medical Research
o Study DesignPrinciples
Main Types
o Data and Presentationo Types of datao Graphical Methodso Tables
3
Introduction
o what is statistics and why do we need it?
o statistics is the science of collecting, analysing, presenting and interpreting data
o it enables the objective evaluation of research questions of interest
o it provides the means to weigh up how much evidence the collected data provide for and against the research hypothesis of interest
4
Examples of Research Hypotheses
o The main aim of this prospective cross-over study was to introduce one additional cleaner into a surgical ward from Monday to Friday and measure the effect on the clinical environment. After 6 months the cleaner was switched to another matched surgical ward so that each ward acted as a control for the other.
Measuring the effect of enhanced cleaning in a UK hospital: aprospective cross-over studyStephanie J Dancer, Liza F White, Jim Lamb, E Kirsty Girvan and Chris RobertsonBMC Medicine 2009, 7:28 doi:10.1186/1741-7015-7-28
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Examples of Research Hypotheses
o The aim of this review was to assess whether the reported rate of infection (i.e. incidence) or reported rate of death among patients with CDAD for any particular month within an acute hospital, or any particular acute hospital, differs from other months, other acute hospitals, or the national average in Scotland.
Report on Review of Clostridium difficile Associated Disease Cases and Mortality in all Acute Hospitals in Scotland from December 2007 ─ May 2008
Health Protection Scotland, 2008http://www.documents.hps.scot.nhs.uk/hai/sshaip/publications/cdad/cdad-review-2008-07.pdf
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Examples of Research Hypotheses
o The aims of the survey were: To provide the HAITF with baseline information on the total prevalence of HAI in Scottish hospitals and its burden in terms of health service utilisation and costs. This information would be available to guide priority setting in the development of strategy and policy.
NHS Scotland National HAI Prevalence Survey. Volume 1 of 2. Final Report Health Protection Scotland, 2007http://www.hps.scot.nhs.uk/haiic/publicationsdetail.aspx?id=34832
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Statistics and Medical Research
o statistics plays an increasingly important role in medical research
o it is not possible, for example, to have a new drug treatment approved for use without solid, statistical evidence to support claims of efficacy and safety
o over the last few decades, many new statistical methods have been developed which have particular relevance for medical researchers
o these methods can be applied routinely using statistical software packages
o easy to use but difficult to use correctly
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Importance of Statistics
Medical researchers should understand some basic statistical concepts to ensure …
o appropriate study design in terms of the number of participants
o application of the correct method of statistical analysis when using software
o accurate and honest reporting of data gathered from research studies
o adequate understanding of claims made by other researchers when reviewing medical literature
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The study design
o one of the main areas of research in which statisticians can work with other researchers to design the optimal studies
o describe the broad class of study design using standard terminology e.g. case study, cross-sectional study, cohort study, case-control study, clinical trial
o study intervention should be explainedo objectives should be clearly statedo state the outcome measure of interesto distinction between pre- and post-study hypotheseso inclusion and exclusion criteria of patient populationo source of study subjects
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Study design (cont.)
o choice of control group – concurrent or historicalo blinding – ideal is to use double blinding if possible and
justification for not should be giveno randomisation with details of any factors by which the
stratification had been carried outo power and sample size – details of how the sample size was
chosen including the power and minimum clinically important effect
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Study Design
1. research idea
2. broad research questions
3. primary research question
4. primary hypothesis
5. secondary research questions
6. secondary hypotheses
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Randomised Controlled Trials
Interventional
population sample inclusion/exclusion criteria randomisation – treatments A or B comparison of outcomes between A and B using
statistical tests
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Cohort Study (longitudinal/prospective)
Observational
subjects without the disease (cohort) either exposed (e.g. smoker) or not exposed (e.g. non-
smoker) proportion of each group will develop the disease (e.g.
lung cancer) compare proportions in each group using statistical tests
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Case/Control (retrospective)
Observational
people with and without the disease (i.e. cases and controls)
observe the exposure factor (e.g. past smoking habits) compare proportions in cases and control who were
exposed to the variable of interest (e.g. smoking)
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Cross-sectional (prevalence)
o usually carried out using a survey (questionnaire)o used to quantify specified characteristics of a defined group
of peopleo number of people with attribute at a specified point in time
reported as a proportion of the population of interest (prevalence)
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Examples
o a survey of HPV Prevalence among school children in Scotland
o cross sectional survey
o evaluation of the effect of an additional cleaner on the total coliform count on hand touch sites in a ward
o randomised trial
o exposure to unfiltered water increases the risk of campylobacter infection
o case control study
o association between H1N1v Influenza vaccination and the risk of hospitalisation for flu like symptoms
o cohort study
Presentation of Statistical Data
Keep it clear and simple Methods used depend upon the types of
data recorded do not include graphs of relatively
unimportant data where the number of observations is
small, plots are not useful (e.g. mean values with error bars)
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Types of Data
categorical data
• nominal – the data can be classified into a number of specific categories with no particular ordering e.g. blood type, HAI (Yes/No), Test Outcome (Positive/Negative/Ambiguous)
• ordinal – the data can be classified into a number of specific categories which can be placed in some order of importance e.g. pain scores (mild, moderate, severe or unbearable), deprivation category score within Glasgow (ranges 1–7 from affluent to poor classified by postcodes)
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Types of Data
numerical data
• discrete – data are recorded as a whole number and usually only take specific values e.g. number of cigarettes smoked in a day, number of children, number of admissions
• continuous – data are recorded to the precision of the measuring instrument and usually take any value within a certain range e.g. height, weight, blood pressure,
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Numerical presentation of data
o appropriate numerical summaries should give an overall unambiguous impression of the data
o means should be quoted to at most one extra decimal place relative to the precision with which the original measurements were recorded
o standard deviations and standard errors may be quoted with two additional decimal places
o medians and IQR handled as for meanso avoid use of since there is no convention – use e.g. mean
128.5 (SD 10.35)mmHg
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Presentation of the analysis results
o formal analysis should be chosen to most efficiently answer the study hypotheses
o actual p-values should be quoted e.g. p=0.21, p=0.003, p<0.001
o confidence intervals are preferable to p-valueso assumptions must be validated (e.g. normally distributed)o problems arising from multiple testing should be addressed
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NHS Scotland National HAI Prevalence Survey. Volume 1 of 2. Final Report
Health Protection Scotland, 2007http://www.hps.scot.nhs.uk/haiic/publicationsdetail.aspx?id=34832
23
Whenever you have a table with percentages or means
ALWAYS INCLUDE
The number of observations on which the mean or percentage is based
Gives you an impression of precision
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Weekly Influenza Situation Report (Including H1N1v) Wednesday 28 October 2009http://www.documents.hps.scot.nhs.uk/respiratory/swine-influenza/situation-reports/weekly-influenza-sitrep-2009-10-29.pdf
Doubled
Increase
Over 75s immune
Decrease
Decrease
25
0
10
20
30
40
50
60
70
0-4 5-14 15-44 45-64 65-74 75+
Perc
enta
ge
Age
Swab Positivity
Week 42
Week 43
0
10
20
30
40
50
60
70
0-4 5-14 15-44 45-64 65-74 75+
Perc
enta
ge
Age
Swab Positivity
Week 42
Week 43
0
10
20
30
40
50
60
70
0-4 5-14 15-44 45-64 65-74 75+
Perc
enta
ge
Age
Swab Positivity
Week 42
Week 43
Using graphs without numbers or precision is just as bad
26
Weekly Influenza Situation Report (Including H1N1v) Wednesday 28 October 2009http://www.documents.hps.scot.nhs.uk/respiratory/swine-influenza/situation-reports/weekly-influenza-sitrep-2009-10-29.pdf
27
Weekly Influenza Situation Report (Including H1N1v) Wednesday 28 October 2009http://www.documents.hps.scot.nhs.uk/respiratory/swine-influenza/situation-reports/weekly-influenza-sitrep-2009-10-29.pdf
28
Weekly Influenza Situation Report (Including H1N1v) Wednesday 28 October 2009http://www.documents.hps.scot.nhs.uk/respiratory/swine-influenza/situation-reports/weekly-influenza-sitrep-2009-10-29.pdf
Most hospitalisations among 15-24
Relatively flat distribution up to 54
29
30
Males
Age
Fre
qu
en
cy
0 20 40 60 80
02
04
06
0
Females
Age
Fre
qu
en
cy
0 20 40 60 80
02
04
06
0
Easily See
Peak at 0-4 in both males and female
More boys 0-4 in hospital than girls 0-4
Peak 20-24 year old women
31
Report on Review of Clostridium difficile Associated Disease Cases and Mortality in all Acute Hospitals in Scotland from December 2007 ─ May 2008
Health Protection Scotlandhttp://www.documents.hps.scot.nhs.uk/hai/sshaip/publications/cdad/cdad-review-2008-07.pdf
32
Week
Gro
wth
0 10 20 30 40 50
10
50
10
0
Ward 4 CleanW6 No CleanW4 No CleanW6 Clean
Change Over
Total Growth During Study
Measuring the effect of enhanced cleaning in a UK hospital: aprospective cross-over studyStephanie J Dancer, Liza F White, Jim Lamb, E Kirsty Girvan and Chris RobertsonBMC Medicine 2009, 7:28 doi:10.1186/1741-7015-7-28
33
Summary
o Statistical presentation of results must provide scientific evidence to back up claims made in a report
o conclusions must be reliable and based upon data key aspect of statistics is design, analysis and presentation
of results in the presence of VARIABILITY. honest presentation requires the inclusion of information to
assess precision (variability) of results sample sizes, standard deviations, confidence intervals
34
Recommended Text Books
o An introduction to medical statistics – J. Martin Blando Practical statistics for medical research – Douglas G.
Altmano Essential medical statistics – Betty Kirkwood and Jonathan
Sterneo BMJ series of statistical methods (Martin Bland/Douglas
Altman)o http://openwetware.org/wiki/BMJ_Statistics_Notes_serieso http://www-users.york.ac.uk/~mb55/pubs/pbstnote.htm
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