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Medical Statistics – Medical Statistics – The Basics The Basics Dr Vivek Baliga BDr Vivek Baliga B
Consultant Internal Medicine, Consultant Internal Medicine, Baliga Diagnostics Pvt. LtdBaliga Diagnostics Pvt. Ltd
What is Statistics?• Science of collecting, organising
and interpreting numerical facts • Science of learning from data :
– Design the data collection– Prepare the data for analysis– Analyse the data– Communicate the results of the data
Topics to cover• Types of data• Types of studies• Displaying data
Types of data• Quantitative
(How much?)– Measured : BP,
Height– Counted : Attacks
of asthma a week
• Categorical (What type?)– Nominal : Sex
(m/f), hair colour– Ordinal : Grade of
breast Ca– Binary :
Male/Female, Dead/alive
Measures of Effect• Describe the measure that is used
to compare treatment effects in 2 or more comparison groups
Measure of Effect• Quantitative Variables
– Mean– Median
• Categorical Variables– Risks– Odds Ratio
• Mean 1+2+3+6+7+12+18 = 49
Mean = 49/7 =7• Median (Odd number N)
1+2+3+6+7+12+18 Median =6
• Median (Even number N) 2+3+6+7+12+18
Median = 6+7/2 = 6.5
Normal Distribution Curve
Standard Deviation
2+8+10+13+22 = 55Mean = 55/5 =11
Variance = (2-11)2+(8-11)2+(10-11)2+(13-11)2+(22-11)2
N-1 = 216/4 = 54
Standard Deviation = √54 = 7.2
Standard deviation• Estimate of variability of
observations• Larger sample provides a better
and more precise estimate of the standard deviation.
Measures of Effect• Absolute risk : A/A+C• Relative Risk :
A/A+C÷B/B+D• Absolute risk
reduction : A/A+C-B/B+D
• Number needed to treat : 1/ARR
D+ D-
Ex+ A B
Ex- C D
A+C B+D
Types of studies• Randomised control trials• Cohort studies• Case control studies• Cross sectional studies• Case reports
Randomised Control Trials
• Gold standard in medical research• Best to study cause vs effect• Various components
– Randomisation– Blinding– Controlled
Randomised Control TrialsSelect a population
Select a Sample
Make necessary exclusions
Randomise
Experimental group Control group
Randomised Control Trials
• Randomisation– Each patient has an equal chance of
each treatment option– Fair unbiased comparison of
treatment
Randomised Control Trials
• Blinding – Single blind : patient cannot predict
which treatment they get– Double blind : neither patient nor
investigator knows– Triple blind : Neither pt, investigator
or person administering treatment (eg pharmacist) knows
Randomised Control Trials
• Controlled trial– Placebo controlled : Simvastatin vs
placebo– Active control : Simvastatin vs
Pravastatin– Active – placebo –control :
Simvastatin vs pravastatin vs placebo
Randomised Control Trials
• Advantages– Prospective design– Rigorous
evaluation of a single variable
– Eradicates bias– Uses null
hypothesis
• Disadvantages– Expensive– Time consuming
Cohort studies• Cohort is a group of people who share a
common characteristic or experience within a defined time period
• Eg : People born in 1980= birth cohort• Cohort studies are done to obtain
additional evidence that there is an association between a suspected cause and disease.
Cohort studies• Prospective
– Follow up in years– Can collect confounding factors– Expensive, time consuming– E.g.: Framingham heart study
• Retrospective– Incomplete information– Confounding factors may not be collected– Quick, cheap– E.g.: angiosarcoma in relation to poly-vinyl chloride
Cohort studies- Elements
• Selection of subjects– General population– Special groups eg: Dolls study of
smoking and lung cancer in British doctors in 1951
– Exposure groups : eg radiologists and X-rays
Cohort studies- Elements
• Obtaining data– Interviews/questionnaires – dolls study– Review of records– Medical examination and special tests– Environmental surveys – exposure etc
Cohort studies- Elements
• Selection of comparison groups– Internal – within the cohort– External – eg radiologists vs
ophthalmologists– General population
Cohort studies- Elements
• Follow up– Periodic examination - best method– Questionnaires– Review of records periodically
Cohort studies- Elements
• Analysis– Incidence rates– Estimation of risk
• Relative risk• Attributable risk
Cohort studies- Elements
• Incidence rates– Exposed 70/7000 =
10 per 1000– Non Exposed 3/3000
= 1 per 1000• Relative risk =10/1 = 10• Attributable risk =
[(10-1)/10]x100 = 90%
Cigarette smoking
Ca +
Ca - Total
Yes 70 (a) 6930 (b)
7000 (a+b)
No 3(c) 2997 (d)
3000 (c+d)
Cohort studies- Risks• Relative risk
– Incidence among exposed Incidence among non exposed– RR = 1 means no association– RR > 1 implies ‘positive’ association– Smokers are 10 times at risk of lung Ca that
non smokers.
Cohort studies- Risks• Attributable risks
– Incidence among exposed-non exposed x100Incidence among exposed
– Tells us to what extent the disease under study can be attributed to the exposure.
Cohort studies• Strengths
– Valuable if exposure is rare
– Examine multiple effects of an exposure
– Can measure incidence of a disease
• Limitations– Cannot evaluate
rare diseases– Expensive and
time consuming if prospective
– Several losses to follow up can effect validity
Case Control Study• Retrospective study• Both exposure and outcome have
occurred before the start of the study
• Uses a ‘control’ or comparison group
Case Control Study• Selection of cases and controls• Matching• Measurement of exposure• Analysis and interpretation
Case Control Study- Analysis
• Exposure rates • Relative risk• Odds ratio
Case Control Study• Exposure rates
– Cases a/(a+c) =94.2%– Controls b/(b+d) = 67%
• Relative risk = a/a+c ÷b/b+d
• Odds ratio = ad/bc = 8.1– Smokers of < 5/day have a
risk of developing lung cancer 8.1 times that of non-smokers.
Cases (with lung Ca)
Controls (without Lung Ca)
Smokers (<5/day)
33 (a) 55 (b)
Non Smokers
2(c) 27(d)
Total 35 (a+c)
82 (b+d)
Bias in Case Control Study
• Confounding factors – alcoholism and oesophageal cancer; smoking is a confounding factor.
• Recall bias• Selection bias• Interviewers bias
Cross sectional studies• ‘Prevalence study’• Based on a single examination of a
cross section of population at one point in time.
Meta-analysis• Statistical analysis of the results
from independent studies, which generally aims to produce a single estimate of treatment effect.
Displaying Data• Bar Charts• Histogram• Line diagrams• Pie charts• Scatter plots• Forest plots
THANK YOU!