appropriate techniques of statistical analysis
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Appropriate techniques of statistical analysis. Anil C Mathew PhD Professor of Biostatistics & General Secretary ISMS PSG Institute of Medical Sciences and Research Coimbatore 641 004. Types of studies. Case study Case series Cross sectional studies Case control study Cohort study - PowerPoint PPT PresentationTRANSCRIPT
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Appropriate techniques of statistical analysis
Anil C Mathew PhD
Professor of Biostatistics &
General Secretary ISMS
PSG Institute of Medical Sciences and Research
Coimbatore 641 004
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Types of studies
• Case study• Case series• Cross sectional studies• Case control study• Cohort study• Randomized controlled trials• Screening test evaluation
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Data analysis-Case series
Measures of averages• Mean, Median, Mode• Length of stay for 5 patients
1,3,2,4,5
Mean length of stay 3 days
Median length of stay 3 days
Mode length of stay No mode
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Which is the best average
Mean Median Mode
DBP 81 79 76
Height 180 180 180
SAL 7.5 7.6 8.1
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Data analysis-case series
• Frequency distribution
RBC Frequency Relative frequency
5.95-7.95 1 0.029
7.95-9.95 8 0.229
9.95-11.95 14 0.400
11.95-13.95 9 0.257
13.95-15.95 2 0.057
15.95-17.95 1 0.029
Total 35 1.000
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Design of Cohort Study
Time
Direction of inquiry
Population People without the disease
Exposed
Not Exposed
no disease
disease
no disease
disease
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Is obesity associated with adverse pregnancy outcomes? Women with a Body Mass Index > 30 delivering singletons. Ref- University of Udine, Italy,2006
Preterm Birth No preterm birth
%
Obese 16 35T=51
31.4
Normal 46 487T=533
8.6
RR=3.65
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Design of Case Control Study
Disease
No Disease
Not Exposed
Exposed
Not Exposed
Exposed
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Results of a Case Control Study
Lung Cancer
(D+)
No Lung Cancer
(D-)
Totals
Exposed (E+) 80 a 30 b a + b
Non exposed (E-)
20 c 70 d c + d
Totals 100 a + c 100 b + d
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Analysis of Case-control study
Odds ratio = a*d/b*c =80*70/30*20 =9.3
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Data Analysis-Screening Test Evaluation-Whether the plasma levels of (Breast Carcinoma promoting factor) could be used to diagnose breast cancer?
Positive criterion of BCPF >150 units vs. Breast Biopsy (the gold standard)
D+ D-
BCPF Test
T+ 570 150 720
T- 30 850 880
600 1000 1600
TP = 570 FN = 30
FP = 150 TN = 850
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Sensitivity = P (T+/D+)=570/600 = 95%
Specificity = P(T-/D-) = 850/1000 = 85%
False negative rate = 1 – sensitivity
False positive rate = 1 – specificity
Prevalence = P(D+) = 600/1600 = 38%
Positive predictive value = P (D+/T+) = 570/720 = 79%
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Tradeoffs between sensitivity and specificity
When the consequences of missing a case are potentially grave
When a false positive diagnosis may lead to risky treatment
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Data analysis-case series
Measures of variation
• Range• Standard deviation
Group 1 Group 2
29 25
30 30
31 35
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Data analysis- Analytical studies
• Tests of significance
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Case Study 1: Drug A and Drug B
• Aim: Efficacy of two drugs on lowering serum cholesterol levels
• Method: Drug A – 50 Patients
Drug B – 50 Patients
• Result: Average serum cholesterol level is lower in those receiving drug B
than
drug A at the end of 6 months
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What is the Conclusion?
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A) Drug B is superior to Drug A in lowering cholesterol levels :
Possible/Not possible
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B) Drug B is not superior to Drug A, instead the difference may be due to chance:
Possible/Not possible
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C) It is not due to drug, but uncontrolled differences other than treatment between the sample of men receiving drug A and drug B account for the difference:
Possible/Not possible
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D) Drug A may have selectively administrated to patients whose serum cholesterol levels were more refractory to drug therapy:
Possible/Not possible
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Observed difference in a study can be due to
1) Random change
2) Biased comparison
3) Uncontrolled confounding variables
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Solutions: A and B• Test of Significance – p value• P<0.05, means probability that the
difference is due to random chance is less than 5%
• P<0.01, means probability that the difference is due to random chance is less than 1%
• P value will not tell about the magnitude of the difference
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Solutions: C and D
• Random allocation and compare the
baseline characteristics
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Figure 1
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Table 1-Baseline CharacteristicsCharacteristic Vitamin group
(n = 141) Placebo group
(n = 142)
Mean age ± SD, y 28.9 ± 6.4 29.8 ± 5.6
Smokers, n (%) 22 (15.6) 14 (9.9)
Mean body mass index ± SD, kg/m2 25.3 ± 6.0 25.6 ± 5.6
Mean blood pressure ± SD, mm HgSystolicDiastolic
112 ± 1567 ± 11
110 ± 1268 ± 10
Parity, n %)01 2 >2
91 (65)39 (28)
9 (6)2 (1)
87 (61)42 (30)
8 (6)5 (4)
Coexisting disease, n (%)Essential hypertensionLupus/antiphospholipid syndromeDiabetes
10 (7%)4 (3%) 2 (1%)
7 (5%) 1(1%) 3 (2%)
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“t” TestHo: There is no difference in mean birth weight of children from HSE and LSE in the population
CR = t = | X1 - X2 |
SD 1 + 1
n1 n2
SD = (n1-1)SD12 + (n2-1)SD22
n1 + n2- 2
SD = 14*0.272 + 9*0.222 = 0.25
23
t = | 2.91 – 2.26| = 6.36
0.25 1 + 1
15 10
DF = n1 + n2 – 2
CAL > Table REJECT Ho
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GENERAL STEPS IN HYPOTHESIS TESTING
1) State the hypothesis to be tested
2) Select a sample and collect data
3) Calculate the test statistics
4) Evaluate the evidence against the null hypothesis
5) State the conclusion
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Commonly used statistical tests
• T test-compare two mean values• Analysis of variance-Compare more than
two mean values• Chi square test-Compare two proportions• Correlation coefficient-relationship of two
continuous variables
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Data entry formatTreatment Age weight Diabetes Painscore-b Painscore-a Vomiting
1 21 50 1 9 6 0
1 24 53 0 10 9 0
1 25 55 1 9 9 1
1 28 50 0 10 6 1
1 29 60 0 10 5 0
1 20 65 0 10 8 0
0 26 60 0 9 9 0
0 25 90 1 9 9 1
0 24 80 1 9 9 1
0 28 89 0 10 8 1
0 22 86 1 10 9 1
0 22 45 0 10 9 0
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Example t test
Body temperature c
Simple febrile seizureN = 25
Febrile without seizureN =25
P value
Mean 39.01 38.64 P<0.001
SD 0.56 0.45
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Example-Analysis of variance
• Serum zinc level in simple febrile patients based on duration of seizure occurred
Duration min
n Mean SD P value
< 5 3 10.27 0.25 P <0.001
5 to 10 18 9.02 0.81
>10 4 6.90 0.98
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Example Chi-square test
• Characteristics of patients in the two groups
Duration of fever (hour)
Simple febrile seizure
Febrile without seizure
P value
< 24 16 6 P<0.05
More than 24 9 19
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Example Correlation
• We found a negative correlation between serum zinc level and simple febrile seizure event r = - 0.86 p <0.001
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Type 1 and Type 2 Errors
Ho True Ho False / H1 True
Accept Ho
Reject Ho
Power = 1- β
Correct decision Type 2 error β = P (Type 2 error)
Type 1 errorα = P (Type 1 error)
Correct decision
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Multivariate problem
• Main outcome
• Continuous variable-Linear regression• Dichotomous variable-Logistic regression
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Bradford Hills Questions
• Introduction- Why did you start?• Methods-What did you do?• Results- What did you find?• Discussion- What does it mean?
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How to begin writing?
• Data Tables Methods, Results Introduction , Discussion Abstract
Title, Key words, References
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Thank you