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Statistics for AKT
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Mean: true average Median: middle number once ranked Mode: most repetitive Range : difference between largest and smallest.
Discriptive Statistics
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Find out the Mean, Median, Mode and Range for following. 8, 9, 9, 10, 11, 11, 11, 11, 12, 13
The mean is the usual average: (8 + 9 + 9 + 10 + 11 + 11 + 11 + 11 + 12 + 13) ÷ 10 = 105 ÷ 10 = 10.5
The median is the middle value. In a list of ten values, that will be the (10 + 1) ÷ 2 = 5.5th value which will be 11.
The mode is the number repeated most often. 11
The largest value is 13 and the smallest is 8, so the range is 13 – 8 = 5.
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Normal Distribution: Mean=Median=Mode Positive Skewed: Mean>Median>Mode Negative Skewed: Mean<Median<Mode
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Skewed Data
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Test Result Disease Present Disease Absent
Positive TP FP
Negative FN TN
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Sensitivity: How good is the test at detecting those with the condition
TRUE POSITIVESACTUAL NUMBER OF CASES
Specificity: How good is the test at excluding those without the condition
TRUE NEGATIVESACTUAL NUMBER OF PEOPLE WITHOUT CONDITION
Sensitivity and Specificity
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Positive Predictive Value: How likely is a person who tests +ve to actually have the condition
TRUE POSITIVESNUMBER OF PEOPLE TESTING POSITIVE
Negative Predictive Value: How likely is a person who tests –ve to not have the condition
TRUE NEGATIVESNUMBER OF PEOPLE TESTING NEGATIVE
Predictive Values
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Incorporates both sensitivity and specificity
Quantifies the increased odds of having the disease if you get a positive test result, or not having the disease if you get a negative test result.
Positive Likelihood ratio:Sensitivity
(1 – Specificity)
Negative Likelihood ratio:(1-Sensitivity)
Specificity
Likelihood Ratios
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Odds are a ratio of the number of people who incur a
particular outcome to the number of people who do not incur the outcome.
NUMBER OF EVENTS NUMBER OF NON-EVENTS
Odds: what are the chances
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Odds ratio:
The odds ratio may be defined as the ratio of the odds of a particular outcome with experimental treatment and that of control.
Odds ratios are the usual reported measure in case-controlstudies.
It approximates to relative risk if the outcome of interest israre.
ODDS IN TREATMENT GROUPODDS IN CONTROL GROUP
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For example, if we look at a trial comparing the use of paracetamol for dysmenorrhoea compared to placebo we may get the following results
Total no of Patients
Pain relief achieved
Paracetamol 60 40
Placebo 90 30
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The odds of achieving significant pain relief with paracetamol = 40 / 20 = 2
The odds of achieving significant pain relief with placebo = 30 / 60 = 0.5
Therefore the odds ratio = 2 / 0.5 = 4
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Prevalence: rate of a disorder in a specified population
Incidence: Number of new cases of a disorder developing over a given time (normally 1 year)
Incidence and Prevalence
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Questions
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Relative risk (RR) is the ratio of risk in the experimental group (experimental event rate, EER) to risk in the control group (control event rate, CER).
Relative risk is a measure of how much a particular risk factor (say cigarette smoking) influences the risk of a specified outcome such as lung cancer, relative to the risk in the population as a whole.
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Absolute risk: Risk of developing a condition
Relative risk: Risk of developing a condition as compared to another groupEVENTS IN CONTROL GROUP – EVENTS IN TREATMENT
GROUP EVENTS IN CONTROL GROUP
X 100- My lifetime risk of dying in a car accident is 5% - If I always wear a seatbelt, my risk is 2.5%
- The absolute risk reduction is 2.5%- The relative risk reduction is 50%
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For example, if we look at a trial comparing the use of paracetamol for dysmenorrhoea compared to placebo we may get the following results
Total no of Patients
Pain relief achieved
Paracetamol 100 60
Placebo 80 20
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Experimental event rate, EER = 60 / 100 = 0.6
Control event rate, CER = 20 / 80 = 0.25
Therefore the relative risk = EER / CER = 0.6 / 0.25 = 2.4
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Relative risk reduction (RRR) or relative risk increase (RRI) is calculated by dividing the absolute risk change by the control event rate Using the above data,
RRI = (EER - CER) / CER (0.6 - 0.25) / 0.25 = 1.4 = 140%
Relative Risk Reduction
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Numbers needed to treat (NNT) is a measure that indicates how many patients would require an intervention to reduce the expected number of outcomes by one
It is calculated by 1/(Absolute risk reduction)
Absolute risk reduction = (Experimental event rate) - (Control event rate)
Numbers needed to treat and absolute risk reduction
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A study looks at the benefits of adding a new anti platelet drug to aspirin following a myocardial infarction. The following results are obtained:
Percentage of patients having further MI within 3 months Aspirin 4% Aspirin + new drug 3%
What is the number needed to treat to prevent one patient having a further myocardial infarction within 3 months?
NNT = 1 / (control event rate - experimental event rate) 1 / (0.04-0.03) 1 / (0.01) = 100
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Remember that risk and odds are different.
If 20 patients die out of every 100 who have a myocardial infarction then the risk of dying is 20 / 100 = 0.2 whereas the odds are 20 / 80 = 0.25.
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The null hypothesis is that there are no differences between two groups.
The alternative hypothesis is that there is a difference.
Null Hypothesis
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Type 1 error:- Wrongly rejecting the null hypothesis- False +ve
Type II error:- Wrongly accepting the null hypothesis- False -ve
Study Error
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Probability of establishing the expected difference between the treatments as being statistically significant- Power = 1 – Type II error (rate of false –ve’s)
Adequate power usually set at 0.8 / 80%
Is increased with- increased sample size- increased difference between treatments
Power of the study
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A result is called statistically significant if it is unlikely to have occurred by chance
P values
- Usually taken as <0.05
- Study finding has a 95% chance of being true
- Probability of result happening by chance is 5%
Significance
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Statistical Tests
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1. Parametric / Non-parametricParametric if: - Normal distribution
- Data can be measured
2. Paired / Un-pairedPaired if data from a single subject group (eg before and after intervention)
3. Binomial – ie only 2 possible outcomes
Types of Tests
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Student’s T-test- compares means- paired / unpaired
Analysis of variance (ANOVA)- use to compare more than 2 groups
Pearsons correlation coefficient- Linear correlation between 2 variables
Parametric Tests
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Mann Whitney- unpaired data
Kruskal-Wallis analysis of ranks / Median test
Wilcoxon matched pairs- paired data
Friedman's two-way analysis of variance / Cochran Q
Spearman or Kendall correlation- linear correlation between 2 variables
Non Parametric Data
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Compares proportions
Chi squared ± Yates correlation (2x2)
Fisher’s exact test- for larger samples
Binominal Data (non-parametric)
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The standard deviation (SD) represents the average difference each observation in a sample lies from the sample mean
SD = square root (variance)
Standard Deviation
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In statistics the 68-95-99.7 rule, or three-sigma rule, or empirical rule, states that for a normal distribution nearly all values lie within 3 standard deviations of the mean
About 68.27% of the values lie within 1 standard deviation of the mean.
Similarly, about 95.45% of the values lie within 2 standard deviations of the mean.
Nearly all (99.73%) of the values lie within 3 standard deviations of the mean.
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Normal Distribution
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Thank you for all your patience!!!!