Statistics for AKT
Feb 24, 2016
Statistics for AKT
Mean: true average Median: middle number once ranked Mode: most repetitive Range : difference between largest and smallest.
Discriptive Statistics
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.
Normal Distribution: Mean=Median=Mode Positive Skewed: Mean>Median>Mode Negative Skewed: Mean<Median<Mode
Skewed Data
Test Result Disease Present Disease Absent
Positive TP FP
Negative FN TN
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
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
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
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
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
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
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
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
Questions
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.
Absolute risk: Risk of developing a condition
Relative risk: Risk of developing a condition as compared to another group
EVENTS IN CONTROL GROUP – EVENTS IN TREATMENTGROUP 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%
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
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
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
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
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
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.
The null hypothesis is that there are no differences between two groups.
The alternative hypothesis is that there is a difference.
Null Hypothesis
Type 1 error:- Wrongly rejecting the null hypothesis- False +ve
Type II error:- Wrongly accepting the null hypothesis- False -ve
Study Error
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
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
Statistical Tests
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
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
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
Compares proportions
Chi squared ± Yates correlation (2x2)
Fisher’s exact test- for larger samples
Binominal Data (non-parametric)
The standard deviation (SD) represents the average difference each observation in a sample lies from the sample mean
SD = square root (variance)
Standard Deviation
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.
Normal Distribution
Thank you for all your patience!!!!