1. Basic statistics
11/09/13

2. Topics to cover
Averages: Mean, Median, Mode, Range, Confidence intervals, Standard deviation
Incidence and prevalence
Screening tests – positive and negative predictive values, sensitivity and specificity

3. Central Tendencies and Spread of Data
Basic statistics
Central Tendencies and
Spread of Data

4. Measures of central tendency
15 patients with epilepsy were recruited into a trial. They were asked to record the number of seizures they had in a six month period. The results are presented below.

5. Measures of central tendency
Calculate the:
Mean
Median
Mode
Range

6. Measures of central tendency
Calculate the:
Mean = 4
Median = 2
Mode = 1
Range = 12

7. Measures of central tendency
Mean: sum of the observations divided by the number of observations
( ) / 15 = 4
Median: the middle value when the total observations are arranged in order of increasing value
Mode: the most commonly occurring value
Range: the difference between the highest and lowest values in a set of data
13 – 1 = 12

8. Standard deviation A measure of the spread of the data
Can be used to calculate confidence intervals

9. Normal Distribution

10. Confidence intervals Used to assess statistical significance
Provides a measure of the extent to which a sample estimate is likely to differ from the true population value
Indicates with a standard level of certainty (usually 95%), the range of values within which the true population mean is likely to lie e.g. 25±5

11. Confidence intervals contd.
For a given level of confidence:
a narrow interval indicates that the sample estimate has good (high) precision
a wide interval indicates that the sample estimate has poor (low) precision
Confidence intervals become narrower as:
the sample size increases
the variability of the data decreases
the degree of confidence required for the population mean decreases e.g. 90%, 95%, 99%

12. Incidence and Prevalence
Basic statistics
Incidence and Prevalence

13. Incidence
In the last year there have been 24 new cases of colorectal carcinoma in your practice (list size 10276). What is the incidence of colorectal carcinoma?
Incidence = 24 / =
Incidence per 1000 = 2.30 per 1000

14. Incidence
Number of new cases diagnosed in a population per unit of time
Incidence rate = (number of new cases diagnosed in a given period of time / population size) x 100, 000 (or 1000 etc.)

15. Prevalence
2593 of the 8725 patients registered with your practice have a BMI of 30 or more. What is the prevalence of obesity?
Prevalence = (2593 / 8725) x 100 = 29.7%
Prevalence = (2593 / 8725) x 1000 = per 1000

16. Prevalence
Total number of cases per population at a particular point in time (e.g. number per 100,000 population)
Prevalence rate = (number of cases in population / total size of population) x 100,000 (or 1000 etc.)
Prevalence = incidence x duration of condition

17. Relationship between incidence and prevalence
Prevalence = incidence x duration of condition
Increase incidence → increase prevalence
Cure more patients → lower prevalence
More patient die → lower prevalence
Enhance survival → increase prevalence

18. Screening Test Statistics
Basic statistics
Screening Test Statistics

19. Screening tests
Cervical cancer present
Cervical cancer absent
New test positive
100
True positives (TP) 50
False positives
(FP)
New test negative 10
False negatives
(FN)
840
True negatives
(TN)
A blood test to help diagnose cervical cancer has been developed. A study is done on 1000 patients comparing this test to the standard technique

20. Positive and negative predictive values
Positive predictive value (PPV): proportion of people who test positive who actually have the disease
PPV = TP / (TP + FP)
Negative predictive value (NPV): proportion of people told they don’t have the disease that really don’t have it
NPV = TN / (TN + FN)
Give an indication of the reliability of a positive or negative test result

21. PPV and NPV 100 50 10 840 PPV = 100 / (100+50) NPV = 840 / (840+10)
Cervical cancer present
Cervical cancer absent
New test positive
100 50
New test negative 10
840
PPV = 100 / (100+50)
= 0.67 = 67%
NPV = 840 / (840+10)
= 0.99 = 99%
The higher the PPV, the more likely it is that a patient with a positive test result does have the disease
The higher the NPV, the more likely it is that someone who has tested negative really doesn’t have the disease

22. Sensitivity and specificity
Sensitivity: the proportion of people with a disease who are detected by the test (proportion of positives found)
Sensitivity = TP / (TP + FN)
Specificity: the proportion of people who don’t have a disease who test negative (proportion of negatives found)
Specificity = TN / (TN + FP)
Indicate the proportion of the population with/without the disease which will be detected by the test

23. Sensitivity and specificity
Cervical cancer present
Cervical cancer absent
New test positive
100 50
New test negative 10
840
Sensitivity = 100 / (100+10)
= 0.91 = 91%
Specificity = 840 / (840+50)
= 0.94 = 94%
High sensitivity = few missed diagnoses
High specificity = few false positives