1. HaDPop Measuring Disease and Exposure in Populations (MD) &
Introduction to Medical Statistics (MS)

2. Overview Prevalence (MD) Incidence (MD) Confidence Intervals (MS)
Standard Error
Error Factor
Null Hypothesis (MS)
P-values (MS)
Ratios (MD)
Confounders (MD)
SMR (MD)

3. No. of existing cases / No. of persons
Prevalence
No. of existing cases / No. of persons
in the population
A measure of how much of a disease there is (both new and old cases)
Period and point prevalence
It gives a proportion of the population
Useful for studying long term conditions and service provision

4. Prevalence Example
In a hypothetical office (total 1000 people), 12 were off work with the flu today.
Point Prevalence (today): 12/1000 = 1.2%
Over the past year, 150 took off work due to flu.
Period Prevalence (past year): 150/1000 = 15%

5. Incidence
No. of new cases / In a defined population in a specified time interval (person-years)
A measure of the frequency of new cases (it is a rate)
Useful for tracking infectious diseases and exploring the cause of disease (aetiology)
Person years
Person years means per person per year

6. Incidence Example
Over the last 5 years, 4000 people have been diagnosed with lung cancer (total population: 200,000)
4000/(200,000 x 5) = or 4 per 1000 per year

7. Types of Incidence Time (t)
Numerator
Disease free - 100
Denominator
New Cases
= 10
Non Cases
= 90
Time (t)
Incidence Rate – different length of follow up
Cumulative Incidence (or risk) – same length of follow up
Odds of Disease – ratio between having the disease or not
Incidence = No. of new cases = 10 = n per person per year
Person-yrs of follow-up pyr
Cumulative = No. new cases = 10 = = 10%
Incidence (risk) No. disease-free persons at start (times years studied)
Odds of disease = No. new cases = = = 11%
No. persons still at risk

8. Medical Statistics
Statistics are used to estimate information about the general population (its not practical to measure everyone!)
This estimate is the known as the observed value and this varies from the true value due to sampling variation
The accuracy of an estimate is calculated using confidence intervals
Sampling variation – due to the fact that you are taking a sample

9. Confidence Intervals (CI)
The confidence interval is a range of values around the observed value within which the true value lies
The most common range used is the 95%CI, which means 95 times out of 100 the real value will be within that range
The way the are calculated is different depending on the statistics you are using
Proportions (i.e. prevalence) use standard error (SE)
Ratios/rates (i.e. incidence) use error factors (EF)
95% CI - has a constant of 1.96
Larger constant means higher accuracy but a larger range (all to do with the normal distribution), after 95% a small increase in accuracy leads to a much larger increase in the range
Have to use a different formula for prevalence and incidence because “apparently” rates and ratios can’t be negative!

10. Standard Error (Prevalence)
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒 𝑜𝑓 𝑝𝑟𝑒𝑣𝑎𝑙𝑒𝑛𝑐𝑒 (𝑝) = 𝑁𝑜. 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠 𝑘 𝑁𝑜. 𝑖𝑛 𝑆𝑎𝑚𝑝𝑙𝑒 𝑛
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒 𝑆𝐸 = 𝑝 (1− 𝑝 )/𝑛
𝟗𝟓% 𝑪𝑰 =( 𝒑 + 𝟏.𝟗𝟔×𝑺𝑬 , 𝒑 − 𝟏.𝟗𝟔×𝑺𝑬 )
Note Accuracy Depends on Sample Size
For prevalence you add or subtract the 1.96xSE from the observed value
Note accuracy is dependent on sample size
Note 1.96 is a constant used for working out 95% CI’s
It changes if you want different CI’s

11. Standard Error Example
Prevalence of diabetes, sample of 1000 subjects (n = 1000), 243 found to have diabetes (k = 243)
Prevalence = k/n, so 𝑃 = 243/1000 = 24.3%
Standard error (SE) = 𝑝 (1− 𝑝 )/𝑛 , so − = × = 0.013

12. Standard Error Example Cont.
SE = 0.013
Original prevalence estimate ( 𝒑 ): 24.3% population had diabetes
𝟗𝟓% 𝑪𝑰 =( 𝒑 + 𝟏.𝟗𝟔×𝑺𝑬 , 𝒑 − 𝟏.𝟗𝟔×𝑺𝑬 )
= (0.243 – 1.96(0.013), (0.013)
= (0.218, 0.268) = (21.8%, 26.8%)

13. Difference between two prevalences
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑃 1 − 𝑃 2
𝑆𝐸 𝑃 1 − 𝑃 2 = 𝑃 1 (1− 𝑃 1 ) 𝑛 𝑃 2 (1− 𝑃 2 ) 𝑛 2
95% 𝐶𝐼=𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒 𝑜𝑓 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒± 1.96×𝑆𝐸

14. Error Factor (Incidence)
𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝑟𝑎𝑡𝑒 ( 𝑟 )= 𝑁𝑒𝑤 𝑐𝑎𝑠𝑒𝑠 (𝑑) 𝑁𝑜. 𝑜𝑓 𝑃𝑒𝑟𝑠𝑜𝑛 𝑌𝑒𝑎𝑟𝑠 (𝑌)
𝐸𝑟𝑟𝑜𝑟 𝐹𝑎𝑐𝑡𝑜𝑟 (𝐸𝐹)=exp 1.96× 1/𝑑
𝟗𝟓%𝑪𝑰= 𝒓 ÷𝑬𝑭, 𝒓 ×𝑬𝑭
Note Accuracy Depends on No. cases
For incidence you multiply or divide the observed value by the EF
Note accuracy is dependent on number of cases

15. Error Factor Example
24 new cases of diabetes per 1000 population per year (i.e. d = 24)
Error factor = exp(1.96 x 1/𝑑 )
= exp(1.96 x 1/24 ) = 1.5
𝟗𝟓%𝑪𝑰= 𝒓 ÷𝑬𝑭, 𝒓 ×𝑬𝑭 = (0.0024/1.5, x 1.5)
= (0.0016, )
= (16, 36) cases per 1000 p-y
R = 0.024
I just converted this figure to 1000’s before putting it into the equation rather than converting it at the end

16. Key Points for CI’s Proportions (prevalence)
95%CI = “Estimate ± (‘constant’ x SE)”
Rates/ratios (incidence and SMR’s)
95%CI= (Estimate/EF , Estimate x EF)
How to calculate the Standard error or Error factor will be given in the exam

17. Null Hypothesis (H0)
This is used to make a comparison between different groups to see if there is a statistical difference between them
E.g. differences between different drugs
The null hypothesis is when there is no statistical difference between the two groups
Differences – null hypothesis is 0
Ratios – null hypothesis is 1
SMR – null hypothesis is 100

18. Null Hypothesis
If the 95% CI includes the null hypothesis then the data agrees with the null hypothesis can’t be rejected and there is no statistical difference between the two groups
You can never accept the null hypothesis!

19. P-values
p-values state how likely the results in the study would have occurred by chance if the null hypothesis was true
P-values <0.05 (5%) are good! They mean that the results are statistically significant and that the null hypothesis can be rejected
If the 95%CI overlap with the null hypothesis then p>0.05 and the results are not statistically significant
I personally wouldn’t worry about

20. Relative measures of exposure (Relative risk) see slide 7
𝑰𝒏𝒄𝒊𝒅𝒆𝒏𝒄𝒆 𝑹𝒂𝒕𝒆 𝑹𝒂𝒕𝒊𝒐 𝑰𝑹𝑹 = 𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝑟𝑎𝑡𝑒 𝑖𝑛 𝑡ℎ𝑒 𝐸𝑥𝑝𝑜𝑠𝑒𝑑 𝑔𝑟𝑜𝑢𝑝 𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝑟𝑎𝑡𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑈𝑛𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑔𝑟𝑜𝑢𝑝 = 𝐶/𝐸 𝐷/𝐹
𝑹𝒊𝒔𝒌 𝑹𝒂𝒕𝒊𝒐= 𝑅𝑖𝑠𝑘 𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝑖𝑛 𝑡ℎ𝑒 𝐸𝑥𝑝𝑜𝑠𝑒𝑑 𝐺𝑟𝑜𝑢𝑝 𝑅𝑖𝑠𝑘 𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑈𝑛𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝐺𝑟𝑜𝑢𝑝 = 𝐶/𝐴 𝐷/𝐵
𝑶𝒅𝒅𝒔 𝒓𝒂𝒕𝒊𝒐= 𝑂𝑑𝑑𝑠 𝑜𝑓 𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑖𝑛 𝑡ℎ𝑒 𝐸𝑥𝑝𝑜𝑠𝑒𝑑 𝐺𝑟𝑜𝑢𝑝 𝑂𝑑𝑑𝑠 𝑜𝑓 𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑈𝑛𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝐺𝑟𝑜𝑢𝑝 = 𝐶/(𝐴−𝐶) 𝐷/(𝐵−𝐷)
Note – an exposure can be to a treatment, therefore it can be used to find out which treatments are best
Exposed
Unexposed
No. at Risk at Start A B
New Cases C D
P-Years at Risk E F
Used to compare different groups of people (i.e. by exposures, either to “harmful things” or treatments)
All these ratios are similar with low incidence however they vary with higher incidence. The null hypothesis for ratios is 1.
If the relative risk ratio is:
= 1 then there is no association between the exposure and the disease
> 1 then there is a positive association (increased risk with the exposure)
< 1 then there is a negative association (decreased risk with the exposure)

21. Incidence Rate Ratio Example
In one group of 1000 pizza eaters that were followed for 1.5 years (‘exposed’) it was found that 33 new cases (d1) of obesity developed
In another group of 1000 non-pizza eaters that were followed for 2 years (unexposed) it was found that 27 new cases (d2) of obesity developed

22. Incidence Rate Ratio Example Cont.
In the exposed group: 33/(1000 x 1.5) = (or 22 per 1000 pop. per year)
So in the unexposed group: 27/(1000 x 2) = (or 14 per 1000 pop. per year)
𝑰𝑹𝑹= 𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝑟𝑎𝑡𝑒 𝑖𝑛 𝑡ℎ𝑒 𝐸𝑥𝑝𝑜𝑠𝑒𝑑 𝑔𝑟𝑜𝑢𝑝 𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝑟𝑎𝑡𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑈𝑛𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑔𝑟𝑜𝑢𝑝 = =1.57
Error factor = exp(1.96 x 1 𝑑1 + 1 𝑑2 )
= exp(1.96 x ) = 1.66
It is a ratio therefore can’t be negative therefore need to use error factors

23. Incidence Rate Ratio Example Cont.
Estimate (IRR) = 1.57
EF = 1.66
95% CI = (est / EF, est x EF)
= (1.57/1.66, 1.57x1.66) = (0.95, 2.61)
IRR = 1.57 (0.95, 2.61)
Interpreting data:
5 points can be made (think in these steps, so less likely to miss a point):-
Comment on results and whether indicates damaging/protective/no effect (i.e. its relation to the null hypothesis = 1)
State “we are 95% confident that the true value lies between…and…”
State whether C.I. includes 1 or not and subsequently whether p<0.05
Reject Null hypothesis or not?
Association between exposure and disease?

24. Incidence Rate Ratio Example Cont. Interpretation of results
IRR of 1.57 indicates that the observed value indicates a damaging effect of eating pizza on becoming obese on (i.e. >1)
We are 95% confident that the true IRR lies between 0.95 and 2.61.
The 95% confidence interval includes the null hypothesis (IRR=1) and so the result is not statistically significant at the p<0.05 level.
Null hypothesis cannot be rejected.
The results do not indicate an association between eating pizza and obesity.

25. Absolute Measures of Risk (attributable risk)
Risk difference = risk exposed - risk non-exposed
Attributable Risk = IR exposed - IR non-exposed = events saved per 1,000
Attributable Risk (%) = Attributable Risk / IR exposed
The additional risk, above the background risk, that can be attributed to exposure to a risk factor. This gives differences rather than risk ratios.
The null hypothesis for differences is 0
They are used to indicate the proportion of disease that can be prevented if a specific exposure is removed

26. Examples of attributable risk?
People with lung cancer can be smokers and non smokers
Thus the attributable risk of smoking is the difference between the incidence of smokers and non smokers
Ie the attributable risk is the risk above background risk (the non smokers with lung cancer have suffered from the background risk)

27. Confounders
A Confounder is a factor that is associated with the exposure under study and independently affects disease risk

28. Standardised mortality ratio (SMR)
Compares the observed number of deaths in the population under study with the expected number of deaths based on the standard population
It accounts for common confounders such as age and gender
𝑆𝑀𝑅= 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑛𝑜. 𝑜𝑓 𝑑𝑒𝑎𝑡ℎ𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑛𝑜. 𝑜𝑓 𝑑𝑒𝑎𝑡ℎ𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 ×100
Uses error factors for 95% CI

29. Thanks for listening
Any questions please Facebook me!!!