HaDPopMeasuring Disease and Exposure in Populations (MD)

&Introduction to Medical Statistics (MS)

Overview

• Prevalence (MD)• Incidence (MD)• Confidence Intervals (MS)

• Standard Error• Error Factor

• Null Hypothesis (MS)• P-values (MS)• Ratios (MD)• Confounders (MD)• SMR (MD)

Prevalence

No. of existing cases / No. of personsin 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

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%

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

Incidence Example

• Over the last 5 years, 4000 people have been diagnosed with lung cancer (total population: 200,000)– 4000/(200,000 x 5) = 0.004 or 4 per 1000 per year

Types of Incidence

• 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

Numerator

Disease free - 100

Denominator

New Cases

= 10

Non Cases

= 90

Time (t)

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

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)

Standard Error (Prevalence)

• Note Accuracy Depends on Sample Size

Note 1.96 is a constant used for working out 95% CI’sIt changes if you want different CI’s

Standard Error Example

• Prevalence of diabetes, sample of 1000 subjects (n = 1000), 243 found to have diabetes (k = 243)

• Prevalence = k/n, so = 243/1000 = 24.3%• Standard error (SE) , so = = 0.013

Standard Error Example Cont.

• SE = 0.013

• Original prevalence estimate (): 24.3% population had diabetes

– = (0.243 – 1.96(0.013), 0.243 + 1.96(0.013)– = (0.218, 0.268) = (21.8%, 26.8%)

Difference between two prevalences

Error Factor (Incidence)

• Note Accuracy Depends on No. cases

Error Factor Example

• 24 new cases of diabetes per 1000 population per year (i.e. d = 24)

• Error factor = exp(1.96 x )– = exp(1.96 x ) = 1.5

• = (0.0024/1.5, 0.0024 x 1.5)– = (0.0016, 0.0036) – = (16, 36) cases per 1000 p-y

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

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

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!

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

Relative measures of exposure(Relative risk) see slide 7

• 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

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

Incidence Rate Ratio Example Cont.

• In the exposed group: 33/(1000 x 1.5) = 0.022 (or 22 per 1000 pop. per year)

• So in the unexposed group: 27/(1000 x 2) = 0.014 (or 14 per 1000 pop. per year)

• Error factor = exp(1.96 x )• = exp(1.96 x ) = 1.66

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)

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.

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

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)

Confounders

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

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

• Uses error factors for 95% CI

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