Prevalence, Incidence and Confidence Intervals PDF

Prevalence, Incidence and Confidence Intervals Saran Shantikumar Registrar and Clinical Lecturer, Public Health [email protected] Learning Outcomes 1. Define and calculate prevalence and incidence 2. Accept that the result of an experiment is unlikely to be the (exact) truth 3...

Prevalence, Incidence and Confidence Intervals Saran Shantikumar Registrar and Clinical Lecturer, Public Health [email protected] Learning Outcomes 1. Define and calculate prevalence and incidence 2. Accept that the result of an experiment is unlikely to be the (exact) truth 3. Be able to calculate and interpret confidence intervals (for proportions) Prevalence Latin praevalere = to be established Prevalence → a measure of how common a disease is How prevalent is freshers’ flu amongst 1st year students? Can be expressed as: 1. Percentage 1% of 1st year students have freshers’ flu 2. Number per n people 1 in 100 1st year students have freshers’ flu 10 per 1000 1st year students have freshers’ flu Types of Prevalence Point prevalence → the proportion of individuals with the condition at a specified point in time Currently, 1% of students have the flu At any given time, 1% of students have the flu Period prevalence Lifetime prevalence Types of Prevalence Point prevalence → the proportion of individuals with the condition at a specified point in time Currently, 1% of students have the flu At any given time, 1% of students have the flu Period prevalence → the proportion of individuals with the condition at any time during a specified time interval 3% of students suffer with the flu each month Lifetime prevalence Types of Prevalence Point prevalence → the proportion of individuals with the condition at a specified point in time Currently, 1% of students have the flu At any given time, 1% of students have the flu Period prevalence → the proportion of individuals with the condition at any time during a specified time interval 3% of students suffer with the flu each month Lifetime prevalence → the proportion of individuals with the condition at any point in their lives 70% of people born today will suffer with the flu during their lifetime Types of Prevalence Point prevalence * → the proportion of individuals with the condition at a specified point in time Currently, 1% of students have the flu * If you just see the word At any given time, 1% of students have the flu “prevalence” without qualification, Period prevalence it usually → the refers toproportion of individuals with the “point prevalence” condition at any time during a specified time interval 3% of students suffer with the flu each month Lifetime prevalence → the proportion of individuals with the condition at any point in their lives 70% of people born today will suffer with the flu during their lifetime Types Prevalence Disease episode An individual BIRTH DEATH Point prevalence Period prevalence Lifetime prevalence  Calculating Prevalence Proportion Numerator = number of people with condition Denominator = number of people in total Of 200 medical students, 4 currently have bunions. What is the (point) prevalence of bunions in this group? Prevalence = Number of students with bunions Total number of students = 4 / 200 = 2 / 100 or 2% The point prevalence of bunions in these medical students is 2% (or 2 per 100) Calculating Prevalence Often present prevalence as “per 1000” or “per 100,000” etc. when prevalence is low Of 250,000 Coventrians, 100 have bunions. What is the (point) prevalence of bunions in this group (per 100,000)? Prevalence = Number of Coventrians with bunions x 100,000 Total number of Coventrians = (100 / 250,000) × 100,000 = (1 / 2500) × 100,000 = 40 The prevalence of bunions in Coventrians is 40 per 100,000 (This is better than saying “0.04%” or “0.04 people per 100 have bunions”) The use of prevalence Used to gauge the burden of disease But prevalence can be affected by disease duration CHRONIC DISEASE: affected 4 in 10, ACUTE DISEASE: affected 10 in 10, point prevalence = 4 in 10 point prevalence = 0 in 10 Incidence Latin incidere = to happen upon A.k.a. incidence rate Incidence (rate) → the rate at which new events occur in a population, over a defined period of time What is the incidence of freshers’ flu in 1st year students? Can be expressed as: 1. per n people per time period 100 cases per 1000 students per year 2. per n person-years 100 cases per 1000 student-years NOTE that these are essentially the same thing! Person-years (an aside) Person-years → a measurement combining the number of people observed and the number of years they were observed for person-years = number of people × number of years Study 1 person for 100 years = 100 person-years Study 100 people for 1 year = 100 person-years Study 50 people for 2.5 years = Calculating Incidence Numerator = number of new cases Denominator = number of people × years observed 2000 music undergrads were observed for the duration of their 3-year course. Over this time, 6 people developed tinnitus. What is the incidence of tinnitus in this group (per 1000 person-years)? Incidence = Number of new cases of tinnitus × 1000 Total number of students x years observed = { 6 / (2000 × 3) } × 1000 = { 6 / 6000 } × 1000 =1 The incidence of tinnitus in music undergrads is 1 per 1000 person-years (or 1 per 1000 music undergrads per year)  Relating Incidence and Prevalence High incidence Low incidence Common, not brief condition: Uncommon, long-term condition: High Common cold Type 2 diabetes prevalence Common, very brief condition: Uncommon, short-term Low Nose bleeds condition: prevalence Pancreatic cancer Factors Affecting Prevalence Transfer (bidirectional) Factors that affect prevalence Incidence rate Recovery (cure) rate The epidemiologist’s bathtub Death rate Transfer (migration) rate  Statistical Inference Experiment TAKE A SAMPLE POPULATION Statistical FORM A CONCLUSION ABOUT Inference YOUR POPULATION Statistical Inference Given that we can’t know the truth, we make a best guess (based on data) We also describe our level of uncertainty around the best guess Point Estimation The point estimate is our best guess based on sample data On which side do new mums prefer to hold their babies? Sample: 500 new mums Observation: 400 held the baby on their left Point estimate: 80% hold baby on the left What does it tell us about the population of LEE SALK all new mums? What would happen if we repeated the experiment? Sampling Error Imagine you repeated the same experiment lots of times The point estimates from each experiment can be different They will be clustered around the true value The differences between the sample point estimates and the truth is the sampling error Sampling Error To eliminate sampling error you have to test the whole population Rarely feasible To reduce sampling error, you can test a larger sample In other words, the larger your sample size, the more likely it is that your best guess is close to the truth Standard Error (S.E.) The standard error is a numerical value that represents the sampling error This can be calculated (later) A large S.E. suggests that our best guess may be far from the truth A small S.E. suggests that out best guess is close to the truth The larger your sample size, the smaller the SE will be Confidence Intervals (CI) Lee found that 80% of mums held their baby on the left How confident are we that the exact population proportion is 80%? Can we be confident, say, that the true population proportion is somewhere in between 70% and 90%? When you give an estimate from a sample, you should also give a range of plausible values, to represent your level of uncertainty – this is the confidence interval Interpreting Confidence Intervals EXAMPLE “In our study, we found that 80% of mothers hold their baby on the left. A 95% confidence interval is 75% to 85%.” You can be 95% confident that, in reality, somewhere between 75% and 85% of new mums hold their baby on the left. or The true proportion of mothers who hold their baby on the left is plausibly between 75% and 85% Calculating Confidence Intervals A 95% confidence interval includes all values within 1.96 standard errors of the point estimate Lower bound = point estimate – (1.96 × S.E.) Upper bound = point estimate + (1.96 × S.E.) * There are different formulae for the S.E., depending on the type of data you have, but the formula for the CI is always the same Calculating Confidence Intervals EXAMPLE The standard error of a proportion is given by * 𝑝(1 − 𝑝) p is the sample proportion 𝑛 n is number of observations What is the CI for Lee Salk’s proportion estimate? Step 1. Calculate S.E. S.E. = √ [(0.8×0.2) ÷ 500] = 0.02 Step 2. Calculate CI CI = estimate ± (1.96 × S.E.) = 0.8 ± (1.96 × 0.02) = 0.8 ± 0.04 95% CI is (0.76, 0.84) * For information only, you don’t need to learn it Interpreting Confidence Intervals For the above study, we have: Sample proportion 0.8 95% CI of (0.76, 0.84) In words: In our study, we found that 80% of mothers held their babies on the left However, we can be 95% confident that the true proportion of mothers that hold their babies on the left is somewhere between 76% and 84% Interpreting Confidence Intervals The width of a confidence interval gives an indication of how precise our estimate is A wide confidence interval means you cannot be precise about the truth We found that 50% of students are male, but we are 95% confident that the real proportion is somewhere between 10% and 90% Larger sample sizes result in narrower confidence intervals A narrow confidence interval is more reassuring! Comparing Confidence Intervals CIs can be used to see if there is a real (statistically significant) difference between two groups Is there a difference in the prevalence of obesity between Birmingham and Coventry? (based on sample data) The prevalence of obesity in Coventry is 20% (95% CI [15%, 25%]) The prevalence of obesity in Birmingham is 18% (95% CI [14%, 22%]) No – the two confidence intervals overlap, so it is plausible that the prevalence of obesity is the same in the two cities (i.e.15-22%) Comparing Confidence Intervals Is there a difference in the prevalence of obesity in Coventry between 1915 and 2015? The prevalence of obesity in 1915 was 2% (95% CI [0.5%, 3.5%]) The prevalence of obesity in 2015 is 20% (95% CI [15%, 25%]) Yes – the two confidence intervals are distinct (no overlap), so it is not plausible that the prevalence of obesity has stayed the same. In other words, the prevalence of obesity has increased between 1915 and 2015 WORKED EXAMPLE The local council want to determine whether there has been a recent reduction in the prevalence of teenage smoking. In 2010, 20 out of 50 sampled teenagers smoked In 2015 15 out of 60 sampled teenagers smoked Step 1. Calculate (point) prevalence of teenage smoking Prevalence in 2010 = 20 ÷ 50 = 40% Prevalence in 2015 = 15 ÷ 60 = 25%  WORKED EXAMPLE Step 2. Calculate the standard errors * 𝑝(1 − 𝑝) 𝑛 SE for 2010 = √ [(0.4)(1-0.4) ÷ 50 ] = 0.07 SE for 2015 = √ [(0.25)(1-0.25) ÷ 60 ]= 0.06 Step 3. Calculate the confidence intervals CI = estimate ± (1.96 × S.E.) CI for 2010 = 0.4 ± (1.96 × 0.07) = (0.26, 0.54) CI for 2015 = 0.25 ± (1.96 × 0.06) = (0.13, 0.37) * Remember, you need not memorise the formulae for calculating S.E. WORKED EXAMPLE Step 4. Interpret the results In 2010, we estimate that the prevalence of teenage smoking was 40%, although a plausible range of values for the true prevalence is 26% to 54% In 2015, we estimate that the prevalence of teenage smoking is 25%, although a plausible range of values for the true prevalence is 13% to 37% Has there been a change in the prevalence of teenage smoking? Given that the confidence intervals for the prevalence at the two time points overlap, it is plausible that there has been no change in the prevalence of teenage smoking between 2010 and 2015. Learning Outcomes 1. Define and calculate prevalence and incidence 2. Accept that the result from an experiment is unlikely to be “the truth” 3. Be able to calculate and interpret confidence intervals  Prevalence, Incidence and Confidence Intervals