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What is a sample? Epidemiology matters: a new introduction to methodological foundations Chapter 4 Seven steps 1. Define the population of interest 2. Conceptualize and create measures of exposures and health indicators 3. Take a sample of the population 4. Estimate measures of association between exposures and health indicators of interest 5. Rigorously evaluate whether the association observed suggests a causal association 6. Assess the evidence for causes working together 7. Assess the extent to which the result matters, is externally valid, to other populations Epidemiology Matters – Chapter 1 2 1. Why take a sample? 2. How to take a representative sample 3. Quantifying sampling variability 4. How to take a purposive sample 5. Study design 6. Summary Epidemiology Matters – Chapter 4 3 1. Why take a sample? 2. How to take a representative sample 3. Quantifying sampling variability 4. How to take a purposive sample 5. Study design Epidemiology Matters – Chapter 4 4 Why take a sample? Epidemiologists take samples to answer healthrelated research questions efficiently A full census is the epidemiologic ideal Reasons not to take a census all the time include lack of time, lack of money, and waste of resources Epidemiology Matters – Chapter 4 5 To take a sample 1. Specify population of interest 2. Specify a research question of interest Epidemiology Matters – Chapter 4 6 Specify population of interest What are the characteristics of the population in which we would like to understand health? Example: Do we want to know what the prevalence of diabetes is within New York City? New York State? The United States? Do we want to know the causes of diabetes? The population of interest has to be specified before the sampling strategy defined Epidemiology Matters – Chapter 4 7 Specifying a question Question of interest can help clarify appropriate way to sample population of interest Questions asked can include estimating population parameters, or estimating causal effects of exposures on outcomes Epidemiology Matters – Chapter 4 8 Example, estimating population parameters Questions concerned with population parameters include What proportion of individuals in the population of interest has breast cancer? What is the mean blood pressure in the population? How many new cases of HIV are diagnosed in the population over three years? Population parameters include estimates of Proportions Means Standard deviations Sample required Representative sample 9 Example, estimating causal effects of exposures on outcomes Questions for which these measures are needed are Does exposure to pollution cause lung cancer? Does suffering abuse in childhood cause depression in adulthood? Does a specific genetic marker cause Alzheimer’s disease? Parameter of interest Causal effect of an exposure on a health outcome Sampling concerns Not representativeness (as in population parameters) Whether individuals exposed to hypothesized cause of interest are comparable to individuals not exposed Purposive sample sufficient 10 Representative and purposive A representative sample is one where the sample that is taken has characteristics similar to the overall population A purposive sample selects from the population base on some criterion A representative sample may or may not include individuals who are comparable with respect to causal identification A purposive sample may or may not be representative of a particular population of interest Epidemiology Matters – Chapter 4 11 1. Why take a sample? 2. How to take a representative sample 3. Quantifying sampling variability 4. How to take a purposive sample 5. Study design 6. Summary Epidemiology Matters – Chapter 4 12 How to take a representative sample The simplest approach: a simple random sample Each member of the population has an equal probability of being selected into the sample A successful simple random sample should have the same basic characteristics as the original population Epidemiology Matters – Chapter 4 13 Taking a simple random sample 1. Enumerate all potential members of population of interest 2. Assign each member a probability of selection 3. Ensure selection of members are independent Epidemiology Matters – Chapter 4 14 Example: Sampling Farrlandia 30 residents in Farrlandia Options for random selection: --Every 4th home, dice roll for selection within home Challenges include (a) clustered exposures, (b) unequal ‘home’ size Selected for sample Epidemiology Matters – Chapter 4 15 Example: Sampling Farrlandia 30 residents in Farrlandia Select every Nth person in phone book Challenges include that not everyone is in phone book Selected for sample Epidemiology Matters – Chapter 4 16 The perfect sample? There is no perfect sample The goal in epidemiology is to understand limitations of sampling methods and account for them Epidemiology Matters – Chapter 4 17 Sampling Farrlandia Epidemiology Matters – Chapter 4 18 Sampling Farrlandia We want to collect our sample in such a way that the sample also has 50% exposed and 30% dotted. Epidemiology Matters – Chapter 4 19 Sampling Farrlandia We can use a simple random sample ½ the population (25) Probability of selection 1/50 or 2% Random number generator Epidemiology Matters – Chapter 4 20 Sampling Farrlandia Original Population Black solid 15 30% Black dots 10 20% Total black 25 50% Gray solid 20 40% Gray dots 5 10% Total gray 25 50% Epidemiology Matters – Chapter 4 21 Sampling Farrlandia Original Population Sample Black solid 15 30% Black solid 8 32% Black dots 10 20% Black dots 5 20% Total black 25 50% Total black 13 52% Gray solid 20 40% Gray solid 10 40% Gray dots 5 10% Gray dots 2 8% Total gray 25 50% Total gray 12 48% Epidemiology Matters – Chapter 4 22 1. Why take a sample? 2. How to take a representative sample 3. Quantifying sampling variability 4. How to take a purposive sample 5. Study design 6. Summary Epidemiology Matters – Chapter 4 23 Quantifying sampling variability Sampled population will not have the exact same population parameters as complete population census The ‘truth’, i.e., the population parameter of original population is called the true population parameter Epidemiology Matters – Chapter 4 24 Variations in possible samples Epidemiology Matters – Chapter 4 25 Variations in possible samples Epidemiology Matters – Chapter 4 26 Variations in possible samples Epidemiology Matters – Chapter 4 27 Variations in possible samples 38,760 different possible samples of 5 Epidemiology Matters – Chapter 4 28 Quantifying uncertainty, Central Limit Theorem (CLT) 1. Average proportion across all possible samples = true population proportion Example: 50% of true population has diabetes Sample 1 has 100% diabetes Sample 2 has 0% diabetes Average of all samples will have 50% diabetes Epidemiology Matters – Chapter 4 29 Quantifying uncertainty, CLT 2. Variance around average sample proportions (standard error) p = sample proportion n = sample size Epidemiology Matters – Chapter 4 30 Quantifying uncertainty, CLT 3. Large samples will have normally distributed samples > 30 people No group < 5 people Epidemiology Matters – Chapter 4 31 Quantifying uncertainty, CLT Therefore the principal drivers of uncertainty are 1. Prevalence in the sample 2. Sample size The larger the sample size, the smaller the amount of uncertainty in the sample estimate Epidemiology Matters – Chapter 4 32 1. Why take a sample? 2. How to take a representative sample 3. Quantifying sampling variability 4. How to take a purposive sample 5. Study design 6. Summary Epidemiology Matters – Chapter 4 33 Purposive sample Eligibility criteria for study is the central design element; entry is based on exposure status, or sometimes on health outcome status Epidemiology Matters – Chapter 4 34 1. Why take a sample? 2. How to take a representative sample 3. Quantifying sampling variability 4. How to take a purposive sample 5. Study design 6. Summary Epidemiology Matters – Chapter 4 35 Study design Study design considerations are similar for representative or purposive sample Study design reflects decisions made at one time point or over time Timing of disease process can inform the study design Epidemiology Matters – Chapter 4 36 Study design options 1. Sample one moment in time, irrespective of disease status, measure disease and potential cause simultaneously 2. Sample over time, start with disease free individuals only, measure disease over time 3. Sample one moment in time, based on disease status Epidemiology Matters – Chapter 4 37 Farrlandia population Epidemiology Matters – Chapter 4 38 Farrlandia population Epidemiology Matters – Chapter 4 39 Farrlandia population Epidemiology Matters – Chapter 4 40 Farrlandia population Epidemiology Matters – Chapter 4 41 Farrlandia population Epidemiology Matters – Chapter 4 42 Farrlandia population Epidemiology Matters – Chapter 4 43 Farrlandia population Epidemiology Matters – Chapter 4 44 Farrlandia population Epidemiology Matters – Chapter 4 45 Farrlandia population Epidemiology Matters – Chapter 4 46 Option 1, Cross-sectional Epidemiology Matters – Chapter 4 47 Option 2, Cohort Epidemiology Matters – Chapter 4 48 Option 3, Case-control Epidemiology Matters – Chapter 4 49 1. Why take a sample? 2. How to take a representative sample 3. Quantifying sampling variability 4. How to take a purposive sample 5. Study design 6. Summary Epidemiology Matters – Chapter 4 50 Summary 1. Samples are efficient, representative or purposive 2. Representative sample; e.g., simple random sample 3. Sampling variability, standard error 4. Purposive sample, selection on exposure or disease status 5. Study designs can be cross-sectional, cohort, casecontrol Epidemiology Matters – Chapter 4 51 Seven steps 1. Define the population of interest 2. Conceptualize and create measures of exposures and health indicators 3. Take a sample of the population 4. Estimate measures of association between exposures and health indicators of interest 5. Rigorously evaluate whether the association observed suggests a causal association 6. Assess the evidence for causes working together 7. Assess the extent to which the result matters, is externally valid, to other populations Epidemiology Matters – Chapter 1 52 epidemiologymatters.org Epidemiology Matters – Chapter 1 53