1 Sampling for EHES Principles and Guidelines Johan Heldal & Susie Cooper Statistics Norway

2 Overview Why this kind of sampling? Target population & sample size Sampling frames. Probability sampling Two-stage sampling - PSUs Stratification Stage 1 sampling  Sample sizes  Sampling PSUs with PPS Stage 2 sampling A cost model Age-gender stratification Further aspects

3 Why? Goals for EHES: To estimate distribution of risk levels within national populations. To compare risk levels among national populations. To predict levels of disease in the future. Different from ordinary goals for epidemiologists: to establish risk factors and models for risk.

4 Ideal Target Population Core: All persons years at a given date with permanent residence in a country.  Can be extended by age to 18+.  Should also include institutionalized. Sample size: At least 500 in each of (M,W) x (25-34, 35-44, 45-54, 55-64):  Total ≥ 4000 persons.  For pilot ≥ 200 persons.

5 Main Sampling Frame List of persons/addresses from which to take a sample (register or census).  Should cover the target population but may need ”adds-on”.  ”adds-on”: List of institutions A good list frame may be unavailable. Can use ”Map frames” (NHANES). Telephone directories may be complicated.

6 Probability sampling Sampling in scientific surveys is carried out as Probability Sampling (e.g. simple random sampling) Every sampling unit and every target unit has a defined probability of being selected. It must be possible to calculate this probability at least for all units being sampled.

7 Two stage sampling Primary Sampling Unit: Area that can be handled by one examination site. Small enough that every person living there can easily travel to the site. Or be easily visited. Can be created from small census tracts, municipalities, electoral districts, post code areas or …. Divide the country into disjoint PSUs.

8 Two stage sampling Stratification: Group the PSUs into groups of ”close PSUs”, Strata. Use geography and other known information to group similar PSUs together. Stage 1: Take a probability sample of PSUs in each stratum. Stage 2:Then take a probability sample of persons/-households/-addresses in each sampled PSU.

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10 Strata consists of PSUs PSU sizes:  N i = # persons, households, addresses of PSU no. i.  Can vary, but not too much within a stratum.  Recommended N i ≥ Stratum size: N = N 1 + … + N M A sample of m ≥ 2 PSUs and n persons or addresses, is taken from the stratum.

11 Stage 1 sampling Selection probabilities for PSUs i : π i = mN i /N (PPS sampling) Each PSU gets the same sample size p = n/m (persons, addresses). Gives every person in the same stratum equal probability of being selected. m and p can be calculated in a cost- variance optimal way in each stratum. The program EHESsampling takes care of the calculations and performs sampling.

12 Stage 2 sampling Sampling of persons or addresses within each of the PSUs sampled at stage 1. Simple random sampling of p = n/m (persons, addresses) in every sampled PSU.

13 A cost model C 1 = cost of establishing an extra PSU C 2 = cost of inviting an extra person to the PSU. Total variable cost budget model C = C 1 m + C 2 n m and p = n/m can be calculated to minimize variance given the size of this budget. EHESsampling can do this.

14 Age-gender stratification At stage 2: Sample separately for each of the eight (M,W) x 4 age domains. An option only if the main sampling frame consists of individual persons. Gives better control of sample size within each age-gender domain. Not necessary if sampling size very large.

15 With address frames Address: 1.A dwelling or 2.A house with many dwellings 1.Dwelling: Invite all eligible persons in the dwelling, if not too many 2.Sample some dwellings at the address with a Kish grid. (Stage 3) Then do as in 1.

16 Time and place aspects A HES takes time (say a year). Avoid confoundation between time of year and geography. A randomized design for the order of visiting the PSUs recommended. Simpler to handle if many teams work in parallel.

17 Thank you!