1. g.burnside@liv.ac.uk School of Dental Sciences BASCD Survey Sampling Girvan Burnside University of Liverpool

2. g.burnside@liv.ac.uk School of Dental Sciences Survey sampling British Association for the Study of Community Dentistry (BASCD) guidance on sampling for surveys of child dental health. A BASCD coordinated dental epidemiology programme quality standard. C.M. Pine, N.B. Pitts and Z.J. Nugent. Community Dental Health (1997) 14. (Supplement 1). 10-17 The sampling principles detailed in this paper stand. This presentation shows how they can be applied to the new requirement to report at both LA and PCT level.

3. g.burnside@liv.ac.uk School of Dental Sciences Sampling schools CDH paper suggests Small schools: ≤15 pupils – examine all Medium schools: 16-49 pupils – examine 1 in 2 Large schools: ≥50 pupils – examine 1 in 4 Suggested alternative Small schools: <30 pupils – examine all Large school: ≥30 pupils – examine 1 in 2

4. g.burnside@liv.ac.uk School of Dental Sciences Example of sampling School sizeNumber of schools Number of children <3066851 ≥30512688 Total1173539

5. g.burnside@liv.ac.uk School of Dental Sciences Example of sampling School size Number of schools Number of children % of populatio n Sample required <306685124%120 ≥3051268876%380 Total1173539100%500

6. g.burnside@liv.ac.uk School of Dental Sciences Sampling procedure follows the same steps as detailed in Appendix 1 to Pine et al (1997) Recommended minimum number sampled in each sampling unit is 300

7. g.burnside@liv.ac.uk School of Dental Sciences Scenario 1 LA exactly matches PCT LA 1 PCT 1

8. g.burnside@liv.ac.uk School of Dental Sciences Scenario 1 Sampling unit is LA Aim for minimum of 250 children examined Estimates for LA and PCT calculated normally, no weighting required Estimates for LA/PCT are identical

9. g.burnside@liv.ac.uk School of Dental Sciences Scenario 2 Multiple LAs completely contained in one PCT LA 1 LA 3 LA 2 LA 4 PCT 1

10. g.burnside@liv.ac.uk School of Dental Sciences Sampling unit is LA Aim for minimum 250 children examined in each LA Estimates for each LA calculated normally, no weighting required Estimates for PCT must be calculated using weighting

11. g.burnside@liv.ac.uk School of Dental Sciences Scenario 3 One LA which contains multiple PCTs PCT 1 PCT 2 PCT 3 PCT 4 LA 1

12. g.burnside@liv.ac.uk School of Dental Sciences Sampling unit is PCT Aim for minimum 250 children examined in each PCT Estimates for each PCT calculated normally, no weighting required Estimates for LA must be calculated using weighting

13. g.burnside@liv.ac.uk School of Dental Sciences Weighting This procedure for calculation of weighted estimates is detailed in Pine et al., (1997) Example: One PCT, containing 4 local authorities, each with 250 children examined.

14. g.burnside@liv.ac.uk School of Dental Sciences Weighting example For each LA, we need to know: The number of children in the 5-year-old population (N) The number of children examined (n) The sample mean (y) The sample standard deviation (s), or sample variance (s 2 )

15. g.burnside@liv.ac.uk School of Dental Sciences Weighting example (cont) LAPopnNumber examined Sample mean Sample s.d Sample variance WeightWeight squared 110002502.53.46120.130.018 220002501.12.8380.270.071 35002503.23.87150.070.004 440002502.23.16100.530.284 Total75001000 Weights are calculated as the proportion of the total population in the area. So, for LA1, the weight is 1000/7500 = 0.13 Note the variance is the square of the standard deviation

16. g.burnside@liv.ac.uk School of Dental Sciences Weighting example (cont) To calculate the estimate of the mean for the whole PCT = (1000 x 2.5) + (2000 x 1.1) + (500 x 3.2) + (4000 x 2.2) =2.01 7500 LAPopnNumber examined Sample mean Sample s.d Sample variance WeightWeight squared 110002502.53.46120.130.018 220002501.12.8380.270.071 35002503.23.87150.070.004 440002502.23.16100.530.284 Total75001000

17. g.burnside@liv.ac.uk School of Dental Sciences Weighting example (cont) To calculate the estimate of the standard error for the population mean for the PCT = 0.018 x 12 + 0.071 x 8 + 0.004 x 15 + 0.284 x 10 =0.12 250 250 250 250 LAPopnNumber examined Sample mean Sample s.d Sample variance WeightWeight squared 110002502.53.46120.130.018 220002501.12.8380.270.071 35002503.23.87150.070.004 440002502.23.16100.530.284 Total75001000

18. g.burnside@liv.ac.uk School of Dental Sciences Weighting example (cont) To calculate the 95% confidence interval for the population mean Mean estimate ± 1.96 x S.E. estimate In this example, 95% CI is 2.01 ± 1.96 x 0.12 = 1.78 to 2.25

19. g.burnside@liv.ac.uk School of Dental Sciences Weighted estimates of proportions Some areas may wish to calculate estimates of the proportion affected by caries LAPopnNumber examined Sample proportion Variance of sample proportion WeightWeight squared 110002500.580.130.018 220002500.290.270.071 35002500.650.070.004 440002500.420.530.284 Total75001000

20. g.burnside@liv.ac.uk School of Dental Sciences Weighted estimates of proportions The variance of a sample proportion p is given by p(1-p) So for LA 1, variance is 0.58 x (1 - 0.58) = 0.244 LAPopnNumber examined Sample proportion Variance of sample proportion WeightWeight squared 110002500.580.2440.130.018 220002500.290.2060.270.071 35002500.650.2280.070.004 440002500.420.2440.530.284 Total75001000

21. g.burnside@liv.ac.uk School of Dental Sciences Weighted estimates of proportions LAPopnNumber examined Sample proportion Variance of sample proportion WeightWeight squared 110002500.580.2440.130.018 220002500.290.2060.270.071 35002500.650.2280.070.004 440002500.420.2440.530.284 Total75001000 To calculate the estimate of the proportion for the whole PCT = (1000 x 0.58) + (2000 x 0.29) + (500 x 0.65) + (4000 x 0.42) = 0.42 7500

22. g.burnside@liv.ac.uk School of Dental Sciences Weighted estimates of proportions LAPopnNumber examined Sample proportion Variance of sample proportion WeightWeight squared 110002500.580.2440.130.018 220002500.290.2060.270.071 35002500.650.2280.070.004 440002500.420.2440.530.284 Total75001000 To calculate the estimate of the standard error for the population mean for the PCT = 0.018 x 0.244 + 0.071 x 0.206 + 0.004 x 0.228 + 0.284 x 0.244 =0.019 250 250 250 250

23. g.burnside@liv.ac.uk School of Dental Sciences Weighting estimates of proportions To calculate the 95% confidence interval for the population proportion Proportion estimate ± 1.96 x S.E. estimate In this example, 95% CI is 0.42 ± 1.96 x 0.019 = 0.38 to 0.46

24. g.burnside@liv.ac.uk School of Dental Sciences LA crosses PCT boundaries Scenario 4 LA 1 LA 2 LA 3 LA 5 LA 4 PCT 1 (grey) PCT 2 (white)

25. g.burnside@liv.ac.uk School of Dental Sciences Scenario 4 Here LA 3 crosses between 2 PCTs. Sampling of LA 3 must ensure that valid estimates can be produced for both PCTs.

26. g.burnside@liv.ac.uk School of Dental Sciences Scenario 4 guidelines The 2 parts of LA 3 should be sampled from separately, and weighting applied to calculated estimates If either section only has a few schools, examine all schools in that section Please discuss plans for sampling these areas with me g.burnside@liv.ac.uk

27. School of Dental Sciences List of LAs which cross PCT boundaries Aylesbury Vale Braintree City of Stoke-on-Trent Crewe and Nantwich High Peak North Lincolnshire Runnymede South Oxfordshire Staffordshire Moorlands Vale of White Horse Vale Royal Wealden

28. g.burnside@liv.ac.uk School of Dental Sciences Subgroups Some PCTs may wish to examine subgroups within a local authority This can be done following the guidance in appendix 2 of Pine et al., (1997).

29. g.burnside@liv.ac.uk School of Dental Sciences Example A local authority is made up of an city (5- year old population 2500), and surrounding rural areas (population 500) We want to obtain estimates for both the urban and rural areas of the LA. For subgroup analysis, a minimum sample of 100 in each subgroup is desirable

30. g.burnside@liv.ac.uk School of Dental Sciences Example (continued) It is decided to take a sample of 250 in the urban area, and 100 in the rural areas.

31. g.burnside@liv.ac.uk School of Dental Sciences Example (continued) Mean = (2500 x 2.7) + (500 x 1.4) =2.48 3000 S.E. = 0.694 x 10 + 0.028 x 8 =0.17 250 100 95% CI = 2.48 ± 1.96 x 0.17 = 2.14 to 2.82 LAPopnNumber examined Sample mean Sample variance WeightWeight squared Urban25002502.7100.830.694 Rural5001001.480.170.028 Total3000350

32. g.burnside@liv.ac.uk School of Dental Sciences Example (continued) The LA we have just sampled is part of a PCT which contains one other LA LA 1 LA 2 Rural Urban

33. g.burnside@liv.ac.uk School of Dental Sciences Example (continued) When calculating the estimates for the PCT, it is important to keep the individual sampling units in LA 1 separate LAPopnNumber examined Sample mean Sample variance WeightWeight squared LA1 Urban 25002502.710 LA1 Rural 5001001.48 LA215003003.612 Total4500650

34. g.burnside@liv.ac.uk School of Dental Sciences Example (continued) When calculating the estimates for the PCT, it is important to keep the individual sampling units in LA 1 separate LAPopnNumber examined Sample mean Sample variance WeightWeight squared LA1 Urban 25002502.7100.560.309 LA1 Rural 5001001.480.110.012 LA215003003.6120.330.111 Total4500650

35. g.burnside@liv.ac.uk School of Dental Sciences Mean = (2500 x 2.7) + (500 x 1.4) + (1500 x 3.6) =2.86 4500 S.E. = 0.309 x 10 + 0.012 x 8 + 0.111 x 12 =0.13 250 100 300 95% CI = 2.86 ± 1.96 x 0.13 = 2.59 to 3.12 LAPopnNumber examined Sample mean Sample variance WeightWeight squared LA1 Urban 25002502.7100.560.309 LA1 Rural 5001001.480.110.012 LA215003003.6120.330.111 Total4500650

36. g.burnside@liv.ac.uk School of Dental Sciences Weighting calculations An Excel spreadsheet to perform calculation of weighted means and confidence intervals can be downloaded http://pcwww.liv.ac.uk/~gburnsid/bascd.htm

37. g.burnside@liv.ac.uk School of Dental Sciences Note The confidence intervals here are approximations Approximations are accurate where the number examined is much smaller than the population Where large proportions of the population are examined (e.g. census), the confidence intervals may be too wide The Excel spreadsheet calculates accurate confidence intervals

38. g.burnside@liv.ac.uk School of Dental Sciences Summary Ensure estimates can be calculated at both LA and PCT level Sample at LA level, except where one LA contains multiple PCTs For non-coterminous PCTs/LAs, seek advice This presentation can be downloaded at http://pcwww.liv.ac.uk/~gburnsid/bascd.htm