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BASCD Survey Sampling

BASCD Survey Sampling. Girvan Burnside University of Liverpool. Survey sampling.

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BASCD Survey Sampling

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  1. BASCD Survey Sampling Girvan Burnside University of Liverpool

  2. 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. 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. Example of sampling

  5. Example of sampling

  6. 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. Scenario 1 • LA exactly matches PCT LA 1 PCT 1

  8. 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. Scenario 2 • Multiple LAs completely contained in one PCT LA 1 LA 3 PCT 1 LA 2 LA 4

  10. 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. Scenario 3 • One LA which contains multiple PCTs PCT 1 PCT 3 LA 1 PCT 2 PCT 4

  12. 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. 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. 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 (s2)

  15. Weighting example (cont) 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. 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

  17. 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

  18. 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. Weighted estimates of proportions • Some areas may wish to calculate estimates of the proportion affected by caries

  20. 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

  21. Weighted estimates of proportions 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. Weighted estimates of proportions 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. 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. Scenario 4 • LA crosses PCT boundaries PCT 2 (white) PCT 1 (grey) LA 4 LA 3 LA 1 LA 5 LA 2

  25. 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. 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. 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. 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. 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. Example (continued) • It is decided to take a sample of 250 in the urban area, and 100 in the rural areas.

  31. 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

  32. Example (continued) • The LA we have just sampled is part of a PCT which contains one other LA Urban LA 1 LA 2 Rural

  33. Example (continued) • When calculating the estimates for the PCT, it is important to keep the individual sampling units in LA 1 separate

  34. Example (continued) • When calculating the estimates for the PCT, it is important to keep the individual sampling units in LA 1 separate

  35. 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

  36. 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. 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. 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

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