[email protected] school of dental sciences bascd survey sampling girvan burnside university of...

[email protected] School of Dental Sciences

BASCD Survey Sampling

Girvan Burnside

University of Liverpool


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.


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


Example of sampling

School size Number of schools

Number of children

<30 66 851

≥30 51 2688

Total 117 3539


Example of sampling

School size

Number of schools

Number of children

% of population

Sample required

<30 66 851 24% 120

≥30 51 2688 76% 380

Total 117 3539 100% 500


• 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


Scenario 1

• LA exactly matches PCT

LA 1

PCT 1


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


Scenario 2

• Multiple LAs completely contained in one PCT

LA 1

LA 3

LA 2

LA 4

PCT 1


• 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


Scenario 3

• One LA which contains multiple PCTs

PCT 1

PCT 2

PCT 3

PCT 4

LA 1


• 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


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.


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)


Weighting example (cont)LA Popn Number

examinedSample mean

Sample s.d

Sample variance

Weight Weight squared

1 1000 250 2.5 3.46 12 0.13 0.018

2 2000 250 1.1 2.83 8 0.27 0.071

3 500 250 3.2 3.87 15 0.07 0.004

4 4000 250 2.2 3.16 10 0.53 0.284

Total 7500 1000

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


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

LA Popn Number examined

Sample mean

Sample s.d

Sample variance


1 1000 250 2.5 3.46 12 0.13 0.018

2 2000 250 1.1 2.83 8 0.27 0.071

3 500 250 3.2 3.87 15 0.07 0.004

4 4000 250 2.2 3.16 10 0.53 0.284

Total 7500 1000



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


Sample mean

Sample s.d

Sample variance


1 1000 250 2.5 3.46 12 0.13 0.018

2 2000 250 1.1 2.83 8 0.27 0.071

3 500 250 3.2 3.87 15 0.07 0.004

4 4000 250 2.2 3.16 10 0.53 0.284

Total 7500 1000



• 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


Weighted estimates of proportions

• Some areas may wish to calculate estimates of the proportion affected by caries


Sample proportion

Variance of sample proportion


1 1000 250 0.58 0.13 0.018

2 2000 250 0.29 0.27 0.071

3 500 250 0.65 0.07 0.004

4 4000 250 0.42 0.53 0.284

Total 7500 1000



• 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


Sample proportion



1 1000 250 0.58 0.244 0.13 0.018

2 2000 250 0.29 0.206 0.27 0.071

3 500 250 0.65 0.228 0.07 0.004

4 4000 250 0.42 0.244 0.53 0.284

Total 7500 1000




Sample proportion



1 1000 250 0.58 0.244 0.13 0.018

2 2000 250 0.29 0.206 0.27 0.071

3 500 250 0.65 0.228 0.07 0.004

4 4000 250 0.42 0.244 0.53 0.284

Total 7500 1000

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




Sample proportion



1 1000 250 0.58 0.244 0.13 0.018

2 2000 250 0.29 0.206 0.27 0.071

3 500 250 0.65 0.228 0.07 0.004

4 4000 250 0.42 0.244 0.53 0.284

Total 7500 1000

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


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


• LA crosses PCT boundaries

Scenario 4

LA 1

LA 2

LA 3

LA 5

LA 4

PCT 1 (grey)

PCT 2 (white)


Scenario 4

• Here LA 3 crosses between 2 PCTs.

• Sampling of LA 3 must ensure that valid estimates can be produced for both PCTs.


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

• [email protected]


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


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).


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


Example (continued)

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


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


Sample mean

Sample variance


Urban 2500 250 2.7 10 0.83 0.694

Rural 500 100 1.4 8 0.17 0.028

Total 3000 350


Example (continued)

• The LA we have just sampled is part of a PCT which contains one other LA

LA 1

LA 2Rural

Urban


Example (continued)

• When calculating the estimates for the PCT, it is important to keep the individual sampling units in LA 1 separate


Sample mean

Sample variance


LA1 Urban

2500 250 2.7 10

LA1 Rural

500 100 1.4 8

LA2 1500 300 3.6 12

Total 4500 650


Example (continued)

• When calculating the estimates for the PCT, it is important to keep the individual sampling units in LA 1 separate


Sample mean

Sample variance


LA1 Urban

2500 250 2.7 10 0.56 0.309

LA1 Rural

500 100 1.4 8 0.11 0.012

LA2 1500 300 3.6 12 0.33 0.111

Total 4500 650


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


Sample mean

Sample variance


LA1 Urban

2500 250 2.7 10 0.56 0.309

LA1 Rural

500 100 1.4 8 0.11 0.012

LA2 1500 300 3.6 12 0.33 0.111

Total 4500 650


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


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


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

[email protected] school of dental sciences bascd survey sampling girvan burnside university of...

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