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Table 1 Recommended sample sizes and decision rules for numbers of clusters up to n min for the community health worker data quality assessment example

From: The effect of clustering on lot quality assurance sampling: a probabilistic model to calculate sample sizes for quality assessments

Number of clusters
   2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
ICC = 0.01 samples per cluster, k 13 7 5 4 5 3 4 3 2 2 3 2 2 2 2 2 2 2 1
  total sample size, n 26 21 20 20 30 21 32 27 20 22 36 26 28 30 32 34 36 38 20
  decision rule, d 4 3 3 3 4 3 5 4 3 3 5 4 4 4 5 5 5 5 3
  α 0.093 0.081 0.096 0.095 0.040 0.077 0.073 0.069 0.092 0.062 0.036 0.081 0.056 0.038 0.071 0.050 0.035 0.024 0.091
  β 0.048 0.091 0.079 0.078 0.065 0.087 0.022 0.045 0.076 0.096 0.034 0.040 0.050 0.062 0.021 0.027 0.033 0.041 0.075
  Expected Costs, Scenario 1 † $1,260 $1,710 $2,200 $2,700 $3,300 $3,710 $4,320 $4,770 $5,200 $5,720 $6,360 $6,760 $7,280 $7,800 $8,320 $8,840 $9,360 $9,880 $10,200
  Expected Costs, Scenario 2 ‡ $1,900 $1,950 $2,200 $2,500 $3,300 $3,150 $4,000 $4,050 $4,000 $4,400 $5,400 $5,200 $5,600 $6,000 $6,400 $6,800 $7,200 $7,600 $7,000
ICC = 0.025 samples per cluster, k 14 7 7 4 5 3 4 3 2 2 3 2 2 2 2 2 2 2 1
  total sample size, n 28 21 28 20 30 21 32 27 20 22 36 26 28 30 32 34 36 38 20
  decision rule, d 4 3 4 3 4 3 5 4 3 3 5 4 4 4 5 5 5 5 3
  α 0.084 0.090 0.069 0.100 0.045 0.080 0.077 0.072 0.094 0.063 0.038 0.083 0.057 0.039 0.072 0.051 0.036 0.025 0.091
  β 0.074 0.098 0.062 0.083 0.070 0.090 0.025 0.048 0.078 0.097 0.036 0.041 0.051 0.063 0.022 0.028 0.034 0.042 0.075
  Expected Costs, Scenario 1 $1,280 $1,710 $2,280 $2,700 $3,300 $3,710 $4,320 $4,770 $5,200 $5,720 $6,360 $6,760 $7,280 $7,800 $8,320 $8,840 $9,360 $9,880 $10,200
  Expected Costs, Scenario 2 $2,000 $1,950 $2,600 $2,500 $3,300 $3,150 $4,000 $4,050 $4,000 $4,400 $5,400 $5,200 $5,600 $6,000 $6,400 $6,800 $7,200 $7,600 $7,000
ICC = 0.05 samples per cluster, k 18 10 7 6 5 3 4 3 2 2 3 2 2 2 2 2 2 2 1
  total sample size, n 36 30 28 30 30 21 4 27 20 22 36 26 28 30 32 34 36 38 20
  decision rule, d 5 4 4 4 4 3 5 4 3 3 5 4 4 4 5 5 5 5 20
  α 0.093 0.071 0.082 0.056 0.052 0.085 0.085 0.076 0.097 0.065 0.041 0.086 0.060 0.041 0.075 0.053 0.038 0.026 0.091
  β 0.083 0.095 0.073 0.082 0.078 0.094 0.029 0.052 0.080 0.100 0.040 0.043 0.054 0.065 0.023 0.029 0.036 0.044 0.075
  Expected Costs, Scenario 1 $1,360 $1,800 $2,280 $2,800 $3,300 $3,710 $4,320 $4,770 $5,200 $5,720 $6,360 $6,760 $7,280 $7,800 $8,320 $8,840 $9,360 $9,880 $10,200
  Expected Costs, Scenario 2 $2,400 $2,400 $2,600 $3,000 $3,300 $3,150 $4,000 $4,050 $4,000 $4,400 $5,400 $5,200 $5,600 $6,000 $6,400 $6,800 $7,200 $7,600 $7,000
ICC = 0.1 samples per cluster, k 68‡‡ 15 9 6 5 4 4 3 3 3 3 2 2 2 2 2 2 2 1
  total sample size, n 136 45 36 30 30 28 32 27 30 33 36 26 28 30 32 34 36 38 20
  decision rule, d 17 6 5 4 4 4 5 4 4 5 5 4 4 4 5 5 5 5 3
  α 0.096 0.092 0.090 0.075 0.067 0.082 0.099 0.086 0.052 0.077 0.048 0.091 0.064 0.045 0.080 0.058 0.041 0.029 0.091
  β 0.099 0.093 0.082 0.099 0.093 0.073 0.038 0.060 0.078 0.036 0.047 0.047 0.058 0.070 0.026 0.033 0.040 0.048 0.075
  Expected Costs, Scenario 1 $2,360 $1,950 $2,360 $2,800 $3,300 $3,780 $4,320 $4,770 $5,300 $5,830 $6,360 $6,760 $7,280 $7,800 $8,320 $8,840 $9,360 $9,880 $10,200
  Expected Costs, Scenario 2 $7,400 $3,150 $3,000 $3,000 $3,300 $3,500 $4,000 $4,050 $4,500 $4,950 $5,400 $5,200 $5,600 $6,000 $6,400 $6,800 $7,200 $7,600 $7,000
ICC = 0.15 samples per cluster, k †† 45‡‡ 13 9 6 4 5 3 3 3 3 2 2 2 2 2 2 2 1
  total sample size, n   135 52 45 36 28 40 27 30 33 36 26 28 30 32 34 36 38 20
  decision rule, d   17 7 6 5 4 6 4 4 5 5 4 28 4 5 5 5 5 3
  α   0.099 0.100 0.082 0.087 0.095 0.090 0.096 0.060 0.086 0.055 0.096 0.069 0.049 0.085 0.062 0.045 0.032 0.091
  β   0.099 0.090 0.087 0.080 0.083 0.043 0.067 0.086 0.042 0.053 0.051 0.062 0.074 0.029 0.036 0.043 0.051 0.075
  Expected Costs, Scenario 1   $2,850 $2,520 $2,950 $3,360 $3,780 $4,400 $4,770 $5,300 5830.000 $6,360 $6,760 $7,280 $7,800 $8,320 $8,840 $9,360 $9,880 $10,200
  Expected Costs, Scenario 2   $7,650 $3,800 $3,750 $3,600 $3,500 $4,400 $4,050 $4,500 4950.000 $5,400 $5,200 $5,600 $6,000 $6,400 $6,800 $7,200 $7,600 $7,000
ICC = 0.2 samples per cluster, k †† †† 40 12 9 6 6 4 3 3 3 3 2 2 2 2 2 2 1
  total sample size, n    160 60 54 42 48 36 30 33 36 39 28 30 32 34 36 38 20
  decision rule, d    20 8 7 6 7 5 4 5 5 5 4 4 5 5 5 5 3
  α    0.096 0.099 0.077 0.098 0.091 0.077 0.068 0.095 0.063 0.041 0.073 0.052 0.090 0.066 0.048 0.035 0.091
  β    0.100 0.090 0.091 0.067 0.050 0.071 0.093 0.047 0.060 0.074 0.066 0.078 0.032 0.039 0.047 0.055 0.075
  Expected Costs, Scenario 1    $3,600 $3,100 $3,540 $3,920 $4,480 $4,860 $5,300 $5,830 $6,360 $6,890 $7,280 $7,800 $8,320 $8,840 $9,360 $9,880 $10,200
  Expected Costs, Scenario 2    $9,200 $4,500 $4,500 $4,200 $4,480 $4,500 $4,500 $4,950 $5,400 $5,850 $5,600 $6,000 $6,400 $6,800 $7,200 $7,600 $7,000
  1. This table assumes p u  = 0.25, p l  = 0.05, α max  = β mas  = 0.1.
  2. † Assuming costs of $500 per cluster and $10 per individual sampled. ‡ Assuming costs of $300 per cluster and $50 per individual sampled. †† Too few clusters to determine a system. ‡‡ May not be applicable to CHW problem, as recommended sample size exceeds average number of households per cluster.
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Emerging Themes in Epidemiology

ISSN: 1742-7622