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Table 1 Median, minimum and maximum probability of an observation from an ‘in control’ process falling below the lower limit, and above the upper limit, of 95% and 99.8% funnel plot control limits for the SMR using three different methods to calculate the limits

From: The probability of being identified as an outlier with commonly used funnel plot control limits for the standardised mortality ratio

  Wald confidence interval ‘Exact’ confidence interval Prediction interval
λ Median Min Max Median Min Max Median Min Max
95% control limits         
Lower          
1-50 0.0184 0 0.0250 0.0325 0.0219 0.3679 0.0186 0 0.0250
>50-100 0.0216 0.0172 0.0251 0.0287 0.0248 0.0351 0.0215 0.0172 0.0250
>100-500 0.0233 0.0194 0.0251 0.0267 0.0248 0.0317 0.0233 0.0194 0.0250
>500-1000 0.0240 0.0225 0.0251 0.0261 0.0249 0.0277 0.0239 0.0224 0.0250
>1000-10000 0.0246 0.0232 0.0250 0.0254 0.0250 0.0269 0.0246 0.0232 0.0250
Upper          
1-50 0.0301 0.0203 0.0841 0.0121 0.0003 0.0177 0.0201 0.0052 0.0250
>50-100 0.0280 0.0247 0.0331 0.0166 0.0129 0.0196 0.0220 0.0184 0.0250
>100-500 0.0266 0.0248 0.0307 0.0203 0.0157 0.0225 0.0234 0.0200 0.0250
>500-1000 0.0260 0.0249 0.0275 0.0220 0.0203 0.0232 0.0240 0.0226 0.0250
>1000-10000 0.0254 0.0249 0.0268 0.0238 0.0216 0.0244 0.0246 0.0233 0.0250
99.8% control limits         
Lower          
1-50 0.0002 0 0.0006 0.0028 0.0016 0.3679 0.0006 0 0.0010
>50-100 0.0005 0.0003 0.0007 0.0017 0.0014 0.0026 0.0008 0.0006 0.0010
>100-500 0.0007 0.0005 0.0009 0.0013 0.0012 0.0020 0.0009 0.0007 0.0010
>500-1000 0.0008 0.0007 0.0009 0.0012 0.0011 0.0013 0.0009 0.0009 0.0010
>1000-10000 0.0009 0.0008 0.0010 0.0011 0.0010 0.0012 0.0010 0.0009 0.0010
Upper          
1-50 0.0021 0.0014 0.0133 0.0002 0.0000 0.0004 0.0007 0.0002 0.0010
>50-100 0.0016 0.0013 0.0021 0.0004 0.0002 0.0005 0.0008 0.0007 0.0010
>100-500 0.0013 0.0011 0.0018 0.0006 0.0004 0.0007 0.0009 0.0007 0.0010
>500-1000 0.0011 0.0011 0.0013 0.0007 0.0006 0.0008 0.0009 0.0009 0.0010
>1000-10000 0.0011 0.0010 0.0012 0.0009 0.0007 0.0009 0.0010 0.0009 0.0010
  1. The probabilities here are calculated directly from the cumulative Poisson distribution.