Skip to main content

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.
Back to article page

BMC Medical Research Methodology

ISSN: 1471-2288

Contact us