PROFESSOR J N R JEFFERS. Glenside, Oxenholme Kendal, Cumbria LA9 7RF. Telephone [withheld] Fax [withheld] Mobile [withheld].

19th February 1997

Mrs Elizabeth Vaughan. Croft End, Lowick Bridge Cumbria LA12 8EE

Dear Liz

Thank you for the two small items that you faxed me the other day.

I was interested in the league tables for 5-year and 14-year old children that you sent me a few weeks ago, principally because they are excellent examples of how not to present information - unless you are determined to distort that presentation in favour of a particular argument. I often use data sets of this kind as case studies for my students, and you may be interested to see the case study that I have prepared for these particular data.

As you will see, the way in which districts were chosen for fluoridation does not allow of any rational judgement about the effects - beneficial or otherwise - of the effects of fluoridation.

There are too many other factors which are confounded with the allocation of districts to treated and untreated groups. The league tables would have you believe otherwise.

Yours sincerely

John Jeffers

**Case Study No. 226: English dental health records**

The attached tables give scores of decayed, missing and filled teeth (DMFT) for 5-year old children in 1993/4 and for 14-year old children in 1994/5 from English towns and districts. The data are given in the form of league tables, presumably with the aim of highlighting the advantages of fluoridation of water supplies, the districts receiving fluoridation being shadowed in the tables.

However, merely placing the scores in league tables loses some of the important information which is revealed by the scores themselves. A more formal analysis of the results is required to show the range of the scores and the differences between the two age groups.

The table below shows the mean, standard deviation, minimum, median and maximum for the scores of the two age groups.

Age | 5 | 14 |
---|---|---|

Size | 175 | 178 |

Mean | 1.74 | 1.682 |

StDev | 0.656 | 0.549 |

Min | 0.62 | 0.92 |

LQ | 1.22 | 1.3 |

Med | 1.65 | 1.55 |

UQ | 2.18 | 1.89 |

Max | 3.45 | 3.78 |

The scores for 5-year old children in 1993/4 ranged from 0.62 to 3.45, with a mean of 1.74 and a standard deviation of 0.656. The median score, however, was 1.65. The scores for 14-year old children ranged from 0.92 to 3.78, with a mean of 1.68 and a standard deviation of 0.549. Again, the median score was somewhat lower at 1.55.

**Counts on DMFT of 5-year children**

The distribution of the scores for the 5-year old children is markedly skewed towards the higher scores, with a number of conspicuous outliers at the higher values for districts in the north and west of England.

**Counts on DMFT of 14-year old children**

The distribution of the scores for the 14-year old children is even more highly skewed towards the higher scores than that of the 5-year old children, with a large number of outliers among the higher scores, again for districts in the north and west of England.

Calculating the difference between the scores for the 5-year old children in 1993/4 and the 14-year old children in 1994/5 (i.e. 14-year old score - 5-year old score) for the same districts, gave differences that ranged from -1.4 to 0.74, with a mean difference of -0.055 and a standard deviation of 0.395. There was, therefore, no significant mean difference between the scores for the two age groups of children from the same district (0.085 ± 0.03, t=l.85 with 173 df, p=0.066)

The distribution of the differences, as shown in the figure below, is markedly skewed towards the lower differences, suggesting that there were marked reductions in the DMFT in the 14-year old children by comparison with the 5-year old children in some districts, and especially in Newham and in Bloomsbury.

**Counts on differences in DMFT between 5-year and 14-year old children in the same district**

The relationship between the DMFT values for the 14-year old children in 1994/5 and those for the 5-year old children in 1993/4 is shown in more detail in the figure on the following page. Clearly, the relationship is not linear, the slope of the fitted curve increasing as the DMFT values increase for the 5-year old children.

**Regression of 14-year DFMT on 5-year DFMT**

**Linear Regression Analysis**

Response: log (14-years DMFT)

Col | Name | CoEff | StErr | p-val | SS |
---|---|---|---|---|---|

0 | Cons. | -0.069 | 0.017 | 0 | 7.393 |

1 | 5yrs | 0.158 | 0.009 | 0 | 1.872 |

df: | RSq: | s: | RSS: | ||

172 | 0.632 | 0.08 | 1.091 |

The regression of the logarithm of the 14-year old DMFT values in 1994/5 on the untransformed 5-year old DMFT values in 1993/4 accounts for 63.2% of the variability in the logarithmically transformed values.

Thirty-one of the districts are shown in the records as having fluoride added to the water supplies, and the table below gives the mean DMFT values of 5-year old children in 1993/4 and 14-year old children in 1994/4 for both untreated and treated districts.

Mean DMFT | 5yos | 14yos |
---|---|---|

± standard error | ||

Untreated | 1.85 ± 0.053 | 1.74 ± 0.048 |

Treated | 1.22 ± 0.085 | 1.41 ± 0.044 |

The mean DMFT values for districts recorded as receiving fluoride treatments were appreciably lower than those for the districts which are recorded as having no added fluoride. However, the selection of districts for treatments was not at random from all of the possible districts, and the effects of fluoride treatments may therefore well be confounded with other differences, such as the source of the water supplies, nutrition of the population, unemployment, etc.

The regressions of the 14-year olds DMFT values on those of the 5-year olds for both untreated and treated districts are summarised in the tables on the following page, and also in the following graph.

**Linear Regression Analysis**

Response: DMFT of 14 year-old children

Col | Name | CoEff | StErr | p-val | SS |
---|---|---|---|---|---|

0 | Cons. | 0.382 | 0.090 | 0 | 435.945 |

1 | 5yrs | 0.736 | 0.046 | 0 | 31.358 |

df: | RSq: | s: | RSS: | ||

141 | 0.648 | 0.347 | 17.021 |

**Linear Regression Analysis**

Response: DMFT of 14 year-old children

Col | Name | CoEff | StErr | p-val | SS |
---|---|---|---|---|---|

0 | Cons. | 0.969 | 0.091 | 0 | 61.237 |

1 | 5yrs | 0.358 | 0.070 | 0 | 0.852 |

df: | RSq: | s: | RSS: | ||

29 | 0.475 | 0.18 | 0.94 |

The increase in the DMFT values of 14-year old children with increases in the DMFT values of the 5-year old children in the same district was significantly smaller for districts which had received fluoride treatment than for districts which had not received'any fluoride treatment. However, the same caveat' applied to the differences between the mean values applies equally.to the differences between the regression coefficients. Because the districts treated with fluoride were not selected at random from all possible districts, any differences ascribed to the effects of fluoride are confounded with other environmental or social differences.

This brief analysis emphasises the dangers of presenting these kinds of data as 'league tables'. Anyone scanning the tables is tempted to ascribe any apparent differences to the effects of fluoride, whereas those differences may be due to one or more other factors confounded with the subjective choice of districts for fluoride treatment.

J N R Jeffers. 17 February, 1997.