# Adult Lifespan Cognitive Variability in the Cross-Sectional Cam-CAN Cohort

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*Int. J. Environ. Res. Public Health*

**2015**,

*12*(12), 15516-15530; https://doi.org/10.3390/ijerph121215003

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Cam-CAN Study

**Table 1.**Cam-CAN first-stage participants by age-group, sex, and educational attainment. Individuals were a random sample from the complete population until the end of the study accrual period.

Age | Sex | Highest Qualification | Total | |||||
---|---|---|---|---|---|---|---|---|

Female | Male | None | GCSE | A-Level | Degree | Unknown | ||

18–27 | 117 | 87 | 3 | 38 | 57 | 106 | 0 | 204 |

28–37 | 207 | 157 | 5 | 34 | 47 | 277 | 1 | 364 |

38–47 | 194 | 153 | 7 | 44 | 57 | 239 | 0 | 347 |

48–57 | 131 | 120 | 11 | 34 | 56 | 150 | 0 | 251 |

58–67 | 199 | 160 | 48 | 55 | 73 | 182 | 1 | 359 |

68–77 | 191 | 207 | 90 | 58 | 78 | 168 | 4 | 398 |

78–87 | 374 | 246 | 193 | 73 | 153 | 188 | 13 | 620 |

88+ | 95 | 42 | 55 | 12 | 32 | 31 | 7 | 137 |

Total | 1508 | 1172 | 412 | 348 | 553 | 1341 | 26 | 2680 |

#### 2.2. Variability in Terms of Statistical Properties: Measures of Location and Measures of Spread

#### 2.3. Statistical Multiple Group Tests for Median and Variance

#### 2.4. Illustrating Variability: The Box Plot

#### 2.5. Truncation: Ceiling and Floor Effects

#### 2.6. Simulated Data as Illustration

_{ij}= 150 for i = {18−27}, ⋯, {88+} and j = {≤GCSE}, {≥ A-level}. Each individual, l, within an age-education-group (l = 1, ⋯, n

_{ij}) has a score, x, generated according to a negative binomial, i.e., x

_{ijl}∼ NegBin (mean

_{ij}, sd

_{ij}).

_{ij}to be fixed for j = {≥ A-level} and varying for j = {≤GCSE}; the age-education-group variance was held fixed.

## 3. Results and Discussion

#### 3.1. Age and Heterogeneity: Challenging Perceived Wisdom about Ageing and Variability

**Figure 1.**Box plots of Cam-CAN data by age-groups: (

**a**) Wechsler immediate story recall; (

**b**) Wechsler delayed story recall; (

**c**) Mini-Mental State Examination; (

**d**) Addenbrooke’s Cognitive Examination Revised; (

**e**) category fluency; (

**f**) letter fluency. Note that the verbal fluency measures are not within a bounded range, unlike the MMSE (0–30) or story recall (0–24); the plot ranges from 0–60 to reflect a limit of one response per second. Definition of box plot: box indicates the inter-quartile range, mid-line indicates the median, box-width proportional to square-root of sample size (i.e., $\sqrt{{n}_{i}}$), whiskers extend to largest data value within 1.5 × IQR of the respective quartile, circles correspond to outliers (i.e., data values beyond the whiskers).

**Table 2.**Results of non-parametric statistical tests for equality of median and variance across all groups for measures in Figure 1. For clarity, p-values less than 0.001 are reported as <0.001.

Figure | Outcome | Mood’s Median Test | Fligner’s Variance Test |
---|---|---|---|

1a | Wechsler immediate story recall | <0.001 | 0.004 |

1b | Wechsler delayed story recall | <0.001 | 0.121 |

1c | MMSE | <0.001 | <0.001 |

1d | ACE-R | <0.001 | <0.001 |

1e | Category fluency | <0.001 | 0.013 |

1f | Letter fluency | <0.001 | 0.018 |

#### 3.2. Simulated Data: What Do True Effects Look Like?

**Table 3.**Results of non-parametric statistical tests for equality of median and variance across all groups for measures in Figure 2. The “Truth” column indicates whether the median or variance are fixed or varying (declining and increasing respectively) across the age-groups.

Figure | Outcome | Median | Variance | ||
---|---|---|---|---|---|

Truth | Mood’s Test | Truth | Fligner’s Test | ||

2a | Scenario A | Varies | <0.001 | Fixed | 0.779 |

2b | Scenario B | Fixed | 0.179 | Varies | <0.001 |

2c | Scenario C | Varies | <0.001 | Varies | <0.001 |

2d | Scenario D | Mixture | <0.001 | Fixed | <0.001 |

2e | Scenario D, ≤GCSE | Varies | <0.001 | Fixed | 0.909 |

2e | Scenario D, ≥A-Level | Fixed | 0.884 | Fixed | 0.592 |

5a | Scenario A, Truncated | Varies | <0.001 | Fixed | 0.001 |

**Figure 2.**Box plots of simulated data by age-groups: (

**a**) declining mean and fixed variance; (

**b**) fixed mean and increasing variance; (

**c**) declining mean and increasing variance; (

**d**) Simulated Scenario D is a mixture of two sub-groups (≤ GCSE, ≥A-level) with declining mean and fixed mean respectively, and both with fixed variance; as illustrated in (

**e**). As a result of this mixture of distributions, the combined Scenario D appears similar to Scenario C; within (

**d**) there is an unmeasured confounder.

#### 3.3. Confounders and Variability

**Figure 3.**Box plots of delayed story recall, subdividing age-groups by: (

**a**) sex; (

**b**) education attainment.

(a) Wechsler Delayed Story Recall | (b) Wechsler Immediate Story Recall | ||||||
---|---|---|---|---|---|---|---|

Figure | Sub-Group | Mood’s Median Test | Fligner’s Variance Test | Figure | Sub-Group | Mood’s Median Test | Fligner’s Variance Test |

1b | All | <0.001 | 0.121 | 1a | All | <0.001 | 0.004 |

3a | Female | <0.001 | 0.026 | 4a | Female | <0.001 | 0.002 |

3a | Male | <0.001 | 0.572 | 4a | Male | <0.001 | 0.561 |

3b | None | <0.001 | 0.054 | 4b | None | 0.010 | 0.155 |

3b | GCSE | <0.001 | 0.338 | 4b | GCSE | 0.016 | 0.355 |

3b | A-level | <0.001 | 0.292 | 4b | A-level | <0.001 | 0.441 |

3b | Degree | <0.001 | 0.026 | 4b | Degree | <0.001 | 0.121 |

**Figure 4.**Box plots of immediate story recall, subdividing age-groups by: (

**a**) sex; (

**b**) education attainment.

#### 3.4. Interpreting Variability in the Presence of Truncation: Floor Effects and Ceiling Effects

**Figure 5.**Illustration of the effect of truncating the range of simulated Scenario A to [0,33] (original scale was unbounded, i.e., [0,∞]). (

**a**) Box plot of truncated score, contrast with original in Figure 2a; (

**b**–

**g**) Comparisons of the histograms for the truncated and original scores over the first six age-groups. All original scores above 33 are truncated, i.e., recoded, as 33. Hence the large spikes in the truncated score histograms.

**Table 5.**Comparison of the mean, median and standard deviation across all age-intervals for the original and truncated simulated Scenario A. The true distribution of simulated Scenario A has a declining mean (and median) with constant variance. The median is robust to truncation, as long as the true median is less than the truncated score. The mean is, as expected, under-estimated in the lower age-groups; although in this example the effect is quite small. The variance (standard deviation) is incorrectly estimated for the truncated score.

Age | Mean | Median | Standard Deviation | |||
---|---|---|---|---|---|---|

All | Truncated | All | Truncated | All | Truncated | |

18–27 | 29.84 | 28.96 | 30.00 | 30.00 | 5.31 | 4.13 |

28–37 | 28.11 | 27.57 | 28.00 | 28.00 | 5.28 | 4.44 |

38–47 | 26.79 | 26.32 | 27.00 | 27.00 | 5.68 | 4.80 |

48–57 | 25.71 | 25.47 | 25.50 | 25.50 | 5.27 | 4.81 |

58–67 | 23.80 | 23.74 | 23.50 | 23.50 | 4.99 | 4.88 |

68–77 | 22.95 | 22.82 | 23.00 | 23.00 | 5.48 | 5.19 |

78–87 | 20.51 | 20.47 | 20.00 | 20.00 | 5.33 | 5.22 |

88+ | 19.59 | 19.56 | 19.50 | 19.50 | 5.52 | 5.44 |

**Figure 6.**(

**a**) Repetition of Figure 1c, note the extended y-axis to indicate the likely ceiling effect on the MMSE; (

**b**–

**g**) Histograms of the MMSE scores over the first six age-groups. The MMSE range is [0,30]. The 28–37 age-group (

**c**) have a particularly large “spike” at the maximum score, indicative of a ceiling effect.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Green, E.; Shafto, M.A.; Matthews, F.E.; Cam-CAN; White, S.R. Adult Lifespan Cognitive Variability in the Cross-Sectional Cam-CAN Cohort. *Int. J. Environ. Res. Public Health* **2015**, *12*, 15516-15530.
https://doi.org/10.3390/ijerph121215003

**AMA Style**

Green E, Shafto MA, Matthews FE, Cam-CAN, White SR. Adult Lifespan Cognitive Variability in the Cross-Sectional Cam-CAN Cohort. *International Journal of Environmental Research and Public Health*. 2015; 12(12):15516-15530.
https://doi.org/10.3390/ijerph121215003

**Chicago/Turabian Style**

Green, Emma, Meredith A. Shafto, Fiona E. Matthews, Cam-CAN, and Simon R. White. 2015. "Adult Lifespan Cognitive Variability in the Cross-Sectional Cam-CAN Cohort" *International Journal of Environmental Research and Public Health* 12, no. 12: 15516-15530.
https://doi.org/10.3390/ijerph121215003