Epidemiology and Global Health

Science Forum: Unit of analysis issues in laboratory-based research

University of Warwick, United Kingdom
University of Sheffield, United Kingdom
University of Birmingham, United Kingdom

Jan 10, 2018

https://doi.org/10.7554/eLife.32486

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4 figures and 3 tables

Figures

Figure 1

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A strip plot showing observed lymph node size data by subject (1-12) and sample, after none and a short course of radiotherapy (Short RT).
https://doi.org/10.7554/eLife.32486.004

Figure 2

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Boxplots of residuals (observed values - fitted values) for each subject; symbols ( $∙$ ) are medians, boxes are interquartile ranges (IQR), whiskers extend to 1.5 $\times$ IQR and symbols ( $\circ$ ) outside these are suspected outliers (a).

Quantile-quantile (Q–Q) plot of the model residuals ( $\circ$ ) on the horizontal axis against theoretical residuals from a Normal distribution on the vertical axis (b).

https://doi.org/10.7554/eLife.32486.005

Appendix 1—figure 1

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Naive use of a conventional t-test on correlated (grouped by subject) data, $ρ$ = 0 (black circle ), $ρ$ = 0.2 (red circle) $ρ$ = 0.5 (blue circle) and $ρ$ = 0.8 (green circle), inflates the type I error rate (set at 5%).

(a). The type I error rate can be controlled to the required level by randomly selecting a single measurement for each subject, $ρ$ = 0 (black circle), $ρ$ = 0.2 (red circle), $ρ$ = 0.5 (blue circle) and $ρ$ = 0.8 (green circle), or made conservative ( $\leq$ 5%) by taking the mean of the measurements for each subject, $ρ$ = 0 (black open circle), $ρ$ = 0.2 (red open circle), $ρ$ = 0.5 (blue open circle) and $ρ$ = 0.8 (green open circle) (b). The relative efficiency of treatment effect estimates declines as the number of clusters become smaller and is always higher for the mean than the randomly selected single measurement strategy (c). The scenarios (i) – (vi) are as described in the text.

https://doi.org/10.7554/eLife.32486.008

Appendix 2—figure 1

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Design options for a putative laboratory study testing $n$ samples of experimental material.
https://doi.org/10.7554/eLife.32486.010

Tables

Table 1

Variance inflation factors for cluster sizes ( $m$ ) 2, 5, 10 and 20, and intraclass correlation coefficients (ICC) 0.01, 0.05, 0.1 and 0.5.

https://doi.org/10.7554/eLife.32486.002

$m$	ICC
	0.01	0.05	0.1	0.5
2	1.01	1.05	1.10	1.50
5	1.04	1.20	1.40	3.00
10	1.09	1.45	1.90	5.50
20	1.19	1.95	2.90	10.50

Table 2

Lymph node sizes (mm), by sample slice and subject, by radiotherapy (RT) group, subjects 1 to 6 no RT and subjects 7 to 12 short RT; highlighted cells are those removed to unbalance the design.

https://doi.org/10.7554/eLife.32486.003

None					Short RT
Subject	Sample	Slice			Subject	Sample	Slice
		1	2	3			1	2	3
1	1	1.71	1.98	1.88	7	1	2.37	2.36	2.20
	2	1.72	1.98	1.85		2	2.36	2.62	2.60
2	1	2.51	2.55	2.65	8	1	1.33	1.35	1.15
	2	2.98	3.20	2.80		2	1.90	1.87	1.85
3	1	1.69	1.72	1.80	9	1	1.70	1.78	1.78
	2	1.82	1.97	1.73		2	2.07	1.76	1.85
4	1	1.72	1.78	2.04	10	1	2.23	2.14	2.21
	2	2.50	2.65	2.77		2	2.50	2.33	2.16
5	1	3.32	3.27	3.07	11	1	2.10	1.89	1.75
	2	3.11	3.03	3.11		2	2.11	2.16	2.12
6	1	2.33	2.48	2.53	12	1	2.58	2.54	2.59
	2	2.86	2.87	2.52		2	2.77	2.65	2.60

Table 3

Number of five selected lymph nodes with maximum diameters $\geq$ 2mm, for up to five tissue samples per subject (1-12), after either none or a short course of radiotherapy (Short RT).

https://doi.org/10.7554/eLife.32486.006

None						Short RT
Subject	Sample					Subject	Sample
	1	2	3	4	5		1	2	3	4	5
1	4	4	-	-	-	7	1	0	0	0	0
2	3	4	5	2	-	8	1	2	-	-	-
3	2	3	3	2	-	9	1	0	1	0	2
4	2	4	1	2	1	10	2	1	4	0	2
5	3	4	4	3	5	11	4	2	4	3	3
6	2	5	5	3	3	12	3	4	3	-	-

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Nick R Parsons
M Dawn Teare
Alice J Sitch

(2018)

Science Forum: Unit of analysis issues in laboratory-based research

eLife 7:e32486.

https://doi.org/10.7554/eLife.32486

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A strip plot showing observed lymph node size data by subject (1-12) and sample, after none and a short course of radiotherapy (Short RT).

Boxplots of residuals (observed values - fitted values) for each subject; symbols (∙) are medians, boxes are interquartile ranges (IQR), whiskers extend to 1.5×IQR and symbols (∘) outside these are suspected outliers (a).

Naive use of a conventional t-test on correlated (grouped by subject) data, ρ = 0 (black circle ), ρ = 0.2 (red circle) ρ = 0.5 (blue circle) and ρ = 0.8 (green circle), inflates the type I error rate (set at 5%).

Design options for a putative laboratory study testing n samples of experimental material.

Variance inflation factors for cluster sizes (m) 2, 5, 10 and 20, and intraclass correlation coefficients (ICC) 0.01, 0.05, 0.1 and 0.5.

Lymph node sizes (mm), by sample slice and subject, by radiotherapy (RT) group, subjects 1 to 6 no RT and subjects 7 to 12 short RT; highlighted cells are those removed to unbalance the design.

Number of five selected lymph nodes with maximum diameters ≥2mm, for up to five tissue samples per subject (1-12), after either none or a short course of radiotherapy (Short RT).

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

Boxplots of residuals (observed values - fitted values) for each subject; symbols ( $∙$ ) are medians, boxes are interquartile ranges (IQR), whiskers extend to 1.5 $\times$ IQR and symbols ( $\circ$ ) outside these are suspected outliers (a).

Naive use of a conventional t-test on correlated (grouped by subject) data, $ρ$ = 0 (black circle ), $ρ$ = 0.2 (red circle) $ρ$ = 0.5 (blue circle) and $ρ$ = 0.8 (green circle), inflates the type I error rate (set at 5%).

Design options for a putative laboratory study testing $n$ samples of experimental material.

Variance inflation factors for cluster sizes ( $m$ ) 2, 5, 10 and 20, and intraclass correlation coefficients (ICC) 0.01, 0.05, 0.1 and 0.5.

Number of five selected lymph nodes with maximum diameters $\geq$ 2mm, for up to five tissue samples per subject (1-12), after either none or a short course of radiotherapy (Short RT).