Extending the Statistical Analysis and Graphical Presentation of Toxicity Test Results Using Standardized Effect Sizes

Indications of Toxicity

Toxicity tests are conducted on the assumption that if there are no differences in the expression of the biomarkers between treated and control groups, it is unlikely that the test material is toxic at the dose levels and by the route and protocol tested. This also assumes that there are no other indications of toxicity such as pathological lesions or alterations in growth rate.

Where “statistically significant” changes are noted, their toxicological significance needs to be interpreted by a toxicologist, taking into account likely human exposure and the possibility that it is a false-positive result. The nature of the changes in the biomarkers may also indicate the target organ that has been affected. When a test substance is toxic, the expression of some biomarkers will change, with some going up while others go down. The net effect is to increase the variability between different biomarkers (as seen in several of the examples presented subsequently), an effect that can be quantified and tested statistically if the biomarkers are all measured in SES units. In particular subtle, but statistically insignificant, changes in several biomarkers may be of more toxicological importance than if a single marker is changed “significantly,” particularly as the latter may be a false-positive result. An overall “bootstrap” test, which takes account of changes in all biomarkers simultaneously, is described here. It should help to distinguish between real effects and false positives due to sampling variation.

Tables

When the means and SDs are converted to SESs, all biomarkers are expressed in the same SD units. Tables can then be sorted according to the response, usually at the highest dose level. In most cases, these tables can be abbreviated showing the identity of the biomarker, the units, the sex, and the estimated SES value, perhaps omitting those biomarkers where the SES is less than a certain threshold. This focuses attention on the biomarkers that have changed most.

Dot Plots of a Single Vector of SESs

The distribution of a single vector of SESs (i.e., all the biomarkers for a single treatment level) can be shown graphically using dot plots. The axes need to be reversed (i.e., the X-axis is the SES value and the Y-axis is the biomarker) in order to accommodate the labels. Vertical lines show statistical significance at one or more specified probability levels. These plots are useful when there are only 2 treatments, usually a control and a treated group as only one set of SES1 can be calculated. They may also be used to show the distribution of any single set of SESs such as one comparing the control with the top dose group.

The Quantile–Quantile Plot

Whether a set of observations has a normal distribution can be assessed visually using a quantile–quantile (qq) plot (Crawley 2005). A straight line indicates that the points are normally distributed. Deviation from the straight line will indicate nonnormality such as skewness or kurtosis (flattening or peaking of a normal curve). Outliers are also clearly seen. Such plots can be used for any set of SESs, but they are most powerful for detecting an effect when the SESs are pooled across treatment groups. Empirically, it is observed that a vector of SESs either from a single treatment or by pooling across treatment groups will often be normally distributed in the absence of a treatment effect, although any serious outliers, which may be due to errors, may need to be removed. This is not a rigorous test, but it adds to any general evidence of toxicity.

Line Plots

Line plots join up points relating to the same biomarker across treatments. They show the pattern of response and any outliers. They can be used in many ways such as looking at SESs for individual or a few biomarkers, subsets such as hematology, biochemistry, and organs, or gender differences in response. However, if there are many biomarkers, it can be difficult to follow and label individual lines or assess visually whether the variation is the same in each group because the plots become saturated with lines.

Box and Whisker Plots

A box and whisker plot is useful for assessing the variation in a set of data. The median is shown as a horizontal line. The box is drawn round the interquartile range. The whiskers show the largest and smallest values that lie within 1.5 times the box size. Points outside that range are classified as outliers and are shown as circles (Crawley 2005). Typically, a box plot could be shown for SESs associated with each treatment group.

A Test of Normality of SESs

A Shapiro–Wilks test can be used to assess whether a set of SESs has a normal distribution. It assumes that the data are independent observations. This assumption may not be true for a set of SESs from a single treatment group, where there is a treatment effect, due to correlations between biomarkers. But in the absence of a treatment effect, the variation will be largely due to random effects such as individual differences and measurement error. Pooling the SESs across treatment groups and using the Shapiro–Wilks test for normality may be a suitable way showing the absence of a treatment effect, such as is commonly seen when testing genetically modified (GM) crops. It may lack power if there are less than about 40 SESs and may be oversensitive and detect trivial deviations from normality if there are more than about 400 SESs (Oztuna, Elhan, and Tuccar 2006).

A Bootstrap Test to Compare the Variability Within 2 Sets of SESs

The box plots and line plots may suggest that there is more variation; and therefore, more toxicity among the biomarkers (when transformed to SESs) in higher than that in lower dose groups. In tests involving GM crops, the experiment may include one or more commercial varieties in addition to the isogenic control and the GM food. If the GM food is toxic, the variation among the SESs should be greater in the control versus GM than in the control versus a commercial variety. The test described here is used to investigate both such situations.

The mean of the absolute values of each set of SESs can give an indication of the relative magnitude of a response in experiments where there are 3 or more treatment groups. Confidence intervals could be estimated using the bootstrap method. However, the test described here can be used to test whether the mean absolute response differs among treatment groups.

Most common statistical tests assume that the observations are independent. However, this cannot be assumed in the case of a vector of SESs comprising, say, data on hematological and biochemical biomarkers.

Bootstrap tests, which depend on repeated resampling of the observations with replacement, do not make this assumption (Chihara and Hesterberg 2013). The version given here provides a test of the null hypothesis that the variation is the same in 2 set of SESs. The test could be of value in setting NOELs.

The test is as follows:

This involves repeatedly resampling the vector of differences with replacement. The bootstrap sampling distribution is then used to set a specified confidence interval for the mean. If this confidence interval spans 0, then the variation in 2 sets of SESs do not differ at the specified probability level.

Although this test is not available in most statistical packages, it only takes a few lines of code in the R statistical package (Chihara and Hesterberg 2013). A one-sample t test may be a sufficiently good approximation of the one-sample bootstrap, as SESs seem to behave as though they are independent observations even though they clearly are not.

All calculations and graphics were done using the R statistical package version 2.13.0 (Dalgaard 2003; R Development Core Team 2011). Tables of SESs can also be calculated from means and SDs using an EXCEL spreadsheet. A good statistical package is required to draw the graphs.

Preparation of Data

Tables of means and SDs or standard errors from each published article were copied to an EXCEL spreadsheet and put into a standardized format with the biomarkers as rows and the treatment means and SDs as columns. In some articles, biomarkers appeared to have been measured at or close to the limits of detection. Any biomarker where an SD was given as 0 or as a single digit was deleted, as it is not possible to estimate an SES (or a t value) from such data. Even using data expressed to two significant digits will have resulted in some rounding errors, leading in some cases to excessive numbers of biomarkers with an SES of 0. Such rounding errors should be less of a problem when raw data are available. It is usually suggested that tabular data should be presented with three significant digits (Festing and Altman 2002).

Occasionally authors stated that the results are presented as means and standard errors when the analysis showed that they were means and SDs.

d-Psicose is a rare sugar occurring in small concentrations in natural foods. It was fed to 10 male Wistar rats at the rate of 3% in the diet for 90 days with 3% sucrose as the control (Matsuo, Ishii, and Shirai 2012). Data were published on 42 biomarkers including 13 body and relative organ weights, 7 intestinal (weight, length, area, etc.), and 22 serum biomarkers including clinical chemistry and hematology.

Table 1 shows the means and SDs (from the article), the estimated SESs, Student’s t, and statistical significance at the 5% level according to the authors, with all rows sorted on the SES1 values. For brevity, only the 19 most extreme SES values are shown. A negative value indicates that the observation in the treated group had a lower value than the control group, a positive value indicates the opposite. The table draws attention to the magnitude of the response for those biomarkers that are most altered.

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Table 1.

Data from Matsuo et al. (2012) showing means, standard deviations, and SESs of biomarkers.

Biomarker	Units	Mean1	sd1	Mean2	sd2	T	SES1a	Significanceb
MCH	pg	17.10	0.40	16.30	0.20	−5.66	−2.53	*
MCV	fl	51.00	1.40	48.20	0.80	−5.49	−2.46	*
UA	mg/100 ml	1.06	0.16	0.81	0.07	−4.53	−2.02	*
Ht	%	45.60	0.80	45.00	0.90	−1.58	−0.70
Fe	µg/100 ml	119.00	19.00	107.00	16.00	−1.53	−0.68
23 Biomarkers with SESs > −0.5 and <0.5 are omitted for brevity
Lg.intest.len.	×10−2·m	18.40	1.97	19.60	1.90	1.39	0.62
BUN	mg/100 ml	18.30	3.60	20.50	1.90	1.71	0.76
Lg.intest.wt	g	1.07	0.14	1.19	0.16	1.78	0.80
MCHC		33.50	0.40	33.90	0.40	2.24	1.00	*
Liver	g	8.98	0.92	10.10	1.26	2.27	1.02	*
TG	mg/100 ml	42.20	21.90	68.10	28.00	2.30	1.03
PLT	×104/µl	64.70	6.30	71.80	6.30	2.52	1.13	*
ALBU	g/100 ml	4.63	0.13	4.79	0.15	2.55	1.14	*
TP	g/100 ml	6.01	0.12	6.22	0.22	2.65	1.19	*
RBC	×104/µl	896.00	27.00	936.00	28.00	3.25	1.45	*
GLU	mg/100 ml	142.00	17.00	173.00	18.00	3.96	1.77
Kidneys	g	2.01	0.13	2.30	0.18	4.13	1.85	*
Ca	mg/100 ml	10.00	0.10	10.30	0.20	4.24	1.90
WBC	×102/µl	30.90	5.40	44.40	3.70	6.52	2.92	*

Note: ALBU = albumin; BUN = blood urea nitrogen; Ca = calcium; GLU = glucose; Lg.intest.len. = large intestine length; Lg.intest.wt = large intestine weight; MCH = mean corpuscular hemoglobin; MCHC = mean corpuscular hemoglobin concentration; MCV = mean corpuscular volume; PLT = platelet; RBC = red blood cell; SES = standardized effect size; TG = triglyceride; TP = total protein; UA = urinary acid. For brevity, biomarkers with an SES between −0.5 and +0.5 have been omitted. Student’s t value is also shown. The critical value of t with 2 groups of 10 subjects is 2.228. By equation (3), this corresponds to an SES value of 1.00. Asterisks are by the authors and indicate statistical significance at the 5% level. According to this analysis, TG, GLU, and Ca should have also been judged to be statistically significant.

^a The first S E S = ( 16 . 3 0 − 17 . 1 0 ) / 0 . 4 2 + 0. 2 2 / 2 = − 2 . 53 , as shown in equation (1).

^b According to the authors.

Table 1 contains excessive detail and is only shown to demonstrate the method. An example of the sort of table that might be used to summarize the numerical results is shown in Table 2 (data from Lindeblad et al. 2010). In this case, the means and SDs are not shown as it is assumed that these will be given in accompanying tables as is usual at present. The results are sorted on the top dose group, which is usually the group of most interest. The sexes have been pooled so any sex difference in sensitivity can be assessed. Here the response is about equal to 14/24, of these more extreme values being male and 10/24 being female.

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Table 2.

SESs for 34 biomarkers and 3 dose levels (100, 500, and 2,000 mg/kg/day of pentamethylchromanol administered to rats and sorted by the top dose level (Lindeblad et al. 2010).

	Biomarker	Sex	SES1 (100)	SES2 (500)	SES3 (2,000)
1	HGB	Females	0.00	−1.53	−3.86
2	RBC	Females	0.00	−2.35	−3.79
3	HCT	Females	−0.14	−1.94	−3.63
4	PT	Males	−0.72	−1.63	−3.08
5	HCT	Males	0.54	−0.27	−2.32
6	ALP	Males	−0.21	−0.90	−2.21
7	RBC	Males	0.49	−0.49	−2.10
8	ALP	Females	−0.35	−0.94	−1.83
9	IP	Males	−0.84	−0.85	−1.11
10	HGB	Males	0.46	−0.53	−1.10
Biomarkers where SES3 is >−0.94 and <0.94 omitted for brevity
21	CREA	Males	0.00	0.00	1.00
22	WBC	Females	0.00	0.49	1.31
23	BUN	Females	−0.23	0.26	1.35
24	PLT	Males	0.06	0.96	1.47
25	BUN	Males	−0.12	−0.12	1.88
26	RETIC	Males	0.00	1.46	2.30
27	ALT	Males	0.00	0.12	2.32
28	TP	Females	0.49	1.31	2.43
29	FBGN	Males	0.97	2.04	2.51
30	RETIC	Females	−0.59	1.57	3.14
31	CHOL	Males	−0.07	1.18	3.15
32	TBILI	Females	0.66	1.08	3.16
33	CHOL	Females	1.90	2.49	5.02
34	TBILI	Males	−0.49	0.39	6.98

Note: ALT = alanine aminotransferase; ALP = alkaline phosphatase; BUN = blood urea nitrogen; CHOL = cholesterol; CREA = creatinine; HCT = hematocrit; HGB = hemoglobin; IP = inorganic phosphorus; PT = prothrombin time; PLT = platelet; RBC = red blood cell; RETIC = reticulocyte; SES = standardized effect size; TBILI = total bilirubin; TP = total protein; WBC = white blood cell. The critical value for statistical significance at the 5% level, two tailed is ±0.94.

A dot plot of SES1 data from Table 1 is shown in Figure 1. Biomarkers where there is a statistically significant (p < .05, 2 sided) difference between the treated and the control group stand out quite well. However, the authors concluded that in the absence of any pathological findings “… the present study found no adverse effects of d-psicose in rats fed a diet containing 3% d-psicose for 90 days.”

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Figure 1.

The SES1 from Table 1 shown graphically (Matsuo et al. 2012). Note that the axes have been exchanged in order to accommodate the biomarker labels, and 23 points have been omitted, as in the table. Any biomarker in which the SES falls outside the inner dotted lines is statistically significant at p < .05. Points falling outside the dashed lines are significant at p < .01. SES = standardized effect size.

In contrast, Figure 2 shows a similar dot plot for a comparison of a diet containing a GM maize with its near isogenic control. It clearly shows the problems associated with multiple testing. Altogether there are 6 points that are significant at the 5% level and 1 at the 1% level. But with 90 tests, we would expect nearly that number to arise simply by chance. The bootstrap test that also takes into account any trends in biomarkers that are not significant provides a single p value that is not subject to false positives due to multiple testing.

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Figure 2.

Dot plot of most extreme values of SES1 from a toxicity test comparing GM maize with its isogenic control with 12 rats per group. Data from Delaney et al. (2013). Inner dotted lines indicate statistical significance at p = .05 and dashed lines indicate p = .01. Sixty-four intermediate values have been omitted. Ninety biomarkers are tested here. The statistically significant effects are probably type I errors due to the level of multiple testing. GM = genetically modified; SES = standardized effect size.

A qq plot of the data in Table 1 is shown in Figure 3. Even though the sample size was a bit low for adequate statistical power, the Shapiro–Wilks test gave a p value of <.001, so the null hypothesis that the data are normally distributed should be rejected. In contrast, Figure 4 shows a qq plot from a study of GM maize (Mackenzie et al. 2007) involving 380 SESs pooled across 4 different comparisons. The Shapiro–Wilks test gave a p value of .55. The null hypothesis cannot be rejected, and we can conclude that there is no evidence of a treatment effect in this set of data.

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Figure 3.

A qq plot of the 42 biomarkers (Matsuo et al. 2012). The three points in the lower left-hand region of the plot correspond to MCH, MCV, and UA in Table 1. The points in the right-hand top correspond to the 11 SESs exceeding 1.0 in Table 1. The Shapiro–Wilks test had a value W = 0.9048 and a p value of <.001, so the deviations from normality are unlikely to be due to chance. MCH = mean corpuscular hemoglobin; MCV = mean corpuscular volume; qq = quantile–quantile; UA = urinary acid.

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Figure 4.

qq plot for the combined biomarkers for SES1 and SES2 (both comparing GM with non-GM) and SES5 and SES7 (comparing non-GM with non-GM), a total of 380 SESs (Mackenzie et al. 2007). A p value of .544 using the Shapiro–Wilks test suggests that there is no evidence that the SESs deviate from a normal distribution, although there is clearly an excess of values of 0, probably due to rounding errors. Had the GM corn caused toxicity, deviations from normality would have been expected. GM = genetically modified; qq = quantile–quantile; SES = standardized effect size.

A line plot of SES1–SES3 for 8 selected biomarkers is shown in Figure 5. This shows how the selected biomarkers respond to a higher dose. Means and SDs come from a toxicity test in which groups of 10 male and female Sprague-Dawley rats were dosed orally with pentamethylchromanol at the rate of 0, 100, 500, and 2,000 mg/kg/day for 90 days (Lindeblad et al. 2010).

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Figure 5.

Line plot of 8 selected biomarkers from a toxicity test with a control and 3 groups dosed with pentamethylchromanol at the rate of 0, 100, 500, and 2,000 mg/kg/day for 90 days (Lindeblad et al. 2010). Labeling of the lines is only possible when a small subset of biomarkers is being shown. Dashed lines show statistical significance at p = .05.

A line plot and a box plot of SES1, SES2, and SES3 in the same study are shown in Figure 6. This includes all 36 hematological and biochemical biomarkers and both sexes. In the line plot, it is not possible to label individual biomarkers, but the plot shows the general pattern of response. There was an obvious outlier at the 500 dose level, which was almost certainly due to a transcription error.

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Figure 6.

Line plot (left) and box plot showing all 36 biomarkers pooling sexes in a 90-day repeat-dose toxicity assessment of pentamethylchromanol (Lindeblad et al. 2010). Doses of 0, 100, 500, and 2,000 mg/kg/day were administered to rats by gavage. The box plot clearly shows the increased variation among the biomarkers at higher dose levels. The outlier at the 500 dose level is clearly a misprint in the original article. Dashed lines indicate statistical significance at p = .05.

The box plot shows more clearly the increased variation as the dose group increases: evidence of toxicity. The authors concluded that “in female rats, the NOAEL was not established due to statistically significant and biologically meaningful increases in cholesterol level seen in the 100 mg/kg/day dose group.” A table like Table 2 needs to be included to see which biomarkers were most affected. Sex differences can also be seen if the 2 sexes are pooled.

Line plots and box plots of the results of a study in which Litsea elliptica essential oil was administered by gavage to female Sprague-Dawley rats at doses of 125, 250, and 500 mg/kg, for 28 consecutive days are shown in Figure 7 (Budin et al. 2012). There were some serious outliers, but these were not dose related. The means of the absolute values of the 3 SESs were 0.56, 0.49, and 0.55, implying no dose-related differences, and the box plot shows no evidence of increased variation at higher-dose levels. A table like Table 2 needs to be consulted to see that these outliers are related to hematological parameters. The authors found no histological evidence of toxicity and concluded that “L. elliptica essential oil can be classified in the U group, which is defined as a group unlikely to present an acute hazard according to World Health Organization classification.”

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Figure 7.

Litsea elliptica essential oil was administered by gavage to female Sprague-Dawley rats at doses of 125, 250, and 500 mg/kg, for 28 consecutive days (Budin et al. 2012). (A) Line plot of the SESs for 25 biomarkers at these doses. Dashed lines indicate statistical significance at p = .05. (B) Box and whisker plots of the same data. There is no evidence that the variation among biomarkers is greater at the high doses than at the lower ones. SES = standardized effect size.

Line and box plots for a 90-day oral toxicity study in male and female F344 rats fed a powdered diet containing 0, 0.06, 0.5, 1.5, or 5.0% concentrations of l-serine for 90 days are shown in Figure 8. The plot includes data for 73 biomarkers (Tada et al. 2010). The mean of the absolute values of SES1–SES4 (the 4 dose levels) are 0.46, 0.43, 0.53, and 0.94, respectively, suggesting a response at the top dose level. A bootstrap test (see example subsequently) shows that SES3 does not differ significantly from SES1, but SES1 and SES4 do differ at p < .05.

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Figure 8.

Line and box plots of the SESs for 73 biomarkers at 4 oral dose levels (0, 0.06, 0.5, 1.5, and 5.0% corresponding to SES1–SES4) in a 90-day toxicity study of l-serine in F344 rats (Tada et al. 2010). Note that here the line plot is nearly saturated, but the box plot suggests that there is increased variability among the biomarkers at the top dose level. Dashed lines indicate statistical significance at p = .05. SES = standardized effect size.

The line plot is virtually saturated so subsets of the biomarkers, such as hematology, relative organ weight, and biochemistry, may be shown as in Figure 9. This shows that most of the response in the top dose group is due to changes in hematology. A table such as Table 2 needs to be consulted to see which biomarkers are most affected.

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Figure 9.

Line plots showing the hematological, relative organ weight, and biochemical results separately for the study are summarized in Figure 8. Most of the extravariation at the top dose group is associated with hematological parameters. Dashed lines indicate statistical significance at p = .05.

Tests of GM food such as maize often include the GM crop, its isogenic control, and several commercial varieties of the same food. Figure 10 shows box plots of the SESs for 95 biomarkers with all 10 pairwise comparisons of 5 diets from a 91-day oral toxicity study of GM maize using Sprague-Dawley rats of both sexes, with 12 rats per group (Mackenzie et al. 2007). If the genetic modification is toxic, a set of SESs comparing the GM food with its isogenic control should be more variable than a set comparing the isogenic control with a commercial variety. The box plots have been arranged to show the nature of each comparison.

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Figure 10.

Box plots of SESs for all possible pairwise comparisons among 5 treatment groups in a study involving GM maize (Mackenzie et al. 2007). Dotted lines indicate statistical significance at p = .05 for individual SESs. Six of the boxes (B–G) involved a comparison of a GM- with a non-GM-containing diet, 3 (H–J) involved a comparison of 2 non-GM diets, and 1 (A) compared low dose with high-dose GM-containing diets. If there is a difference in the height of the boxes and whiskers in B–G versus H–J, it is small. The bootstrap provides a test of the null hypothesis that the mean of the absolute difference between any pair of SESs is not different from 0, as is the case here. Absolute reticulocyte count (ARET) in males was deleted due to an obvious misprint in the SD in treatment 5. GM = genetically modified; SES = standardized effect size; SD = standard deviation.

The diets in the 5 diet treatment groups contained:

A bootstrap test can be used as an overall test of whether there is evidence that some sets of SESs are more variable than others, implying a greater treatment response in the more variable group. Such tests depend on repeated sampling of a set of data to obtain a bootstrap confidence interval for the variation in the data. It does not make the assumption that the SES sets (or the difference between the absolute values of the 2 sets of SESs in this case) are independent observations.

The data in Table 2 (but including all values) can be used to illustrate the method. The means of the absolute values of SES1, SES2, and SES3 are 0.36, 0.97, and 2.00 SDs, respectively. The difference between SES1 and SES2 is therefore 0.61 SDs. A single-sample bootstrap 95% confidence interval for this was 0.28 to 1.02 (note that slightly different results will be obtained if the bootstrap is repeated due to sampling variation). As it does not span 0, we reject the null hypothesis that there is no difference and conclude that the SES2 values are more variable than the SES1 values. For comparison, a single-sample t test gives a similar 95% confidence interval of 0.21 to 1.00.

A similar test comparing SES2 (mean 0.97) with SES3 (mean 2.00) gave a bootstrap 95% confidence interval of 0.48 to 1.57 (a one-sample t test gives a 95% confidence interval of 0.46–1.60). Again, this does not span 0, so we conclude that there is a significant difference in variability in SES3 compared with SES2. These are overall tests that involve all biomarkers.

The mean of the absolute values of SES1-SES10 in the data shown in Figure 10 involving GM maize ranges from 0.307 to 0.371. The bootstrap 95% confidence interval for the differences between these most extreme values is −0.135 to 0.005. As this spans 0 (just), we conclude that there is no evidence that the variability differs between any of the 10 sets of SESs (note that picking two extreme values and doing a statistical test like this to compare them will substantially increase the chance of a false positive [type I error], so it should be done with caution. A negative result should be a safe negative).

Determination of Sample Size by Power Analysis Using SESs

Power analysis is widely advocated for the determination of sample size in controlled experiments. However, it is difficult to apply in toxicity studies because it would require an estimate of the magnitude of the difference between treated and control means likely to be of toxicological importance for each biomarker. This would clearly be impossible. However, if the effect size is specified as an SES in SD units, then it would be the same for all biomarkers.

Assuming sample size is based on a comparison of the means of the control and top dose group using a two-sample t test, toxicologists would only have to specify (1) the required power (usually 90%), (2) the significance level (usually .05), (3) the sidedness of the test (always two sided in toxicity testing), and (4) whether the SES is likely to be of toxicological significance. Using widely available software (such as R), it is then easy to estimate the required sample size.

Suppose, for example, that a toxicologist wishes to be 90% sure of detecting an SES of >1.5 SDs using a two-sample t test and a 5% significance level, then power analysis software shows that a sample sizes of 11 animals per group would be needed.

Alternatively, it is equally possible to show the effect size that is likely to be detectable for a given number of animals per group. For example, a sample size of 12 animals per group will have a 90% chance of detecting an SES of >1.4 SDs and a 70% chance of detecting an SES of >1.1 SDs, assuming a 5% significance level and a two-sided t test. A sample size of n = 5 would have a 90% chance of detecting an SES of >2.4 SDs and a 70% chance of detecting an SES of >1.8 SDs, with the same assumptions. Once toxicologists become familiar with SESs, they should find it relatively easy to specify the magnitude of the effect size that they wish to be able to detect and therefore the required sample size.