# Analysis of rodent growth data in toxicology studies.

**ABSTRACT** To evaluate compound-related effects on the growth of rodents, body weight and food consumption data are commonly collected either weekly or biweekly in toxicology studies. Body weight gain, food consumption relative to body weight, and efficiency of food utilization can be derived from body weight and food consumption for each animal in an attempt to better understand the compound-related effects. These five parameters are commonly analyzed in toxicology studies for each sex using a one-factor analysis of variance (ANOVA) at each collection point. The objective of this manuscript is to present an alternative approach to the evaluation of compound-related effects on body weight and food consumption data from both subchronic and chronic rodent toxicology studies. This approach is to perform a repeated-measures ANOVA on a selected set of parameters and analysis intervals. Compared with a standard one-factor ANOVA, this approach uses a statistical analysis method that has greater power and reduces the number of false-positive claims, and consequently provides a succinct yet comprehensive summary of the compound-related effects. Data from a mouse carcinogenicity study are included to illustrate this repeated-measures ANOVA approach to analyzing growth data in contrast with the one-factor ANOVA approach.

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- Y Fujinami, T Fukui, K Nakano, T Ara, Y Fujigaki, Y Imamura, T Hattori, S Yanagisawa, T Kawakami, P-L Wang[Show abstract] [Hide abstract]

**ABSTRACT:**Passive smoking is the involuntary inhalation of cigarette smoke (CS) and has an adverse impact on oral health. We examined the effect of CS exposure on saliva and salivary glands (SGs). Cigarette smoke-exposed rats were intermittently housed in an animal chamber with whole-body exposure to CS until killed. Whole saliva was collected before CS exposure (0 day), and 15 and 30 days after the start of CS exposure. Saliva secretion was stimulated by administration of isoproterenol and pilocarpine after anesthesia. SGs were collected on 31 days. The increase in body weight of the CS-exposed rats was less than that of the control rats. Salivary flow rates did not differ at 0, 15 or 30 days after the start of CS exposure. However, the amylase and peroxidase activities and total protein content in the saliva were significantly lower in 15-day CS-exposed rats than in 15-day control rats. Histological examination of the SGs of CS-exposed rats showed vacuolar degeneration, vasodilation and hyperemia. These results suggest that CS exposure has adverse impacts on salivary composition and SGs, which could aggravate the oral environment.Oral Diseases 07/2009; 15(7):466-71. · 2.38 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Body weight data are routinely collected in in vivo general toxicology studies, including 2-year carcinogenicity studies, to help assess the overall health of animals. The effect of the compound on body weight is statistically evaluated for each sex separately using a linear trend test or a many-to-one test by Dunnett. These tests are performed either in the framework of a one-factor analysis of variance (ANOVA) or a repeated measures ANOVA. The one-factor ANOVA with Dunnett's test at each time point is a common practice in industry. Although each individual test is conducted at the 0.05 significance level, one wonders about the overall type I error rate and power for performing many individual Dunnett's tests. A simulation study is conducted to answer this question for general toxicology studies of durations 1 month, 3 months, and 2 years. These results provide guidance to managing multiplicity of body weight analysis of general toxicology studies.Journal of Biopharmaceutical Statistics 02/2008; 18(5):883-900. · 0.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Passive smoking is the involuntary inhalation of cigarette smoke (CS) and has an adverse impact on oral health. We examined the effect of CS exposure on caries risk and experimental dental caries. Experimental dental caries was induced in rat maxillary molars which were inoculated orally with Streptococcus mutans MT8148 and maintained on a cariogenic diet (diet 2000) and high sucrose water during the experimental period. CS-exposed rats were intermittently housed in an animal chamber with whole-body exposure to CS until killed. Whole saliva was collected before CS exposure (day 0) and for 30 days after the start of CS exposure. Saliva secretion was stimulated by administration of isoproterenol and pilocarpine after anesthesia. Maxillary molars were harvested on day 31. The increase in body weight of the CS-exposed rats was less than that of the control rats. Salivary flow rate, concentration of S. mutans in the stimulated saliva and caries activity score did not significantly differ between 0 and 30 days after the start of CS exposure. Histological examination of the caries-affected area on maxillary molars 30 days after CS exposure showed expansion compared to control rats. In the electron probe microanalysis, no differences were observed between the mineral components of the CS-exposed teeth and the control teeth. These results suggest that CS exposure expands the caries-affected area in the maxillary molars of the rat.Caries Research 11/2011; 45(6):561-7. · 2.51 Impact Factor

Page 1

Analysis of Rodent Growth Data in Toxicology Studies

Wherly P. Hoffman,*,1Daniel K. Ness,† and Robert B. L. van Lier†

*Statistics and Information Sciences and †Nonclinical Safety Assessment, Lilly Research Laboratories, Eli Lilly and Company,

Drop Code GL43, 2001 West Main Street, Greenfield, Indiana 46140

Received August 1, 2001; accepted December 11, 2001

To evaluate compound-related effects on the growth of rodents,

body weight and food consumption data are commonly collected

either weekly or biweekly in toxicology studies. Body weight gain,

food consumption relative to body weight, and efficiency of food

utilization can be derived from body weight and food consumption

for each animal in an attempt to better understand the compound-

related effects. These five parameters are commonly analyzed in

toxicology studies for each sex using a one-factor analysis of

variance (ANOVA) at each collection point. The objective of this

manuscript is to present an alternative approach to the evaluation

of compound-related effects on body weight and food consump-

tion data from both subchronic and chronic rodent toxicology

studies. This approach is to perform a repeated-measures ANOVA

on a selected set of parameters and analysis intervals. Compared

with a standard one-factor ANOVA, this approach uses a statis-

tical analysis method that has greater power and reduces the

number of false-positive claims, and consequently provides a suc-

cinct yet comprehensive summary of the compound-related ef-

fects. Data from a mouse carcinogenicity study are included to

illustrate this repeated-measures ANOVA approach to analyzing

growth data in contrast with the one-factor ANOVA approach.

Key Words: one-factor analysis of variance; repeated-measures

analysis of variance; type I error; carcinogenicity study; growth

phase; maintenance phase.

Measures of animal growth are routinely evaluated in toxi-

cology studies and are key to interpretation of compound-

related effects. Growth data based on body weight and food

consumption are collected, analyzed, and interpreted for most

rodent toxicology studies. One way to evaluate the growth data

is to analyze a few profile features from these typically non-

linear curves (Winer, 1962). For example, the linear, quadratic,

and cubic trends of the profile curves across time can be

approximated by polynomials of the 1st, 2nd and 3rd degrees,

respectively. Because it is often important in toxicology studies

to interpret compound-related effects with reference to the

specific time period, the profile analysis is not ideal. At Eli

Lilly and Company, three additional parameters are derived for

each animal: body weight gain, food consumption relative to

body weight, and efficiency of food utilization (EFU). To

smooth the data and lessen the fluctuation in food consumption

and EFU parameters, cumulative food consumption and cumu-

lative EFU values are calculated based on data collected since

the beginning of the study. Therefore, the five parameters

evaluated in rodent toxicology studies are:

● Body weight;

● Body weight gain from initial body weight;

● Cumulative daily food consumption (total food consumed

since study initiation divided by days on study);

● Cumulative daily food consumption relative to body

weight (cumulative daily food consumption divided by average

body weight);

● Cumulative EFU (body weight gain per 100 g food con-

sumed).

Depending on the duration of the study and phase of growth,

body weight and food consumption data are collected either

weekly or biweekly. Each parameter is analyzed using a one-

factor analysis of variance (ANOVA) at each time point for

each sex.

Performing a one-factor ANOVA on each of the five param-

eters for each sex at each collection point leads to an inflated

type I error rate (the probability of declaring a finding positive

when it is in fact false). Higher than expected false-positive

claims could cloud the interpretation of compound-related ef-

fects. The practice of obtaining cumulative food consumption

and cumulative efficiency of food utilization data is an attempt

to “smooth” the data to facilitate evaluation of the overall

effect of the compound on these parameters. However, poten-

tially meaningful increases or decreases are diluted by all the

previous measures. These cumulative quantities, although rea-

sonably smooth, have a limited ability to reflect temporal

effects associated with the treatment. In light of these consid-

erations, the practice of statistically analyzing five parameters

based on body weight and food consumption is re-evaluated.

The objective of this paper is to present an alternative approach

to the evaluation of rodent growth data from both subchronic

and chronic toxicology studies. An example of a 21-month

mouse carcinogenicity study is included to illustrate these

methods of analysis.

1To whom correspondence should be addressed. Fax: (317) 277-4783.

E-mail: hoffman_wherly_p@lilly.com.

TOXICOLOGICAL SCIENCES 66, 313–319 (2002)

Copyright © 2002 by the Society of Toxicology

313

Page 2

METHODS

In the evaluation of statistical methods for rodent growth data, four key

points are discussed:

● The frequency of data collection;

● A set of analysis intervals based on the growth profile of rodents;

● A set of analysis parameters to include only the essential parameters for

data interpretation;

● Statistical analyses for the growth data.

The following criteria are included in the considerations: effects on body

weight and food consumption should be associated with appropriate periods of

time, the number of parameters should be minimized to include only the

essential parameters needed for data interpretation, the statistical methods

should be robust and powerful, and inflation of type I error rate should be

minimized.

Collection Intervals

The frequency of data collection is often determined by considerations for

feeder capacity and dose calculation. In repeat-dose toxicology studies con-

ducted at Eli Lilly and Company, body weight and food consumption data are

collected weekly for up to 14 weeks and biweekly thereafter. These intervals

are chosen based on the limitations of feeder capacity and the need to adjust

doses based on recent body weight.

Analysis Intervals and Phases of Growth.

The number of analyses is kept to a minimum by defining biologically

relevant analysis intervals. Each analysis interval is defined as a collection of

one or more time intervals and is used for the statistical analysis. For example,

an analysis interval may consist of three time intervals, Weeks 6, 7, and 8.

Rodents used for toxicology studies typically begin study at 5–7 weeks of age.

In general, growth is rapid in the first 3 months and slows down thereafter for

both rats and mice (Fig. 1). Mouse body weights are typically more variable

than rat body weights. Upon review of many mouse and rat studies, the

transition point between growth and maintenance phases is determined to be

around the end of the14th week of the study. Data in the growth phase and

maintenance phase are analyzed separately.

To capture compound-related effects during the growth phase with fewer

analysis intervals, growth data are pooled across relevant time intervals to

obtain an interval average for each animal in each analysis interval. Weekly

data are retained for the first 4 weeks. After that, a three-week moving average

is obtained every two weeks at Weeks 5, 7, 9, 11, and 13. For example, the

3-week moving average at Week 7 is calculated as the average of Week 7, one

week before (Week 6), and one after (Week 8). Thereafter, during the main-

tenance phase, the growth rate is diminished and the goal is to track long-term

changes in body weight where transient effects are uncommon. It is sufficient

to pool body weights for analysis so that a single 5-week moving average is

obtained every 4 weeks at Weeks 16, 20, and 24 followed by a 15-week

moving average every 14 weeks at Weeks 33, 47, 61, 75, 89, and the midpoint

of the final analysis interval from Week 96 to the end of the study. For

example, if the duration of a study is 104 weeks, then the final moving average

at Week 100 is the average of Weeks 96–104 (Table 1). Statistical analyses

using a repeated-measures ANOVA (Vonesh and Chinichilli, 1997) on these

analysis interval averages sufficiently capture the growth profiles while keep-

ing the number of analyses to a minimum. The number of false-positive claims

due to an inflated type I error rate is reduced using this set of analysis intervals.

In calculating the analysis interval averages, missing values will lead to

missing observations for the intervals. Toward the latter part of a carcinoge-

nicity study, animals die from a variety of age-related causes and tumors. If an

animal dies in an analysis interval, then the animal will be represented in all

analysis intervals up to the one in which it died. Although data for the animal

will not be represented in the analysis interval in which it died, the loss of

information is likely to be inconsequential, as the impact of the moribundity of

individual animals in the examination of body weight effects is of less interest

than the generalized effect across surviving animals.

Analysis Parameters

Two parameters are defined for evaluating the effects of a compound on

body weight and food consumption. One is interval body weight (IntBW),

defined as the weekly measured body weight during the first 4 weeks or the

average body weight in each analysis interval thereafter. The other is interval

daily food consumption adjusted for body weight (IntFCD_BW), a derived

quantity defined as the food consumed in the analysis interval divided by the

number of days and the average body weight in this analysis interval. In

addition, changes in body weight gain at specific time points are sometimes

desired to assist in interpretation of compound-related effects. For example, for

dose selection for carcinogenicity studies that are for drug safety evaluation

(International Conference on Harmonisation, 1995), a 10% change in body

weight gain is specified as an important criterion. Therefore descriptive sta-

tistics on body weight gain can be calculated and reported without performing

inferential statistical tests, as appropriate statistical analyses are conducted on

IntBW and IntFCD_BW. For comparison purposes, the five analysis parame-

ters commonly analyzed using a one-factor ANOVA as defined in the intro-

duction are also discussed here to contrast with IntBW and IntFCD_BW.

TABLE 1

Numbers of Analysis Intervals for Rodent Studies

Time intervals

Intervals

for one-factor

ANOVAs

Intervals for

repeated-measures

ANOVAs

Weeks 1–4

Weeks 5–14

Weeks 15–26

Weeks 27–104

Weekly (t ? 4)

Weekly (t ? 10)

Every 2 weeks (t ? 6)

Every 2 weeks (t ? 39)

Total (t ? 59)

Weekly (t ? 4)

Every 2 weeks (t ? 5)

Every 4 weeks (t ? 3)

Every 14 weeks (t ? 6)

Total (t ? 18)

Note. t, number of analysis intervals in the specified period.

FIG. 1.

a 21-month carcinogenicity study and the interval body weights calculated by

averaging body weights in the analysis intervals.

Body weight profile of a female mouse in the control group from

314

HOFFMAN, NESS, AND VAN LIER

Page 3

Body weight.

function of the animal’s initial body weight, randomization by body weight

stratification at the beginning of the study is routinely carried out. This practice

minimizes the bias in group means across treatment groups, but maximizes

variability within each treatment group. Maximized variability will contribute

to a loss of statistical power unless the variability is accounted for in the

analysis. In an attempt to adjust for this variability, body weight gain has

historically been statistically analyzed. However, this adjustment is performed

under the assumption that there is a linear relationship between the initial body

weight and subsequent body weights and that the slope of the linear relation-

ship is 1. For data that do not exhibit this relationship, analyzing weight gain

can potentially induce a misleading effect and increase the variability of the

analysis. Therefore, the average body weight obtained in an analysis interval

(IntBW), along with the initial body weight as a covariate, is more appropriate

than either body weight alone or body weight gain for the evaluation of

compound-related effects on body weight.

Food consumption.

Because food consumption may be affected by the

animal’s body weight, comparing daily food consumption among treatment

groups without accounting for the body weight differential may be misleading.

Therefore, compound-related effects on food consumption are evaluated by

calculating relative daily food consumption, which is defined as daily food

consumption divided by average body weight.

As food consumption tends to fluctuate across time, one option to smooth

the data is to calculate the cumulative daily food consumption and cumulative

relative daily food consumption. However, if these cumulative quantities

include data from the beginning of the study up to the time point of interest,

any increases or decreases are diluted by all the previous measures. For

example, for a 26-week study, the actual daily food consumption in the

analysis interval of the last 2 weeks accounts for only 1/13 of the cumulative

daily food consumption and cumulative relative daily food consumption cal-

culated for that interval, thereby blunting the 6-month effects. These cumula-

tive quantities, although reasonably smooth, lose the ability to reflect temporal

effects associated with the treatment. Therefore, the relative daily food con-

sumption obtained in each analysis interval (IntFCD_BW), is more appropriate

than either of the cumulative food consumption parameters for the evaluation

of compound-related effects on food consumption.

Because body weights of an animal across time can be a

Statistical Analyses

Repeated-measures ANOVA is performed on the two analysis parameters,

IntBW and IntFCD_BW. This analysis evaluates the effects of the fixed

factors: treatment, time, and the interaction between treatment and time. The

initial body weight is included as a covariate to reduce variability and improve

precision in the analysis of body weights. The individual animal is the

experimental unit nested within the treatment groups as a random effect in the

statistical model. Compound symmetry is assumed as the default covariance

structure for each animal across time. Other covariance structures may be

selected based on current or historical data. The compound symmetry covari-

ance structure is also called an exchangeable covariance structure, in that the

correlation coefficient is the same between any two time points. For body

weight data, both the initial body weight and the random animal effect are

important to account for animal-to-animal variability. The initial body weight

accounts for the variability in animals that exists prior to treatment, whereas

the random animal effect accounts for the variability that exists during the

treatment. For food consumption data, body weight information is included in

the derivation of IntFCD_BW, and no covariate adjustments are made in the

repeated-measures ANOVA. Compound-related effects are evaluated based on

least squares means of treatment groups, which control other factors in the

model. In the absence of any significant treatment by time interactions, the

evaluation of treatment effects is simply performed on the results pooled across

analysis intervals. However, in the presence of a significant treatment by time

interaction, the treatment effects will be evaluated in each analysis interval to

describe the changing treatment effects across time. For example, consider a

study with a control and three treatment groups of increasing doses. The

contrast for testing for a linear trend in the treatment means in the second of

five time intervals is

?

i?1,...,4, j?1,...,5

cij? ?ij

where cijand ?ijare the contrast coefficient and mean for the ithgroup and jth

time interval, c12? –3, c22? –1, c32? 1, c42? 3, and all other cij? 0.

RESULTS

Female data from a 21-month mouse carcinogenicity study

were selected to illustrate the repeated-measures ANOVA

methods for analysis of the growth data. The statistical analy-

ses were performed using PROC MIXED in SAS 6.12 (SAS

Institute Inc., 1996). This study had one control group and

three treatment groups, each with 60 animals per sex. Although

body weight and food consumption data are usually collected

weekly for up to 14 weeks and biweekly thereafter, growth

data were collected weekly for this sample study. For IntBW

and IntFCD_BW, a total of nine values were obtained for each

animal for each parameter during the growth phase. These nine

values consist of four weekly values measured or derived for

the first 4 weeks and five 3-week moving averages calculated

at Weeks 5, 7, 9, 11, and 13. As the duration of this mouse

study is only 21 months, slight modification was applied to the

data collected during the maintenance phase. Eight interval

averages instead of a typical nine for 24-month studies were

obtained for each animal for each parameter. These eight

interval averages consisted of three 5-week moving averages at

Weeks 16, 20, and 24, and five 14-week moving averages

(there were only 12 weeks available for the last average) for the

rest of the study. Results of repeated-measures ANOVAs per-

formed on IntBW and IntFCD_BW summarized for each anal-

ysis interval are compared with the results from one-factor

ANOVAs on weekly data (Tables 2 and 3).

Both approaches for body weight led to consistent interpre-

tations of the data. For the repeated-measures ANOVA ap-

proach, the low-dose and mid-dose animals were variably

affected between Weeks 4 and 10, the mid-dose animals were

also affected in the first week, and the high-dose animals were

affected throughout the treatment period (Fig. 2, upper panel).

The one-factor ANOVA approach yielded similar results, with

the exception that effects in Weeks 7 and 10 in the low- and

mid-dose groups were not significant (Fig. 2, lower panel). The

magnitude of the decrease in body weight for the low- and

mid-dose groups during Weeks 7–10 was about 2–3% com-

pared with controls. Whereas the one-factor ANOVA approach

declared some 2–3% differences prior to Week 10 to be sig-

nificant, the repeated-measures approach declared a few more

significant effects of similar magnitude because of the added

statistical power. High-dose animals lost weight during the first

2-week period (see the negative weight gain in Fig. 2, lower

panel), and although high-dose animals started gaining weight

after 2 weeks, the mean body weight of the high-dose animals

315

ANALYSIS OF RODENT GROWTH DATA

Page 4

was lower than the control mean throughout the study. Results

of the repeated-measures ANOVA for body weight adjusted

for initial body weight declared a statistically significant high-

dose effect throughout the study. This was also concluded from

the one-factor ANOVA approach on both body weight and

body weight gain.

Significant differences exist in the results of the one-factor

ANOVA and repeated-measures ANOVA approaches for food

consumption because the latter is better able to isolate temporal

effects, controls variability by consolidating information in

intervals, and is more powerful (Fig. 3).

However, these two analysis methods are difficult to com-

pare directly because of considerable differences in the end

points being analyzed, namely, cumulative daily food con-

sumption, cumulative daily food consumption relative to body

weight, and the interval daily food consumption relative to

body weight. For purposes of this discussion, the most mean-

ingful contrast is between the interval daily food consumption

relative to body weight and cumulative daily food consumption

relative to body weight. The low-dose animals were unaffected

throughout the treatment period for both the one-factor

ANOVA and the repeated-measures ANOVA approaches. The

mid-dose animals were not significantly affected according to

the one-factor ANOVA, with the exception of Weeks 58, 59,

71, 72, and 73 of the study (Table 3). In the 2 weeks prior to

and 4 weeks after Weeks 71–73, mid-dose effects were mar-

ginally nonsignificant (0.05 ? p ? 0.07) based on the one-

factor ANOVA approach; however, with the repeated-mea-

sures ANOVA approach, the mid-dose effects were significant

(p ? 0.026) in the entire analysis interval. As a matter of fact,

the 4th interval and all intervals spanning Week 27 to the end

of the study were significant. The magnitude of the change that

was detected by the repeated-measures ANOVA, but not the

one-factor ANOVA approach, was 3–5% relative to controls.

High-dose effects were significant for both approaches from

Week 8 to the end of the study. The repeated-measures

ANOVA approach identified a significant effect in all intervals

earlier than Week 8, with the exception of Week 2, whereas the

one-factor ANOVA approach identified an effect only in

Weeks 1 and 2. The magnitude of the changes detected by the

repeated-measures approach, but not the one-factor ANOVA

method, was 5–9% relative to controls. By reporting data in a

TABLE 2

Summary of Statistically Significant Results on Female Growth Data in Growth Phase

Using One-Factor ANOVAs and Repeated-Measures ANOVAs

ParametersGroup

Time intervals in weeks in growth phase

1234 5, 6 7, 89, 10 11, 12 13, 14

Body weight

Low

Mid

High

—

—

Y

—

—

Y

—

—

Y

Y

Y

Y

— —

— —

Y Y

— Y

— Y

Y Y

Y —

Y —

Y Y

— —

— —

Y Y

— —

— —

Y Y

BWG and IntBW w Covariate

Low

Mid

High

—

Y

Y

—

—

Y

—

—

Y

Y

Y

Y

— —

Y Y

Y Y

z Y

z Y

Y Y

Y z

Y z

Y Y

— —

— —

Y Y

— —

— —

Y Y

CumFCD

Low

Mid

High

—

—

Y

—

—

Y

—

—

Y

—

—

Y

— —

— —

Y Y

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

CumFCD_BW and IntFCD_BW

Low

Mid

High

—

—

Y

—

—

Y

—

—

z

—

z

z

— —

— —

z z

— —

— —

z Y

— —

— —

Y Y

— —

— —

Y Y

— —

— —

Y Y

CumEFU

Low

Mid

High

—

Y

Y

—

—

Y

—

—

Y

—

Y

Y

— —

Y Y

Y Y

— Y

— Y

Y Y

— —

Y —

Y Y

— —

— —

Y Y

— —

— —

Y Y

Note. Y, p ? 0.05 from one-factor ANOVA only; z, p ? 0.05 from repeated-measures ANOVA only; bold Y, p ? 0.05 from both ANOVAs; dash (—)

indicates p ? 0.05 from both ANOVAs. Baseline body weight is included as a covariate in the model for IntBW. One-factor ANOVA is applied to body weight,

BWG (body weight gain), CumFCD (cumulative daily food consumption), CumFCD_BW (cumulative daily food consumption relative to body weight), and

CumEFU (cumulative efficiency of food utilization).The repeated-measures ANOVA is applied to IntBW (interval body weight) and IntFCD_BW (interval daily

food consumption relative to body weight) calculated for each predetermined interval.

316

HOFFMAN, NESS, AND VAN LIER

Page 5

cumulative fashion, the ability to assign a treatment effect to an

interval of time is greatly reduced. The approach of using

repeated-measures ANOVA on data calculated in each analysis

interval is superior at smoothing the irregular nature of food

consumption data, but still allows examination of time-depen-

dent effects. These points are apparent in Figure 3 and the

differential analytical results in the high- and mid-dose groups.

The smoothness in Figure 3, lower panel, is the result of

averaging cumulatively, whereas the peak at Week 33 and dip

at Week 58 in Figure 3, upper panel, reflect the temporal

effects associated with treatment in IntFCD_BW.

DISCUSSION

In contrast to the approach of performing a one-factor

ANOVA at each collection point, the repeated-measures

ANOVA alternative is to perform one repeated-measures

ANOVA for the growth phase and another for the maintenance

phase. The numbers of analyses performed on body weight and

food consumption data for each sex for one rodent study are

presented in Table 4. The repeated-measures approach of tak-

ing into account information in each phase should provide a

more succinct yet comprehensive picture in the evaluation of

compound-related effects. For example, for a typical 2-year

carcinogenicity study, the practice of analyzing weekly or

biweekly data will result in 296 one-factor ANOVAs for each

sex: one for each of the 59 collection points for each of the five

parameters and one for the initial body weight collected on Day

0. If these body weights collected at 60 time points are inde-

pendent, then a 0.05 type I error rate will be inflated to 0.95 if

60 one-factor ANOVAs are performed on the data; i.e. there is

a 95% chance of making a false-positive claim in at least one

of the 60 independent tests. As each of the 60 tests is per-

formed at the 0.05 type I error rate, for each test there is a 5%

chance of making a false-positive claim and a 95% chance of

not making that mistake. Therefore, the chance of not making

any false-positive claims in these 60 tests is 4.6% calculated as

0.046 ? (1–0.05)60, and the chance of making a false-positive

claim is 95.4% as 0.954 ? 1–0.046. Because the interpretation

of compound-related effects is based on scientific judgment,

extra effort is required to sort out and dismiss spurious findings

TABLE 3

Summary of Statistically Significant Results on Female Growth Data in Maintenance Phase

Using One-Factor ANOVA and Repeated-Measures ANOVA

Group 15–18

Time interval in weeks in maintenance phase

19–2223–26 27–3940–5253–65 66–7879–89

Body weight

Low

Mid

High

- - - -

- - - -

YYYY

- - - -

- - - -

YYYY

- - - -

- - - -

YYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - -

- - - - - - - - - - -

YYYYYYYYYYY

BWG and

IntBW w Cov

Low

Mid

High

- - - -

- - - -

YYYY

- - - -

- - - -

YYYY

- - - -

- - - -

YYYY

- - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - -

- - - - - - - - - - -

YYYYYYYYYYY

CumFCD

Low

Mid

High

- - - -

- - - -

- - - -

- - - -

- - - -

- - - -

- - - -

- - - -

- - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - - - -

- - - - - - - - - - -

- - - - - - - - - - -

- - - - - - - - - - -

CumFCD_BW and

IntFCD_BW

Low

Mid

High

- - - -

- - - -

YYYY

- - - -

- - - -

YYYY

- - - -

- - - -

YYYY

- - - - - - - - - - - - -

z z z z z z z z z z z z z

YYYYYYYYYYYYY

- - - - - - - - - - - - -

z z z z z z z z z z z z z

YYYYYYYYYYYYY

- - - - - - - - - - - - -

z z z z z YY z z z z z z

YYYYYYYYYYYYY

- - - - - - - - - - - - -

z z z z z YYY z z z z z

YYYYYYYYYYYYY

- - - - - - - - - - -

z z z z z z z z z z z

YYYYYYYYYYY

CumEFU

Low

Mid

High

- Y Y -

- Y Y -

YYYY

- - Y-

- - Y-

YYYY

- - - -

- - - -

YYYY

- - - - - - - - - - - - -

- - - - - - Y - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - - - -

- - - - - - - - - - - - -

YYYYYYYYYYYYY

- - - - - - - - - - -

- - - - - - - - - - Y

YYYYYYYYYYY

Note. Y, p ? 0.05 from one-factor ANOVA only; z, p ? 0.05 from repeated-measures ANOVA only; bold Y, p ? 0.05 from both ANOVAs; dash (-)

indicates p ? 0.05 from both ANOVAs. Baseline body weight is included as a covariate in the model for IntBW. One-factor ANOVA is applied to body weight,

BWG (body weight gain), CumFCD (cumulative daily food consumption), CumFCD_BW (cumulative daily food consumption relative to body weight), and

CumEFU (cumulative efficiency of food utilization). Repeated-measures ANOVA is applied to IntBW (interval body weight) and IntFCD_BW (interval daily

food consumption relative to body weight) calculated for each predetermined interval.

317

ANALYSIS OF RODENT GROWTH DATA

Page 6

due to the high incidence of false-positive claims. Although

growth data collected from the same animal are not expected to

be independent, weak dependency can still drive the type I

error rate much higher than 0.05. In addition, when the type I

error rate is held at the same level, there is a loss of power by

performing a one-factor ANOVA on partial data at each time

point instead of performing a more comprehensive repeated-

measures ANOVA using the full set of information available in

each phase of growth. The alternative analysis approach for

IntBW and IntFCD_BW includes two repeated-measures

ANOVAs each on eight or nine analysis interval averages.

Depending on the significance of the treatment and time inter-

action, the compound-related effects could be evaluated either

for each analysis interval or for the entire phase. For the former

case, the number of analyses performed using the repeated-

measures ANOVA approach is only 13% of that of the one-

factor ANOVA approach. The exact reduction in the type I

error rate could be estimated through simulations, but it suf-

fices to say that the reduction would be dramatic for each of the

two parameters.

Specific comparisons of group means can be evaluated based

on the purpose of the study. For example, for a typical toxicity

study with a control and increasing doses of a compound, the

interaction of interest between treatment and time may be

defined as a linear trend in treatment and time. If a signifi-

cant interaction were observed, the evaluation of a dose-

response relationship can then be performed using a trend test

in a sequential fashion (Tukey et al., 1985) for each analysis

interval.

Efficiency of food utilization is not calculated or analyzed on

a regular basis. Although it may assist in toxicological inter-

pretation for molecules with certain mechanisms of action

FIG. 3.

weight (least squares mean ? SEM) versus week for females from a mouse

carcinogenicity study. Lower panel, cumulative daily food consumption rela-

tive to body weight (mean ? SEM) versus week for females from a mouse

carcinogenicity study.

Upper panel, interval daily food consumption relative to body

FIG. 2.

versus week for females from a mouse carcinogenicity study. Lower panel,

body weight gain (mean ? SEM) versus week for females from a mouse

carcinogenicity study.

Upper panel, interval body weight (least squares mean ? SEM)

318

HOFFMAN, NESS, AND VAN LIER

Page 7

(e.g., certain metabolic perturbations), it is quite variable and is

not needed in a majority of rodent toxicology studies.

In summary, for evaluation of growth data in rodent toxi-

cology studies, we illustrated an approach that uses a powerful

statistical analysis method, reduces the number of false-posi-

tive claims, and consequently provides a succinct yet compre-

hensive summary of the compound-related effects. Only two

key parameters are statistically examined: body weight

(IntBW) and body weight-normalized daily food consumption

(IntFCD_BW) obtained for each predetermined analysis inter-

val. The preselected intervals for IntBW and IntFCD_BW are

defined as weekly intervals for the first 4 weeks; 2-week

intervals (3-week moving averages) for up to Week 14; 4-week

intervals (5-week moving averages) for up to Week 26; and

14-week intervals to the end of a 2-year study. Repeated-

measures ANOVA is performed on data for the growth and

maintenance phases separately for each parameter for each sex.

In general, similar overall conclusions are expected from the

one-factor ANOVA and repeated-measures ANOVA ap-

proaches, but the latter streamlines interpretation of results and

is a better-suited statistical approach for growth data.

ACKNOWLEDGMENTS

The authors gratefully acknowledge Ms. Cindy Lee for computing support,

Drs. Wendell Smith, Michael Dorato, Gerald Long, Mary Jeanne Kallman,

Lorrene Buckley, Judy Henck, Mr. James Hoffman, Ms. Kathy Piroozi, Ms.

Judith Hoyt, Ms. Susan Christopher, and Mr. Patrick Cocke for their helpful

insight into this analysis strategy. We also thank Dr. Karl Lin (U.S. FDA) and

Professor Raymond Carroll (Texas A&M) for their review of the statistical

analysis approaches.

REFERENCES

International Conference on Harmonisation (1995). Guideline on Dose Selec-

tion for Carcinogenicity Studies of Pharmaceuticals. Federal Register 60,

1278–1281.

SAS Institute Inc. (1996). The MIXED procedure. In: SAS/STAT Software:

Changes and Enhancements through Release 6.12, pp. 571–702. SAS In-

stitute Inc., Cary, NC.

Tukey, J. W., Ciminera, J. L., and Heyse, J. F. (1985). Testing the statistical

certainty of a response to increasing doses of a drug. Biometrics 41, 295–301.

Vonesh, E. F., and Chinichilli, V. M. (1997). Linear and Nonlinear Models for

the Analysis of Repeated Measurements. Marcel Dekker, New York.

Winer, B. J. (1962). Statistical Principles in Experimental Design, 2nd ed.

McGraw-Hill, New York.

TABLE 4

Numbers of Analyses Performed on Body Weight and Food Consumption Data for Each Sex for One Rodent Study

Study duration

(weeks)

Weekly or biweekly intervals

for one-factor ANOVAsa

Analysis intervals for

repeated-measures ANOVAsb,c

No. analyses for repeated-measures ANOVAS/no.

analyses for one-factor ANOVAs (%)

4 21

71

101

166

296

10

20

28

32

38

48

28

28

19

13

14

26

52

104

aBody weight, food consumption, and three derived parameters are analyzed using a one-factor ANOVA for each sex at each time point including Day 0. For

example, for a 14-week study, the combination of 5 parameters and 15 time points (Day 0 gives 1 more time point than the total number of analysis intervals,

14, in Table 1) results in 71 analyses in total.

bCount refers to the maximum number of analyses needed to perform using a repeated-measures ANOVA with follow-up analyses in the presence of a

significant treatment-by-time interaction. For example, for a 14-week study, body weight and relative food consumption data in nine time intervals (four from

the first 4 weeks and five from Weeks 5-14) result in 20 analyses at most (one repeated-measures ANOVA and nine follow-up tests for each parameter).

cDay 0 body weight is included in the repeated-measures ANOVA as a covariate for the body weight analysis.

319

ANALYSIS OF RODENT GROWTH DATA