PHARMACEUTICAL STATISTICS

Pharmaceut. Statist. 2006; 5: 237–239

Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/pst.237

Literature Review Non-clinical Statistics

December 2005–May 2006

Ludwig A. Hothornn,y

University of Hannover, Institute of Biostatistics, Herrenhaeuser Str. 2, D-30419

Hannover, Germany

INTRODUCTION

This review covers the following journals received during the

period from December 2005 to end of May 2006:

* Applied Statistics, volume 55, parts 1–3.

* Biometrical Journal, volume 46, part 6 and volume 47, parts

1–2.

* Biometrics, volume 61, part 4 and volume 62, part 1.

* Biometrika, volume 93, part 1.

* Biostatistics, volume 7, parts 1–2.

* Drug Information Journal, volume 39, part 4 and volume 40,

part 1.

* Journal of Biopharmaceutical Statistics, volume 16, parts

1–3.

* Pharmaceutical Statistics, volume 4, part 4, volume 5, parts

1–2.

* Statistics in Medicine, volume 24, parts 23–24, volume 25,

parts 1–12.

* Statistical Methods in Medical Research, volume 14, part 6,

volume 15, parts 1–3.

* Statistical Applications in Genetics and Molecular Biology,

volume 5, articles 1–14.

Relevant statistical articles from other journals are also

included, as appropriate.

SELECTED HIGHLIGHTS FROM THE

LITERATURE

Toxicology

The evaluation of developmental toxicological data is com-

monly litter-based, i.e. the correlation between the pups within

a litter is modeled appropriately. Two types of endpoints can be

distinguished: continuous, e.g. pup weights or dichotomous,

e.g. malformation rates. For modeling such endpoints, a

beta-binomial distribution is assumed. Here, a shared response

model is proposed that allows a random number of fetuses

within the same litter to share a common response. With this

model litter-based determination of benchmark and lower

effective dose can be performed. An extension to bivariate

endpoints, e.g. the simultaneous analysis of visceral and skeletal

malformation rates is discussed.

* Pang Z, Kuk AYC. A shared response model for clustered

binary data in developmental toxicity studies. Biometrics

2005; 61:1076–1084.

The objective of many toxicological studies is the evaluation

of a dose–response relationship for a design including a

negative control and several dose groups. To increase the

power the alternative hypothesis is commonly reduced to a

monotonic order. However, in some assays a downturn

phenomenon at high dose levels may occur, i.e. increasing

effects up to a certain dose and a decreasing effect for higher

doses. The inference is referred as ‘umbrella ordering’. Several

papers for parametric and non-parametric approach useful in

toxicology were published. Here a Bayesian approach for

proportions and total order, simple tree order or umbrella order

with an a priori unknown umbrella changepoint is described.

This is suitable to evaluate dose–response relationships for

crude tumor rates in carcinogenicity assays. Information from

historical studies, e.g. spontaneous tumor rates, can be

incorporated in the analysis via the prior distribution.

Inferences on all parameters can be computed from a single

run of a Gibbs sampler.

* Hans C, Dunson DB. Bayesian inferences on umbrella

orderings. Biometrics 2005; 61:1018–1026.

Clustered survival data arises in litter-matched carcinogenesis

assays where ni rats (subunits) in each of N female litters

(clusters) are randomly allocated to a treatment or control

group. The prolongation of the time to tumor appearance in the

treatment vs the control group is of interest whereby animals

within a litter share common characteristics, and therefore their

Copyright # 2006 John Wiley & Sons, Ltd.Received \60\re /teci

nCorrespondence to: Ludwig A. Hothorn, University ofHannover, Institute of Biostatistics, Herrenhaeuser Str. 2,D-30419 Hannover, Germany.yE-mail: hothorn@biostat.uni-hannover.de

times to tumor appearance are correlated. The variance

estimators of rank tests for independent samples such as the

logrank test need to be adjusted for intracluster correlations

both within and between treatment groups for testing equality

of marginal survival distributions. Here a general form of

variance estimators of rank tests when subunits from the same

cluster are randomized into different treatment groups is

proposed. Extensive simulation studies are conducted to

investigate the performance in small sample.

* Jeong J-H, Jung S-H. Rank tests for clustered survival data

when dependent subunits are randomized. Statistics in

Medicine 2006; 25:361–373.

Many toxicological studies are based on a design including a

negative control and several dose groups. Some of the

endpoints are dichotomous, e.g. finding, mortality or tumor

rates. For incidental tumors the study time will be divided into

k strata. Therefore, trend tests for proportions in stratified

designs are relevant. The power of the commonly used stratified

Mantel-extension trend test was compared with those of

adjusted single contrast tests. For monotonic shapes the

contrast tests revealed higher power.

* Leuraud K, Benichou J. A comparison of stratified and

adjusted trend tests for binomial proportions. Statistics in

Medicine 2006; 25:529–535.

From the perspective of the proof of safety in toxicological

studies including a negative control and several dose groups the

objective is the identification of the maximum safe dose, i.e. the

highest dose which is at least non-inferior to control and all

lower doses too.

The sample sizes necessary on the control and each of the

dose groups to guarantee a specified power requirement are

calculated under two least favorable configurations, namely a

linear and step dose response function.

* Tamhane AC, Shi K, Strassburger K. Power and sample

size determination for a stepwise test procedure for finding

the maximum safe dose. Journal of Statistical Planning and

Inference 2006; 136:2163–2181.

The evaluation of toxicological interactions, i.e. departures

from additivity among chemicals in a mixture is an important

issue. A basic property is the change in slope of the dose–

response curves, i.e. no interaction exists if the slope of one

chemical does not change in the presence of another chemical.

This zero interaction approach is equivalent to the common

additivity models.

* Gennings C, Carter WH, Carchman RA. A unifying

concept for assessing toxicological interactions: changes in

slope. Toxicological Sciences 2005; 88:287–297.

The comet mutagenicity assay is a simple technique to

quantify DNA damage in different tissues. The primary

endpoint, the tail moment, has usually a skewed distribution.

AIC-based model selection between pre-specified mixed models

including Weibull, exponential and logistic is performed

allowing heterogeneity between the treatment groups. The

treatment effect is estimated as a relative risk to control with a

p-value (but not a confidence interval). A related R program

(using the packages survreg and MASS) is provided together

with a real data set.

* Verde PE, Geracitano LA, Amado LL. Application of

public-domain statistical analysis software for evaluation

and comparison of comet assay data. Mutation Research –

Genetic Toxicology and Environmental Mutagenesis 2006;

604:71–82.

Materials used for in vitro fertilization will be tested for

toxicity by mice embryo assay. For each of n mice the 2m

number of embryos is divided into m embryos for a control

group and m for a treatment test group. As the primary

endpoint, the number of embryos which successfully develop

from zygote to blastocyst is counted. The null hypothesis that the

proportion of reduced development is zero can be tested by a

beta-binomial model which takes the split-cluster design with the

between and within cluster variance estimates into account. This

paper focuses on the sample size determination for this test.

* Hendriks JCM, Teerenstra S, Punt-Van der Zalm JPE.

Sample size calculations for a split-cluster, beta-binomial

design in the assessment of toxicity. Statistics in Medicine

2005; 24:3757–3772.

In acute oral toxicity testing adaptive designs has the

advantage over the traditional fixed sample design of global

reductions in the number of animals and in the number exposed

to lethal doses. Constrained optimal designs are proposed in

which no animal is exposed to a dose higher than that at which

a death has been observed. The optimal designs lead to the

correct classification rates and reducing the expected number of

animal deaths.

* Stallard N. Optimal adaptive designs for acute oral toxicity

assessment. Journal of Statistical Planning and Inference

2006; 136:1781–1799.

Pharmacology

Tumor multiplicity is a commonly measured phenotype in

animal studies of cancer biology. In an experiment on murine

intestinal tumors according to Haigis and Dove (Nature

Genetics 2003; 33:33–39) a control group and three groups

which carried different forms of the incomplete Robertsonian

translocation (Rb9) gene. The evaluation in the original paper

was directed to all-pairs comparisons between the three

genetically groups using Tukey–Kramer multiple comparison

procedure as well as Wilcoxon test between the pooled

heterozygous groups vs the homozygous group. The above

Copyright # 2006 John Wiley & Sons, Ltd. Pharmaceut. Statist. 2006; 5: 237–239

Literature Review238

paper focuses on another aspect. If the tumor counts are

Poisson-distributed a mechanism can be proven by which the

adenomatous polyposis coli gene is inactivated during tumor

initiation. Several types of hypothesis testing strategies, model

choice and Bayesian approaches were used to quantify the

positive evidence favoring Poisson variation.

* Newton A, Hastie DI. Assessing Poisson variation of

intestinal tumour multiplicity in mice carrying a Robertso-

nian translocation. Journal of the Royal Statistical Society

Series C 2006; 55:123–138.

Tumor growth in in vivo studies is commonly characterized

by repeatedly measured tumor volumes for fast growing tumors

in a control and treatment group. For the modeling approach

the Gompetz model is frequently used. However, the Gompertz

curve describes the three phases: slow growth, rapid growth and

saturation. Pharmacological studies avoid the saturation phase

due to ethical limitation and use fast growing tumors, so that

only the rapid growth phase is relevant. For these data, an

additive model with a linear and exponential part was

proposed. Several estimation approaches were compared and

illustrated with a photodynamic tumor therapy example.

* Demidenko E. The assessment of tumour response to

treatment. Journal of the Royal Statistical Society Series C

2006; 55:365–377.

Potential anticancer drugs are characterized by their in vitro

cytotoxic activity against several cancer cell lines. From the

relationship between the optical density and the dose the GI50

measure is estimated. This is the dose at which the growth of the

cell line is 50% of what it would have been in the absence of the

drug. A Bayesian non-linear mixed model approach applied to

the full set of cell lines was used. For the different compounds

the point estimator for GI50 and its two-sided 95% credible

intervals were reported.

* Baharitht LA, Al-Khouli A, Raab GM. Cytotoxic assays

for screening anticancer agents. Statistics in Medicine 2006;

25:2323–2339.

Shelf-life estimation/stability

Several approaches for pooling of different batches in a drug

stability study were published, e.g. the tests on interaction

between slopes and intercepts within the analysis of covariance.

However, to pool the data, failure to reject the null hypothesis

of equality of slopes and equality of intercepts, does not prove

that slopes and intercepts from different levels of factors are the

same. Here an equivalence approach is proposed using

simultaneous ð1� 2aÞ confidence intervals for the pairwise

differences yjðT0Þ � yj0 ðT0Þ at a pre-specified time T0 where the

yjðT0Þ ¼ aj þ bjT0 is the mean of the quantitative attribute for

batch j.

* Liu JP, Tung SC, Pong YM. An alternative approach to

evaluation of poolability for stability studies. Journal of

Biopharmaceutical Statistics 2006; 16:1–14.

Optimal designs in drug stability studies are a challenge

because quite different optimality criteria can be formulated.

Several criteria were formulated starting from the simple

criteria ‘a best design’ is the design with the best precision for

shelf life estimation given a fixed total sample size. For a two-

factor, three levels design, examples for the optimal allocation

of the time points for balanced, complete, fractional and

uniform designs were calculated.

* Hedayat AS, Yan X, Lin L. Optimal designs in stability

studies. Journal of Biopharmaceutical Statistics 2006; 16:

35–59.

Literature Review 239

Copyright # 2006 John Wiley & Sons, Ltd. Pharmaceut. Statist. 2006; 5: 237–239