Literature review non-clinical statistics: June 2006–May 2007

PHARMACEUTICAL STATISTICS

Pharmaceut. Statist. 2007; 6: 247–250

Published online 8 August 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/pst.296

Literature Review Non-clinical Statistics:

June 2006–May 2007

Ludwig A. Hothorn*,y

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

Hannover, Germany

INTRODUCTION

This review covers the following journals receivedduring the period from June 2006 to end of May2007:

* Journal of the Royal Statistical Society; SeriesC – Applied Statistics, volume 55, parts 4 and 5;volume 56, parts 1–3.

* Biometrical Journal, volume 48, parts 3–6;volume 49, parts 1 and 2.

* Biometrics, volume 62, part 4; volume 63, part 1.* Biometrika, volume 93, parts 2–4; volume 94,

parts 1 and 2.* Biostatistics, volume 7, parts 3 and 4; volume 8,

parts 1 and 2.* Drug Information Journal, volume 40, parts 2–4;

volume 41, parts 1–3.* Journal of Biopharmaceutical Statistics, volume

16, parts 4–6; volume 17, parts 1–3.* Pharmaceutical Statistics, volume 5, parts 3 and

4; volume 6, parts 1 and 2.* Statistics in Medicine, volume 25, parts 13–24;

volume 26, parts 1–16.* Statistical Methods in Medical Research, vo-

lume 15, parts 4–6; volume 16, parts 1 and 2.* Statistical Applications in Genetics and Molecu-

lar Biology, volume 5, articles 15–30; volume 6,articles 1–16.

Relevant statistical articles from other journals arealso included, as appropriate.

SELECTED HIGHLIGHTS FROM THE

LITERATURE

Toxicology

Frequently, the difference of two dose–responsecurves is characterized by overlapping of theirtwo-sided 95% confidence intervals of the LC50s.An alternative appropriate approach is whetherthe confidence interval of ratio of the LC50scontains 1 or the log-ratio contains 0. Thisapproach is less conservative compared with thesimple overlapping technique.

* Wheeler MW, Park RM, Bailer AJ. Comparingmedian lethal concentration values using con-fidence interval overlap or ratio tests. Environ-mental Toxicology and Chemistry 2006;25(5):1441–1444.

The tumor–time relationships in long-term carci-nogenicity bioassays can be evaluated withoutcause-of-death information. A modification of thepoly-k trend test is proposed by replacing the time-at-risk weight to a function of the tumor onsetsurvival function via closed-form solutions forconstrained maximum likelihood estimates.

* Kim W, Ahn H, Moon H. A dose–response testvia closed-form solutions for constrained MLEs

Copyright # 2007 John Wiley & Sons, Ltd.

Received \60\re /teci

yE-mail: [email protected]

*Correspondence to: Ludwig A. Hothorn, Leibniz Universityof Hannover, Institute of Biostatistics, Herrenhaeuser Str. 2,D-30419 Hannover, Germany.

in survival/sacrifice experiments. Statistics inMedicine 2007; 26:694–708.

Tumor–time relationships in long-term carcino-genicity bioassays can be evaluated by the poly-ktrend test without cause-of-death information.Free available software for a bootstrap-basedpoly-k trend test is proposed.

* Moon H, Ahn H, Kodell RL. A computationaltool for testing dose-related trend using an age-adjusted bootstrap-based poly-k test. Journal ofStatistical Software 2006; 16:0007.

The Cochran-Armitage trend test is the standardtrend test for 2� k table data, e.g. the evaluationof tumor rates in carcinogenicity studies. Severalexact versions of this test were investigated forsmall sample behavior by means of a simulationstudy. The exact unconditional approach is super-ior to the exact conditional approach with respectto level a and exact power.

* Tang ML, Ng HKT, Guo JH, Chan W, ChanBPS. Exact Cochran-Armitage trend tests:comparisons under different models. Journalof Statistical Computation and Simulation 2006;76(10):847–859.

Multiple tests and simultaneous confidence inter-vals for comparing several dose groups against azero-dose control is an issue since Dunnett’s (1955)famous approach. Here, an approach based onmaximum likelihood estimators for a simple-treealternative is proposed. By simulation its power isbetween Dunnett’s test for non-monotonic dose–response relationships and Williams test formonotonic ones.

* Peddada SD, Haseman JK, Tan X, Travlos G.Tests for a simple tree order restriction withapplication to dose–response studies. Journal ofthe Royal Statistical Society – Series C AppliedStatistics 2006; 55:493–506.

Malformations in reproductive studies cannot besimply modelled by the binomial distributionbecause of intra-litter correlation and over-disper-sion. Many proposals to evaluate such exchange-able binary data exist.

A trend test that is based on the fit of asaturated model by the EM algorithm according toStefanescu and Turnbull (Biometrics 2003; 59:18–24) was modified by taking the variability of anestimated null expectation into account.

* Pang Z, Kuk AYC. Test of marginal compat-ibility and smoothing methods for exchangeablebinary data with unequal cluster sizes. Bio-metrics 2007; 63:218–227.

The direct evaluation of continuous outcomes inreproductive studies, such as pup weight, can bebiased by competing risks as mortality and littermates. A new approach where effects are definedwithin principal strata that are a function of thesurvival status of the pups at each of the possibledose levels is discussed.

* Elliott MR, Joffe MM, Chen Z. A potentialoutcomes approach to developmental toxicityanalyses. Biometrics 2006; 62:352–360.

Binary, count, and continuous outcomes occursimultaneously in toxicological dose–responseproblems. Taking the correlation between thesedifferent-scaled endpoints into account will im-prove the evaluation. A modification of a GEEapproach for simultaneous analysis of binary,count, and continuous outcomes with non-linearthreshold models that incorporates the intra-subject correlation is proposed.

* Coffey T, Gennings C. The simultaneousanalysis of mixed discrete and continuousoutcomes using nonlinear threshold models.Journal of the Agricultural Biological andEnvironmental Statistics 2007; 12:55–77.

In toxicology, the characterization of mixturesof low-dosed chemicals is of particular interest.For sub-threshold doses often additivity can beassumed. Testing for additivity in the sense ofBerenbaum (Advances in Cancer Research, 1981)based on the equivalence tests where the nullhypothesis of interaction is rejected for thealternative hypothesis of additivity is proposed.

* Stork LG, Gennings C, Carchman RA. Testingfor additivity at select mixture groups of

Copyright # 2007 John Wiley & Sons, Ltd. Pharmaceut. Statist. 2007; 6: 247–250

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interest based on statistical equivalence testingmethods. Risk Analysis 2006; 26:1601–1612.

Pharmacology

In cancer chemoprevention studies, the tumoronsets of palpable tumors are observed. Therefore,the within-subject dependency in the multipleevent times in such data can be taken into accountby a dynamic frailty model and a Bayesiansemiparametric approach. Alternatively, non-parametric dynamic random effects in generalizedlinear models for joint longitudinal and survivaldata can be used.

* Pennell ML, Dunson DB. Bayesian semipara-metric dynamic frailty models for multipleevent time data. Biometrics 2006; 62:1044–1052.

In cancer chemoprevention studies human tumorcells are inoculated into mice, the tumor volumesover time are recorded and the area under thetumor volume curve is evaluated by rank testsfor Lehman alternative, i.e. a mixing distributionfor responder and non-responder is assumed. Arelated approach for power estimation is proposedfor two- and k-sample test.

* Heller G. Power calculations for preclinicalstudies using a K-sample rank test and theLehmann alternative hypothesis. Statistics inMedicine 2006; 25:2543–2553.

Four-parameter model of pharmacological agon-ism is used for both single and multiple dose–response curves. By means of non-linear mixedeffects model these parameters can be estimated,where pairs of curves (e.g. treatment and control)share some parameter. Moreover, tests and con-fidence intervals for the comparison between twocurves are provided.

* Frigyesi A, Hoessjer O. Estimating the para-meters of the operational model of pharmaco-logical agonism. Statistics in Medicine 2006;25:2932–2945.

Psychotropic drug classification can be performedby the evaluation of sleep–wake behavior of rats.These complex data were analyzed by a flexible

hierarchical discriminant analysis, mixed modelsin combination with fractional polynomials.

* Wouters K, Ahnaou A, Abrahantes JC, Mo-lenberghs G. Pharmaco-electroencephalogramstudies are used to characterize psychotropicdrugs. Journal of the Royal Statistical Society –Series C Applied Statistics 2006; 56:223–234.

The objective of drug combination studies is oftento characterize whether the drug combination issynergistic, additive, or antagonistic. Commonresponse surface models based on the Loeweadditivity reference model require constant relativepotency and use a single parameter claimingsynergy, additivity, or antagonism. A generalizedresponse surface model is proposed with a func-tion of doses instead of a one single parameter toidentify and quantify departure from additivity.This model can incorporate varying relativepotencies among multiple drugs.

* Kong M, Lee JJ. A generalized response surfacemodel with varying relative potency for asses-sing drug interaction. Biometrics 2006; 62:986–995.

One aim of QT/QTc studies is to prove that a drug isnon-inferior to placebo in terms of QT/QTc prolon-gation. Here, an approximate confidence interval isproposed for the largest difference in populationmean QT/QTc between drug and placebo.

* Eaton ML, Muirhead RJ, Mancuso JY, KolluriS. A confidence interval for the maximal meanQT interval change caused by drug effect. DrugInformation Journal 2006; 40:267–271.

Quantal bioassay experiments are common inpharmacology and toxicology. Studies exist wherethe binary response, e.g. mortality, is recordedover time. A dose–time–response model is pro-posed for this type of experiments and a cumula-tive multinomial generalized linear model thatincorporates time and covariates is developed.

* Chen DG. Dose–time–response cumulativemultinomial generalized linear model. Journalof Biopharmaceutical Statistics 2007; 17:173–185.

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Several approaches are available to demonstratepharmacokinetic dose proportionality. A commonapproach is the ANOVA model, where doseproportionality is evaluated using bioequivalencelimits. Alternatively, a mixed-effects power modelis proposed, where dose proportionality is assessedfor the estimated slope.

* Sethuraman VS, Leonov S, Squassante L,Mitchell TR, Hale MA. Sample size calculationfor the power model for dose proportionalitystudies. Pharmaceutical Statistics 2007; 6:35–41.

Drug stability and shelf-life estimation

Commonly stability studies are performed for drugproducts with a single active ingredient. A statisticalmethod for determining the shelf-life of a drugproduct with multiple active ingredients is proposed.

* Chow S-C, Shao J. Stability analysis for drugswith multiple active ingredients. Statistics inMedicine 2007; 26:1512–1517.

One problem in drug stability studies is thecriterion to pool several batches before estimatingshelf-life. Here, constant-width simultaneous con-fidence bands are proposed to quantify themagnitude of the difference between differentbatches, with an aim to establish the practicalequivalence of different batches.

* Liu W, Jamshidian M, Zhang Y, Bretz F, HanXL. Pooling batches in drug stability study byusing constant-width simultaneous confidencebands. Statistics in Medicine 2007; 26:2759–2771.

The statistical evaluation of accelerated thermo-stability studies based on Arrhenius model is animportant issue for biologicals. A related softwareand its validation are described.

* Shin JH, Nam J. Validation of a computersoftware program for statistical analysis ofaccelerated stability studies on biological stan-dards. Biologicals 2007; 35:27–30.

Two types of accelerated thermo-stabilitystudies are distinguished: isothermal and non-isothermal. Isothermal studies are analyzed bylinear regression models, whereas non-isothermalstudies are analyzed by non-linear regressionor linear regression after appropriate transfor-mations.

* Oliva A, Llabres M, Farina JB. Data analysis ofkinetic modelling used in drug stability studies:isothermal versus nonisothermal assays. Phar-maceutical Research 2006; 23:2595–2602.

Bioassay

The evaluation of an in vitro microtiter-basedbioassay is described by means of generalizedlinear mixed model configured with a reciprocallink function, a gamma error distribution, andthree sources of design variation: plate-to-plate,well-to-well, and the interaction between plate-to-plate variation and dose.

* Rey deCastro B, Neuberg D. The statisticalperformance of an MCF-7 cell culture assayevaluated using generalized linear mixed modelsand a score test. Statistics in Medicine 2007;26:2501–2518.

The comparison of two or several linearizedgrowth curves is one objective in evaluatingin vivo bioassays, i.e. to demonstrate that theyare practically equivalent. A simultaneous con-fidence band is proposed which provides an upperbound on the largest possible difference betweenthe two models, in units of the standard error ofthe observations, over a given region of thecovariates.

* Liu W, Hayter AJ, Wynn AP. Operabilityregion equivalence: simultaneous confidencebands for the equivalence of two regressionmodels over restricted regions. BiometricalJournal 2007; 49:144–150.


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Literature review non-clinical statistics: June 2006–May 2007