Biometrical Journal Research Articles

Quantifying the predictive accuracy of time-to-event models in the presence of competing risks

Prognostic models for time-to-event data play a prominent role in therapy assignment, risk stratification and inter-hospital quality assurance. The assessment of their prognostic value is vital not only for responsible resource allocation, but also for their widespread acceptance. The additional presence of competing risks to the event of interest requires proper handling not only on the model building side, but also during assessment. Research into methods for the evaluation of the prognostic potential of models accounting for competing risks is still needed, as most proposed methods measure either their discrimination or calibration, but do not examine both simultaneously. We adapt the prediction error proposal of Graf et al. (Statistics in Medicine 1999, 18, 2529–2545) and Gerds and Schumacher (Biometrical Journal 2006, 48, 1029–1040) to handle models with competing risks, i.e. more than one possible event type, and introduce a consistent estimator. A simulation study investigating the behaviour of the estimator in small sample size situations and for different levels of censoring together with a real data application follows.

Graft-Versus-Tumor Effect In Patients with Graft-Versus-Host Disease Defined by NIH Consensus Criteria

AbstractAbstract 2343 Background.The National Institutes of Health consensus criteria (NCC) for chronic graft-versus-host disease (GVHD) are based on clinical manifestations rather than onset time after transplantation. Previous studies about the feasibility of the new criteria have been performed in patients who survived beyond 100 days after transplantation and had GVHD presenting after day 100. In order to investigate and compare the clinical impact of acute and chronic GVHD by NCC on survival, a cohort including patients with GVHD presenting ‘before’ as well as ‘after’ day 100 is needed. Additionally, a proper statistical tool should be applied to clarify the effect of GVHD on survival outcomes, because the occurrence of GVHD is a well known time-dependent event. In this context, we examined a cohort including all patients who underwent allogeneic stem cell transplantation (SCT) in order to investigate clinical impact of acute or chronic GVHD by NCC on survival outcomes. Methods.We retrospectively investigated 771 patients who underwent allogeneic SCT between January 2002 to December 2008. To study a homogenous cohort, patients received 2 allogeneic SCT and/or donor-lymphocyte-infusion was excluded. We used time-dependent analyses to reveal the effect of GVHD on survival outcomes. In particular, to approach the effects of GVHD as a time-dependent covariate on competing risks [relapse or transplant-related mortality (TRM)], we analyzed cause-specific hazards by Cox proportional hazards regression model (Cartese G, Andersen PK. Biometrical Journal 2009;51:138–158). Results.The median age was 36 years (range, 15–68). Patients had various hematologic malignancies (AML/ALL/CML/MDS/MM, 361/226/86/67/31, respectively) and were transplanted from matched sibling (n=485), well-matched unrelated donors (n=154), partially-matched unrelated donors (n=101), and mismatched unrelated donors (n=31). Conditioning regimens consisted of myeloablative (n=536) and reduced-intensity regimens (n=235). GVHD prophylaxis consisted of cyclosporine and short-course methotrexate for related SCT and tacrolimus and short-course methotrexate for unrelated SCT. Among 771 patients, 540 patients were diagnosed with GVHD after transplantation. According to onset time of GVHD, in 348 patients GVHD developed within 100 days after SCT, whereas in 156 patients GVHD occurred more than 100 days after SCT. Using the NCC, we classified patients as three categories regardless of onset time: (1) acute GVHD (n=215), if patients had only acute features (no chronic features) during the course of GVHD, (2) acute GVHD with following chronic GVHD (n=118), if patients had any chronic features after the occurrence of acute GVHD, and (3) chronic GVHD (n=207), if patients had any chronic features at the onset of GVHD. Multivariate analyses using cause-specific hazards revealed that acute GVHD was significantly associated with lower relapse incidence [HR (95% CI) 0.65 (0.44–0.94), P=0.023]. However, it did not influence disease-free survival (DFS, P=0.602) and overall survival (OS, P=0.294) due to higher TRM in patients with acute GVHD [HR (95% CI) 1.74 (1.15–2.61), P=0.008]. Acute GVHD with following chronic GVHD was also associated with lower relapse incidence [HR (95% CI) 0.31 (0.15–0.66), P=0.002] and higher TRM [HR (95% CI) 2.89 (1.65–5.04), P<0.001], which did not influence DFS (P=0.567) and OS (P=0.820). On the other hand, the occurrence of chronic GVHD significantly reduced relapse rates [HR (95% CI) 0.46 (0.29–0.75), P=0.002] without increasing TRM (P=0.177). Indeed, this effect was translated into improved DFS [HR (95% CI) 0.67 (0.48–0.95), P=0.023]. Conclusions.Our data show that both acute and chronic GVHD by NCC reduced the risk of relapse, demonstrating the presence of graft-versus-tumor (GVT) effect by the occurrence of GVHD and no difference according to the clinical features (acute or chronic) by NCC. However, survival benefit was only observed in chronic GVHD by NCC compared to acute GVHD with/without following chronic GVHD by NCC due to higher TRM. This study represents the first one demonstrating the GVT effect of GVHD defined by NCC in a cohort including GVHD presenting ‘before’ as well as ‘after’ day 100 using appropriate time-dependent analyses by cause-specific hazards by Cox proportional hazards regression model. Disclosures:No relevant conflicts of interest to declare.

“Exact permutation tests for correlated binomial variables” by J. Yu, J. L. Kepner and R. Iyer Biometrical Journal (2009) 51, 899-914 Article: http://dx.doi.org/10.1002/bimj.200900082. Authors' reply: http://dx.doi.org/10.1002/bimj.201000094.

Biometrical JournalVolume 52, Issue 3 p. 436-437 Letter to the Editor “Exact permutation tests for correlated binomial variables” by J. Yu, J. L. Kepner and R. Iyer Biometrical Journal (2009) 51, 899–914 Article: http://dx.doi.org/10.1002/bimj.200900082. Authors' reply: http://dx.doi.org/10.1002/bimj.201000094. Vance W. Berger, Corresponding Author Vance W. Berger vb78c@nih.gov Biometry Research Group, National Cancer Institute, 6130 Executive Boulevard (EPN), MSC 7354, Suite 3131, Bethesda, MD 20892-7354, USAPhone: +1-301-435-5303, Fax: +1-301-402-0816Search for more papers by this author Vance W. Berger, Corresponding Author Vance W. Berger vb78c@nih.gov Biometry Research Group, National Cancer Institute, 6130 Executive Boulevard (EPN), MSC 7354, Suite 3131, Bethesda, MD 20892-7354, USAPhone: +1-301-435-5303, Fax: +1-301-402-0816Search for more papers by this author First published: 17 June 2010 https://doi.org/10.1002/bimj.201000012Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume52, Issue3June 2010Pages 436-437 RelatedInformation

Biometrical Journal and Reproducible Research

Biometrical Journal and Reproducible Research

Alternative Confidence Regions for Bonferroni‐Based Closed‐Testing Procedures that are not Alpha‐Exhaustive

This article complements the results in Guilbaud (Biometrical Journal 2008; 50:678-692). Simultaneous confidence regions were derived in that article that correspond to any given multiple testing procedure (MTP) in a fairly large class of consonant closed-testing procedures based on marginal p-values and weighted Bonferroni tests for intersection hypotheses. This class includes Holm's MTP, the fixed-sequence MTP, gatekeeping MTPs, fallback MTPs, multi-stage fallback MTPs, and recently proposed MTPs specified through a graphical representation and associated rejection algorithm. More general confidence regions are proposed in this article. These regions are such that for certain underlying MTPs which are not alpha-exhaustive, they lead to confidence assertions that may be sharper than rejection assertions for some rejected null hypotheses H when not all Hs are rejected, which is not the case with the previously proposed regions. In fact, various alternative confidence regions may be available for such an underlying MTP. These results are shown through an extension of the previous direct arguments (without invoking the partitioning principle), and under the same general setup; so for instance, estimated quantities and marginal confidence regions are not restricted to be of any particular kinds/dimensions. The relation with corresponding confidence regions of Strassburger and Bretz (Statistics in Medicine 2008; 27:4914-4927) is described. The results are illustrated with fallback and parallel-gatekeeping MTPs.

On defining [formula omitted]-values

The Fisherian prescription of reporting P -values as a summary of a result, as compared to the Neyman–Pearson system of acceptance or rejection of a null hypothesis, is more common in applied science. This popularity is largely due to the fact that the P -value provides a more complete, meaningful and useful evidence regarding the null hypothesis. Conventionally, P -values are defined in the context of one-sided alternatives, although there exist some ideas in the literature concerning two-sided alternatives; see e.g. [Gibbons, J.D., Pratt, J.W., 1975. P -values: Interpretation and methodology. American Statistician 24, 20–25; George, E.O., Mudholkar, G.S., 1990. P -values for two-sided tests. Biometrical Journal 32, 747–751]. This note takes an axiomatic approach for defining P -values which involves at most ordering of the alternatives but is not restricted by their nature. It also involves a correspondence between a P -value and the associated level α test for each α . A P -value turns out to be valid if and only if the associated level α test is unbiased in the traditional sense for each α . Furthermore, it is shown that the resulting optimal tests agree with those given by the Neyman-Person framework when the ordering is stochastic. Thus, a theory based on optimal P -values parallels to the Neyman–Pearson theory and bridges the two approaches to testing of hypotheses.

Celebrating Fifty Years of the Biometrical Journal

The publication of Volume 50 of the Biometrical Journal (formerly Biometrische Zeitschrift) in 2008 provides the perfect opportunity to describe the history of the present journal. We report on the long period of preparation for the journal within the German Region (DR) of the International Biometric Society (IBS). A special paragraph is dedicated to the first ten volumes. We emphasize the role of the journal as a bond between German biometricians on both sides of the border between the two German nations and IBS regions at that time. Furthermore, we report on the development of its thematic spectrum and impact factors and provide citation frequencies.

Editorial – Recent Developments in Capture‐Recapture Methods and Their Applications

In recent years capture-recapture methods have experienced important theoretical developments. New application areas have been added to their spectrum, in turn supporting new developments on the methodological side. Hence it appears appropriate to take a closer look at some of these developments. This is the objective of this special theme in the current issue of the Biometrical Journal. The contributions to this special theme stem from a recent Conference of Recent Developments in Capture-Recapture Methods and their Applications (held on July 12–13, 2007, School of Biological Sciences, University of Reading, UK). Capture-Recapture has its origin in the Biological/Ecological Sciences with the work of Lincoln and Petersen. More than one hundred years ago Petersen (1896) published his landmark paper suggesting what later became known as the Lincoln–Petersen estimator, since it was also independently developed by Lincoln (1930). This estimator and its stabilized version developed by Chapman (1951) are still in use by numerous practitioners. In a way, this issue could be considered a celebration of the centenary of the Lincoln–Petersen estimator. Capture-Recapture methods can be seen to be applied in three major sciences, all represented in various contributions of this special topic issue: The biological sciences, where the size of animal populations and their diversity are of importance. The social sciences, where we are interested in the amount of illegal activities, such as illegal immigration. The life and medical sciences, where we often want to know the size of the hidden disease burden in a population, such as depression or drug use. In the biological sciences the classical book by Seber (1982) characterizes the various biological application fields. In addition, the recent monograph by Borchers, Buckland and Zucchini (2002) supplements a view with biological applications using modern inference tools. More recently, capturerecapture methods have been applied to other areas. The landmark paper by Sekar and Deming (1949) applied capture-recapture methods to estimate the number of births and deaths in an area near Calcutta. This paper started a development of the capture-recapture methodology in demography and social science in general. This development was further supplemented and supported by the appearance of the book by Bishop, Fienberg, and Holland (1975) on multivariate discrete analysis in which the entire chapter 6 was devoted to capture-recapture methods. Yet a further milestone was the establishment of the methodology in medicine and public health by the landmark papers by Hook and Regal (1995) as well as the two papers by the International Working Group for Disease Monitoring and Forecasting (IWGDMF 1995a, b). In the early phases the method was used to develop a more com-

On modeling count data: a comparison of some well-known discrete distributions

In a recent paper, Joe and Zhu [2005, Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution. Biometrical Journal, 47(2), 219–229.] compared the negative binomial and the generalized Poisson distributions. We aim at extending this comparison by including more distributions and more aspects, like tailness and kurtosis. We also aim at describing the related problem, whether from real data one may distinguish between the candidate models. To do this, we consider several aspects of three of the most commonly used mixed Poisson distributions, namely the negative binomial, the Poisson inverse Gaussian and the generalized Poisson distributions. The results show that for small mean and overdispersion, all the models are quite the same, whereas for larger means the generalized Poisson and the Poisson inverse Gaussian distributions have larger tails than the negative binomial, and the differences are much larger. In practice, it is not easy to discriminate between them for small counts and small overdispersion, but for large overdispersion discrimination is relatively easy. Applications to real data are provided to illustrate the ideas.

The scientific work of Peter Bauer

This June, Peter Bauer – chief editor of Biometrical Journal from 2000–2003 and member of the editorial board since 1996 – celebrated his 65th birthday. Peter Bauer became known as one of the originators of the “adaptive designs”, a field of research that recently gained considerable popularity, not only among academia but likewise among regulatory bodies and the pharmaceutical industry. It is characteristic for Peter Bauer, that while “adaptive designs” make their way into main stream statistics, he is already on the search for new challenges and now works, among others, on statistical problems relevant to bioinformatics. His sense for dynamic research areas can be easily seen from his whole professional career where he covered a wide range of research fields including informatics, binomial and poisson processes, model robustness, optimal designs, multiple testing, sequential analysis, adaptive designs and bioinformatics. Peter Bauer started his scientific career at the medical faculty of the University of Vienna, was appointed 1985 as head of the Department of Medical Documentation and Statistics in Cologne and returned to the University of Vienna in 1994 to become the head of the Department of Medical Statistics at the medical faculty. Besides his co-operation in many clinical research projects he built up an active research group. He currently decided to accept the lead of the Core Unit for Medical Statistics and Informatics, the superordinate unit of his and several other departments since the faculty became an independent university in 2004. In view of the proceeding structural changes at the new Medical University taking this lead is just one more example for his persistent willingness to explore new challenges. As a physicist by education, Peter Bauer was part of the pioneering epoch of medical computer science in Vienna. In the late sixties he developed a programming language to model chemical reactions and worked on computer based diagnostic programs for liverdiseases. Confronted with the need for statistical expertise at the medical faculty, he turned to statistics and became a British Council Research Fellow at the Department of Statistics in Edinburgh where David Finney was department head at this time. He returned to Vienna, fascinated by the British school of medical statistics, and got involved in several challenging consulting projects that were the starting point of methodological research papers. Motivated by practical experience with high dimensional compartment models he developed a method to specify the power for the discrimination between different regression models and investigated the related statistical design concept nowadays known as T-optimality. The method was published in two research papers of the “Biometrische Zeitschrift” (Bauer, 1975a, b) one year before the journal was renamed to “Biometrical Journal”. Another example for his practically oriented methodological research is the analysis of a cross-sectional study on the caries protective effects of fluorid. To model the hazard for the occurrence of caries Peter Bauer forestalled the development of frailty models (Bauer et al., 1980, 1982). In a fruitful cooperation with Peter Hackl he contributed to the theory of quality control and multiple testing. Peter Bauer published his first paper on multiple comparisons in 1985 in the Biometrical Journal (Bauer and Hackl, 1985). The multiplicity issue in statistical inference was the subject of many subsequent works with applications in dose finding (e.g. Budde and Bauer, 1989; Bauer and Budde, 1994; Bauer et al., 1998; Bauer, Brannath and Posch, 2000), model selection (Bauer, P tscher and Hackl, 1988), equivalence testing (e.g. Bauer and Bauer, 1994)

ROC Volumes – Should They Be Used?

Invited comment on Alonzo, T.A. and Nakas, C.T. (2007). Comparison of ROC umbrella volumes with an application to the assessment of lung cancer diagnostic markers. Biometrical Journal 49, 654-664. Issues remain as to the appropriateness of volumes as summary measures of accuracy when distinguishing between multiple disease classes and when comparing accuracy of tests.

The Umbrella Volume: Is it Useful in Applications?

Invited comment on Alonzo, T. A. and Nakas, C. T. (2007). Comparison of ROC umbrella volumes with an application to the assessment of lung cancer diagnostic markers. Biometrical Journal 49, 654-664. The umbrella volume, proposed as a parameter for diagnostic validity in a specific three group situation might be difficult to interpret in clinical applications. It should be used very cautiously.

Multiple Targeted Therapies: Is there a Place for Vach Type‐3 or Type‐4 Design Trials

Invited comment on Vach W. and dePoint Christensen R. (2006). Making efficient use of patients in designing phase III trials investigating simultaneously a set of targeted therapies with different targets, Biometrical Journal 48, 897-907. For complexity reasons the designs proposed by Vach et al. will probably not be used in initial drug registration trials. But they may be an option for established study groups that run treatment-optimisation or indication-extension trials investigating targeted drugs that are already registered.

Hypothesis Tests for and against a Simple Order among Proportions Estimated by Pooled Testing

The use of pooled testing as a means of estimating the prevalence of rare traits has received considerable attention in recent years, particularly in the areas of public health, genetics, animal-disease assessment, and plant pathology. In pooled-testing applications, observations are made on pools of individuals amalgamated together. In this paper, we examine order-restricted hypothesis tests involving k >2 binomial proportions estimated by pooled testing, extending the earlier work of Tebbs and Swallow (2003, Biometrika, 90, 471-477 and Biometrical Journal, 45, 618-630). In particular, we focus on (i) testing the equality of proportions versus an isotonic alternative and (ii) testing for a violation of isotonicity. We propose new tests for each scenario and provide results which characterize the small-sample performance of our procedures. We illustrate our methods using two data sets; one from an observational HIV study and one from an agricultural experiment.

Online updating of space-time disease surveillance models via particle filters

Online surveillance of disease has become an important issue in public health. In particular, the space-time monitoring of disease plays an important part in any syndromic system. However, methodology for these systems is generally lacking. One approach to space-time monitoring of health data is to consider the space-time model parameters as the focus and to monitor their changes as multivariate time series (Lawson AB. Some considerations in spatial-temporal analysis of public health surveillance data. In Brookmeyer R, Stroup DF eds. Monitoring the Health of Populations. Oxford University Press, 2004; Vidal Rodeiro CL, Lawson AB. Monitoring changes in spatio-temporal maps of disease. Biometrical Journal 2006; to appear). However with complex space-time models, this becomes very time consuming. Some simplifications may be necessary and these can be made in a number of ways. In this article, the focus is on particle filters that can be used to resample the history of the process and thereby reduce computation time. This article describes a particular case of particle filters, the resample-move algorithm, proposed by Gilks and Berzuini (Gilks WR, Berzuini C. Following a moving target--Monte Carlo inference for dynamic Bayesian models. Journal of the Royal Statistical Society, Series B 2001; 63: 127-46), in the context of disease map surveillance. This is followed by an application to a real data set in which a comparison between the use of Markov chain Monte Carlo methods and the resample-move algorithm is carried out.

Combining Significance of Correlated Statistics with Application to Panel Data*

AbstractThe inverse normal method, which is used to combine P‐values from a series of statistical tests, requires independence of single test statistics in order to obtain asymptotic normality of the joint test statistic. The paper discusses the modification by Hartung (1999, Biometrical Journal, Vol. 41, pp. 849–855), which is designed to allow for a certain correlation matrix of the transformed P‐values. First, the modified inverse normal method is shown here to be valid with more general correlation matrices. Secondly, a necessary and sufficient condition for (asymptotic) normality is provided, using the copula approach. Thirdly, applications to panels of cross‐correlated time series, stationary as well as integrated, are considered. The behaviour of the modified inverse normal method is quantified by means of Monte Carlo experiments.

Some c-sample rank tests of homogeneity against umbrella alternatives with unknown peak

The c-sample location problem with umbrella alternatives is investigated. The umbrella peak l is assumed to be unknown. All test statistics are maxima of substatistics which are constructed for the case of a known peak l. These substatistics are based on ranks. Arbitrary scores and arbitrary sample size configurations are allowed. As special cases we have tests of Chen and Wolfe [Chen, Y.I. and Wolfe, D.A., 1990, A study of distribution-free tests for umbrella alternatives. Biometrical Journal, 32, 47–57.], Hettmansperger and Norton [Hettmansperger, T.P. and Norton, R.M., 1987, Tests for patterned alternatives in k-sample problems. Journal of the American Statistical Association, 82, 292–299.] and Shi [Shi, N.-Z., 1988, Rank test statistics for umbrella alternatives. Communications in Statistics, Theory and Methods, 17, 2059–2073.]. We compute the asymptotic power functions of the constructed tests. For the cases of three or four treatments, some figures give an impression of the asymptotic power functions for various setups. Simulation studies show that the asymptotic results can also be used for moderate sample sizes. In average, over all setups, the Hettmansperger–Norton-type test performs best densely followed by the Chen–Wolfe-type test and the Shi-type test.

Detecting antibodies with similar reactivity patterns in the HLDA8 blind panel of flow cytometry data

The blind panel collected for the 8th Human Leucocyte Differentiation Antigens Workshop (HLDA8; http://www.hlda8.org) included 49 antibodies of known CD specificities and 76 antibodies of unknown specificity. We have identified groups of antibodies showing similar patterns of reactivity that need to be investigated by biochemical methods to evaluate whether the antibodies within these groups are reacting with the same molecule. Our approach to data analysis was based on the work of Salganik et al. (in press) [Salganik, M.P., Milford E.L., Hardie D.L., Shaw, S., Wand, M.P., in press. Classifying antibodies using flow cytometry data: class prediction and class discovery. Biometrical Journal].

Therapeutic Equivalence – Clinical Issues and Statistical Methodology in Noninferiority Trials

AbstractThis special issue on therapeutic equivalence contains a selection of 8 papers presented at the conference ‘Therapeutic Equivalence – Clinical Issues and Statistical Methodology in Noninferiority Trials’ held in Düsseldorf, December 12–13, 2003. The aim of this conference was to gather experts from academics, industry and regulatory agencies in the field of therapeutic equivalence, in particular of noninferiority trials. Originally initiated as a small workshop, it soon turned out that there is obviously strong need to discuss these challenging issues at a broader auditorium. Indeed, the feedback to this conference was overwhelming, finally more than 300 researchers participated. Hence the idea emerged to collect the results and discussions in a single journal issue. It took more than a year to finish it, and various activities in this rapidly developing area have been going on and were incorporated.We are very grateful to the Editors E. Brunner and M. Schumacher of the Biometrical Journal for their encouragement and support to publish this special issue on the occasion of this conference. Further, the technical assistance and expertise of G. Skipka and K. Thangavelu is gratefully acknowledged. We are also indebted to Peter Bauer and Stephen Senn for their discussions of the subsequent articles by Bristol, Freitag, Hauschke, Slacik‐Erben, Hensen and Kaufmann, Hung, Wang and O'Neill, Lange and Freitag, Tsong and Zhang, Wellek, and last but not least we would like to thank Joachim Röhmel for his contribution to this special issue. Joachim Röhmel contributed significantly during the last three decades to various branches of biostatistical research, and in particular to the design and analysis of equivalence trials. The aim of this special issue is therefore twofold, it is also devoted to the occasion of Joachim Röhmel's retirement from BfArM in 2004. In the following we would briefly like to express our deep appreciation of his scientific work. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Robust Analysis of Generalized Linear Mixed Models

The method of maximum likelihood (ML) is widely used for analyzing generalized linear mixed models (GLMM's). A full maximum likelihood analysis requires numerical integration techniques for calculation of the log-likelihood, and to avoid the computational problems involving irreducibly high-dimensional integrals, several maximum likelihood algorithms have been proposed in the literature to estimate the model parameters by approximating the log-likelihood function. Although these likelihood algorithms are useful for fitting the GLMM's efficiently under strict model assumptions, they can be highly influenced by the presence of unusual data points. In this article, the author develops a technique for finding robust maximum likelihood (RML) estimates of the model parameters in GLMM's, which appears to be useful in downweighting the influential data points when estimating the parameters. The asymptotic properties of the robust estimators are investigated under some regularity conditions. Small simulations are carried out to study the behavior of the robust estimates in the presence of outliers, and these estimates are also compared to the ordinary classical estimates. To avoid the computational problems involving high-dimensional integrals, the author proposes a robust Monte Carlo Newton–Raphson (RMCNR) algorithm for fitting GLMM's. The proposed robust method is illustrated in an analysis of data from a clinical experiment described in a biometrical journal.