Circular Strongly Balanced Repeated Measurements Designs

Magda (1980 Magda , C. G. ( 1980 ). Circular balanced repeated measurements designs . Commun. Statist. Theor. Meth. 9 : 1901 – 1918 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Hedayat (1981 Hedayat , A. S. ( 1981 ). Repeated measurements designs-IV: recent advances (with discussion) . Bull. Int. Statist. Inst. 1 : 591 – 610 . [Google Scholar]) first considered the construction of circular strongly balanced repeated measurements designs. Sen and Mukerjee (1987 Sen , M. , Mukerjee , R. ( 1987 ). Optimal repeated measurements designs under interaction . J. Statist. Plann. Infer. 17 : 81 – 91 .[Crossref], [Web of Science ®] , [Google Scholar]) and Roy (1988 Roy , B. K. ( 1988 ). Construction of strongly balanced uniform repeated measurements designs . J. Statist. Plann. Infer. 19 : 341 – 348 .[Crossref], [Web of Science ®] , [Google Scholar]) considered the optimality and existence of circular strongly balanced repeated measurements designs based on the method of differences and Hamiltonian decomposition of lexicographic product of two graphs. In this article, we consider the construction of circular strongly balanced repeated measurements designs using the newly proposed method called cyclic shifts, and propose some new designs for p < v.     

Designs Robust Against the Presence of an Aberration in a Diallel Cross Design Setup

In this article, we find designs insensitive to the presence of an outlier in a diallel cross design setup for estimating a complete set of orthonormal contrasts among the effects of the general combining abilities of a set of parental lines. The criterion of robustness, suggested by Mandal (1989 Mandal , N. K. ( 1989 ). On robust designs . Cal. Stat. Assoc. Bull. 38 : 115 – 119 . [Google Scholar]) in block design setup and used by Biswas (2012 Biswas , A. ( 2012 ). Block designs robust against the presence of an aberration in a treatment-control setup . Commun. Statist. Theor. Meth. 41 : 920 – 933 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in treatment-control setup, is adapted here. Complete diallel cross designs, suggested by Gupta and Kageyama (1994 Gupta , S. , Kageyama , S. ( 1994 ). Optimal complete diallel crosses . Biometrika 81 : 420 – 424 .[Crossref], [Web of Science ®] , [Google Scholar]), and partial diallel cross designs, suggested by Gupta et al. (1995 Gupta , S. , Das , A. , Kageyama , S. ( 1995 ). Single replicate orthogonal block designs for circulant partial diallel crosses . Commun. Statist. A 24 : 2601 – 2607 .[Taylor & Francis Online] , [Google Scholar]) and Mukerjee (1997 Mukerjee , R. ( 1997 ). Optimal partial diallel crosses . Biometrika 84 : 939 – 948 .[Crossref], [Web of Science ®] , [Google Scholar]), are found to be robust under certain conditions.     

Optimum Mixture Design Using Deficiency Criterion

In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe (1958 Scheffe , H. ( 1958 ). Experiments with mixtures . J. R. Statist. Soc. B 20 : 344 – 360 . [Google Scholar], 1963 Scheffe , H. ( 1963 ). Simplex – centroid design for experiments with mixtures . J. R. Statist. Soc. B 25 : 235 – 263 . [Google Scholar]) first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal (2006 Pal , M. , Mandal , N. K. ( 2006 ). Optimum designs for optimum mixtures . Statist. Probab. Lett. 76 ( 13 ): 1369 – 1379 .[Crossref], [Web of Science ®] , [Google Scholar], 2007 Pal , M. , Mandal , N. K. (2007). Optimum mixture design via equivalence theory. communicated. JCISS 32:107–126. [Google Scholar]) attempted to find a solution to this problem by adopting a pseudo-Bayesian approach and using the trace criterion. Subsequently, Pal and Mandal (2008 Pal , M. , Mandal , N. K. ( 2008 ). Minimax designs for optimum mixtures . To appear in Statist. Probab. Lett.  [Google Scholar]) solved the problem using minimax criterion. In this article, the deficiency criterion due to Chatterjee and Mandal (1981 Chatterjee , S. K. , Mandal , N. K. ( 1981 ). Response surface designs for estimating the optimal point . Calcutta Statist. Assoc. Bull. . 30 : 145 – 169 .[Crossref] , [Google Scholar]) has been used as a measure for comparing the performance of competing designs.     

On Universal Optimality of Circular Weakly Neighbor Balanced Designs Under an Interference Model

In this article, the optimal design problem in a fixed effects interference model with left-neighbor effects is studied. It is known (Druilhet, 1999 Druilhet , P. ( 1999 ). Optimality of circular neighbor balanced designs . J. Statist. Plann. Infer. 81 : 141 – 152 .[Crossref], [Web of Science ®] , [Google Scholar]) that circular neighbor balanced designs (CNBDs) are universally optimal in such a model. We prove the universal optimality of circular weakly neighbor balanced designs (CWNBDs), which require a smaller number of blocks than CNBDs. CWNBDs with the number of blocks smaller than the number of treatments belong to the class of partially neighbor balanced designs (PNBDs) defined by Wilkinson et al. (1983 Wilkinson , G. N. , Eckert , R. , Hancock , T. W. , Mayo , O. ( 1983 ). Nearest neighbour (NN) analysis of field experiments . J. Roy. Statist. Soc. Ser. B 45 : 151 – 210 . [Google Scholar]). We give a construction method for some CWNBDs, with examples.     

Some New Series of Partially Balanced Residual Treatment Effects Designs

Blaisdell and Raghavarao (1980 Blaisdell , E. A. , Raghavarao , D. ( 1980 ). Partially balanced change-over designs based on m-associate class PBIB designs . JRSS B 42 : 334 – 338 . [Google Scholar] 1985 Blaisdell , E. A. , Raghavarao , D. ( 1985 ). Efficiency bounds for partially balanced change-over designs based on m-associate class PBIB designs . JRSS B 47 : 132 – 135 . [Google Scholar]) introduced partially balanced residual treatment effects designs and gave methods of construction of these designs. They also gave efficiencies for the estimated direct and residual elementary treatment contrasts of these designs. In this paper, we construct some new series of partially balanced residual treatment effects designs and also give their efficiencies for the estimated direct and residual elementary treatment contrasts.     

Efficient Block Designs for Dependent Observations—A Computer-Aided Search

In this article, the exchange and interchange algorithm of Zergaw (1989 Zergaw , G. ( 1989 ). A sequential method of constructing optimal block designs . Austral. J. Statist. 31 : 333 – 342 .[Crossref] , [Google Scholar]) and Martin and Eccleston (1992 Martin , R. J. , Eccleston , J. A. ( 1992 ). Recursive formulae for constructing block designs with dependent errors . Biometrika 79 : 426 – 430 .[Crossref], [Web of Science ®] , [Google Scholar]) have been modified and used for searching efficient block designs for making all possible pairwise treatment comparisons when observations are dependent. The lower bounds to the A- and D-efficiencies of the designs in a given class of the designs have been obtained for correlated observation structure and the procedure of computing lower bounds to A- and D-efficiencies has been incorporated in the algorithm. The algorithm has been translated into a computer program using Microsoft Visual C++. Using this program, a search for efficient designs for making all possible pairwise treatment comparisons has been made for v ≤ 10, b ≤ 33, k ≤ 10 such that bk ≤ 100 and v > k. The block designs considered are usual block designs (rectangular block designs) and circular block designs. Nearest neighbor (NN), autoregressive of order 1 (AR(1)) correlation structures are studied. The ranges of correlation coefficients for different correlation structures investigated are |ρ|≤0.50 for NN correlation structure in rectangular blocks, |ρ|≤0.45 for NN correlation structure in circular blocks, and |ρ|≤0.95 for AR(1) correlation structure. For these ranges, the matrix of correlation coefficients among observations within a block is positive definite. Robustness aspects of designs that are efficient for a given value of correlation have been investigated against other values of correlation coefficients. Robustness aspects of designs that are efficient for independent observations have also been studied for experimental situations with dependent observations.     

An Improved Solution for Multiple Comparisons with a Control in Response Surface Methodology with Two Predictor Variables

Sa and Edwards (1993 Sa , P. , Edwards , D. ( 1993 ). Multiple comparisons with a control in response surface methodology . Technometrics 35 ( 4 ): 436 – 445 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) first proposed the Multiple Comparisons with a Control problem in Response Surface Methodology. They provided an exact solution for one predictor variable and a conservative solution when number of predictor variables is more than one. Merchant et al. (1998 Merchant , A. , McCann , M. , Edwards , D. ( 1998 ). Improved multiple comparisons with a control in response surface analysis . Technometrics 40 ( 4 ): 291 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]) improved the solution for the latter case. This article improves Merchant et al.'s solution for the case of rotatable designs in two predictor variables.     

A Comparison of Procedures for Controlling the False Discovery Rate in the Presence of Small Variance Genes: A Simulation Study

The Significance Analysis of Microarrays (SAM; Tusher et al., 2001 Tusher , V. G. , Tibshirani , R. , Chu , G. ( 2001 ). Significance analysis of microarrys applied to the ionizing radiation response . Proceedings of the National Academy of Sciences 98 : 5116 – 5121 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) method is widely used in analyzing gene expression data while controlling the FDR by using resampling-based procedure in the microarray setting. One of the main components of the SAM procedure is the adjustment of the test statistic. The introduction of the fudge factor to the test statistic aims at deflating the large value of test statistics due to the small standard error of gene-expression. Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) pointed out that the fudge factor does not effectively improve the power and the control of the FDR as compared to the SAM procedure without the fudge factor in the presence of small variance genes. Motivated by the simulation results presented in Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), in this article, we extend our study to compare several methods for choosing the fudge factor in the modified t-type test statistics and use simulation studies to investigate the power and the control of the FDR of the considered methods.     

Use of Two Decks of Cards in Randomized Response Techniques for Complex Survey Designs

The randomized response (RR) technique with two decks of cards proposed by Odumade and Singh (2009 Odumade , O. , Singh , S. ( 2009 ). Efficient use of two deck of cards in randomized response sampling . Commun. Statist. Theor. Meth. 38 : 439 – 446 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) can always be made more efficient than the RR techniques proposed by Warner (1965 Warner , S. L. ( 1965 ). Randomize response: A survey technique for eliminating evasive answer bias . J. Amer. Statist. Assoc. 60 : 63 – 69 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Mangat and Singh (1990 Mangat , N. S. , Singh , R. ( 1990 ). An alternative randomized response procedure . Biometrika 77 : 349 – 442 .[Crossref], [Web of Science ®] , [Google Scholar]), and Mangat (1994 Mangat , N. S. ( 1994 ). An improved randomized response strategy . J. Roy. Statist. Soc. B 56 : 93 – 95 . [Google Scholar]) by adjusting the proportion of cards in the decks. The proposed method of Odumade and Singh (2009 Odumade , O. , Singh , S. ( 2009 ). Efficient use of two deck of cards in randomized response sampling . Commun. Statist. Theor. Meth. 38 : 439 – 446 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is limited to simple random sampling with replacement (SRSWR) sampling only. In this article, generalization of Odumade and Singh strategy is provided for complex survey designs and a wider class of estimators. The results of Odumade and Singh (2009 Odumade , O. , Singh , S. ( 2009 ). Efficient use of two deck of cards in randomized response sampling . Commun. Statist. Theor. Meth. 38 : 439 – 446 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) can be derived from the proposed method as a special case.     

Rotatability is a Sufficient Condition for A- and D-Rotatability

Designs for estimating axial slopes of a response surface are considered. A design is said to be A- (D-) rotatable if the trace (determinant) of variance–covariance matrix of the estimated slopes at a point in the factor space is a function of the distance of the point from the center of the design. It is shown that for any order d and any dimension k, a design which is rotatable in the Box and Hunter (1957 Box , G. E. P. , Hunter , J. S. ( 1957 ). Multifactor experimental designs for exploring response surfaces . Annals of Mathematical Statistics 28 : 195 – 241 .[Crossref] , [Google Scholar]) sense is automatically A- and D-rotatable. Some specific examples illustrating the validity of this general result are provided.     

Conditions of Slope-Rotatability for Third-Order Polynomial Regression Models

In experimental design for response surface analysis, it is sometimes of interest to estimate the difference of responses at two points. If differences at points close together are involved, the design that reliably estimates the slope of the response surface is important. In particular, Hader and Park (1978 Hader , R. J. , Park , S. H. ( 1978 ). Slope-rotatable central composite designs . Technometrics 20 : 413 – 417 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggested the concept of slope-rotatability and studied slope rotatable central composite designs. Until now, many response surface designs including central composite designs have been suggested for fitting second order response surface models. However, we often need to fit third-order polynomial regression models. In this article, we suggest extended central composite designs (ECCDs) to fit third-order models and find the necessary and sufficient conditions for slope-rotatability over all directions in the third-order polynomial models.     

Aspects of Dependence in Generalized Farlie-Gumbel-Morgenstern Distributions

In this article, we obtained a dependence measure for generalized Farlie-Gumbel-Morgenstern (FGM) family in view of Kochar and Gupta (1987 Kochar , S. G. , Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .[Crossref], [Web of Science ®] , [Google Scholar]) and then compared this measure with Spearman's rho and Kendall's tau in FGM family. Moreover, we evaluated the empirical power of the class of distribution-free tests proposed by Kochar and Gupta (1987 Kochar , S. G. , Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .[Crossref], [Web of Science ®] , [Google Scholar], 1990 Kochar , S. G. , Gupta , R. P. ( 1990 ). Distribution-free tests based on sub-sample extrema for testing against positive dependence . Australian Journal of Statistics 32 : 45 – 51 .[Crossref] , [Google Scholar]) based on exact distribution of a U-statistics. This is derived via a simulation study for sample of sizes n = 6, 8, 10, 12, 16, and 20. Also, we compared our simulation results with those achieved by Amini et al. (2010 Amini , M. , Jabbari , H. , Mohtashami Borzadaran , G. R. , Azadbakhsh , M. ( 2010 ). Power comparison of independence test for the Farlie-Gumbel-Moregenstern family . Communications of the Korean Statistical Society 17 ( 4 ): 493 – 505 .[Crossref] , [Google Scholar]) and Güven and Kotz (2008 Güven , B. , Kotz , S. ( 2008 ). Test of independence for generalized Farlie-Gumbel-Morgenstern distributions . Journal of Computational and Applied Mathematics 212 : 102 – 111 .[Crossref], [Web of Science ®] , [Google Scholar]).     

D-Optimal Chemical Balance Weighing Designs with N ≡ 0 (mod 4) and 3 Objects

In this article, the problem of estimation of the individual weights of three objects using a chemical balance weighing design is considered. We use the criterion of D-optimality. We assume that the covariance matrix of errors is the matrix of first-order autoregressive process. Such problems were discussed in Li and Yang (2005 Li , C. H. , Yang , S. Y. ( 2005 ). On a conjecture in D-optimal designs with n ≡ 0 (mod 4) . Lin. Alg. Applic. 400 : 279 – 290 .[Crossref], [Web of Science ®] , [Google Scholar]) and also in Yeh and Lo Huang (2005 Yeh , H. G. , Lo Huang , M. N. ( 2005 ). On exact D-optimal designs with 2 two-level factors and n autocorrelated observations . Metrika 61 : 261 – 275 .[Crossref], [Web of Science ®] , [Google Scholar]). We present some results of D-optimal designs in certain class of designs with the design matrix X  ∈ M _n×3(±1) such that each column of matrix X has at least one 1 and one ?1.     

Analyzing Supersaturated Designs by Means of an Information Based Criterion

The cost and time consumption of many industrial experimentations can be reduced using the class of supersaturated designs since this can be used for screening out the important factors from a large set of potentially active variables. A supersaturated design is a design for which there are fewer runs than effects to be estimated. Although there exists a wide study of construction methods for supersaturated designs, their analysis methods are yet in an early research stage. In this article, we propose a method for analyzing data using a correlation-based measure, named as symmetrical uncertainty. This method combines measures from the information theory field and is used as the main idea of variable selection algorithms developed in data mining. In this work, the symmetrical uncertainty is used from another viewpoint in order to determine more directly the important factors. The specific method enables us to use supersaturated designs for analyzing data of generalized linear models for a Bernoulli response. We evaluate our method by using some of the existing supersaturated designs, obtained according to methods proposed by Tang and Wu (1997 Tang , B. , Wu , C. F. J. (1997). A method for constructing supersaturated designs and its E(s ²)-optimality. Canadian Journal of Statistics 25:191–201.[Crossref], [Web of Science ®] , [Google Scholar]) as well as by Koukouvinos et al. (2008 Koukouvinos , C. , Mylona , K. , Simos , D. E. ( 2008 ). E(s ²)-optimal and minimax-optimal cyclic supersaturated designs via multi-objective simulated annealing . Journal of Statistical Planning and Inference 138 : 1639 – 1646 .[Crossref], [Web of Science ®] , [Google Scholar]). The comparison is performed by some simulating experiments and the Type I and Type II error rates are calculated. Additionally, Receiver Operating Characteristics (ROC) curves methodology is applied as an additional statistical tool for performance evaluation.     

Some Properties of Semi-Folding Designs

Suppose that some information is available for the particular factor. The experimenter may apply the technique of foldover to isolate the factor and the two-factor interactions involving this factor. In fact, under some situations this can be done by the method of semi-folding. We will discuss this property in detail in this article. Furthermore, we use the computer to search the corresponding optimal semi-folding design for the given 2 ^k?p designs that are tabulated in Chen et al. (1993 Chen , J. , Sun , D. X. , Wu , C. F. J. ( 1993 ). A catalogue of two-level and three-level fractional factorial designs with small runs . International Statistical Review 61 : 131 – 145 .[Crossref], [Web of Science ®] , [Google Scholar]) research.     

Is Each NPMLE of a Continuous Bivariate Distribution Function with Singly Right-Censored Data Really Inconsistent?

We consider non-parametric estimation of a continuous cdf of a random vector (X ₁, X ₂). With bivariate RC data, it is stated in van der Laan (1996 Van der Laan , M. J. ( 1996 ) Efficient estimation in the bivariate censoring model and repairing NPMLE . Ann. Statist. 24 : 596 – 627 .[Crossref], [Web of Science ®] , [Google Scholar], p. 598¹⁰, Ann. Statist.), Quale et al. (2006 Quale , C. M. , van der Laan , M. J. , Robins , J. R. ( 2006 ). Locally efficient estimation with bivariate right-censored data . JASA. 101 : 1076 – 1084 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], JASA) etc. that “it is well known that the NPMLE for continuous data is inconsistent (Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar])).” The claim is based on a result in Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], p.1352, Ann. Statist.) that if X ₁ is right censored but not X ₂, then common ways for defining one NPMLE lead to inconsistency. If X ₁ is right censored and X ₂ is type I right-censored (which includes the case in Tsai et al.), we present a consistent NPMLE. The result corrects a common misinterpretation of Tsai's example (Tsai et al., 1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], Ann. Statist.).     

On Complete Convergence for Arrays of Dependent Random Variables

A complete convergence theorem for an array of rowwise independent random variables was established by Sung et al. (2005 Sung , S. H. , Volodin , A. I. , Hu , T.-C. ( 2005 ). More on complete convergence for arrays . Statist. Probab. Lett. 71 : 303 – 311 .[Crossref], [Web of Science ®] , [Google Scholar]). This result has been generalized and extended by Kruglov et al. (2006 Kruglov , V. M. , Volodin , A. I. , Hu , T.-C. ( 2006 ). On complete convergence for arrays . Statist. Probab. Lett. 76 : 1631 – 1640 .[Crossref], [Web of Science ®] , [Google Scholar]) and Chen et al. (2007 Chen , P. , Hu , T.-C. , Liu , X. , Volodin , A. ( 2007 ). On complete convergence for arrays of rowwise negatively associated random variables . Theor. Probab. Appl. 52 : 393 – 397 . [Google Scholar]). In this article, we extend the results of Sung et al. (2005 Sung , S. H. , Volodin , A. I. , Hu , T.-C. ( 2005 ). More on complete convergence for arrays . Statist. Probab. Lett. 71 : 303 – 311 .[Crossref], [Web of Science ®] , [Google Scholar]), Kruglov et al. (2006 Kruglov , V. M. , Volodin , A. I. , Hu , T.-C. ( 2006 ). On complete convergence for arrays . Statist. Probab. Lett. 76 : 1631 – 1640 .[Crossref], [Web of Science ®] , [Google Scholar]), and Chen et al. (2007 Chen , P. , Hu , T.-C. , Liu , X. , Volodin , A. ( 2007 ). On complete convergence for arrays of rowwise negatively associated random variables . Theor. Probab. Appl. 52 : 393 – 397 . [Google Scholar]) to an array of dependent random variables satisfying Hoffmann-Jørgensen type inequalities.     

Some extensions of circular balanced and circular strongly balanced repeated measurements designs

Repeated measurement designs are widely used in medicine, pharmacology, animal sciences, and psychology. In this paper the works of Iqbal and Tahir (2009 Iqbal, I., and M. H. Tahir. 2009. Circular strongly balanced repeated measurements designs. Communications in Statistics—Theory and Methods 38:3686–96.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Iqbal, Tahir, and Ghazali (2010 Iqbal, I., M. H. Tahir, and S. S. A. Ghazali. 2010. Circular first- and second-order balanced repeated measurements designs. Communications in Statistics—Theory and Methods 39:228–40.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) are generalized for the construction of circular-balanced and circular strongly balanced repeated measurements designs through the method of cyclic shifts for three periods.     

The Identification of Potential Longitudinal Biomarkers and Measurements of Effectiveness for Biomarkers as Surrogates in Multivariate Survival Data

A proposed method based on frailty models is used to identify longitudinal biomarkers or surrogates for a multivariate survival. This method is an extention of earlier models by Wulfsohn and Tsiatis (1997 Wulfsohn , M. S. , Tsiatis , A. A. ( 1997 ). A joint model for survival and longitudinal data measured with error . Biometrics 53 ( 1 ): 330 – 339 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Song et al. (2002 Song , X. , Davidian , M. , Tsiatis , A. A. ( 2002 ). A Semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data . Biometrics 58 ( 4 ): 742 – 753 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). In this article, similar to Henderson et al. (2002 Henderson , R. , Diggle , P. J. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), a joint likelihood function combines the likelihood functions of the longitudinal biomarkers and the multivariate survival times. We use simulations to explore how the number of individuals, the number of time points per individual and the functional form of the random effects from the longitudianl biomarkers influence the power to detect the association of a longitudinal biomarker and the multivariate survival time. The proposed method is illustrate by using the gastric cancer data.     

A Bayes Factor for Replications of ANOVA Results

ABSTRACT

With an increasing number of replication studies performed in psychological science, the question of how to evaluate the outcome of a replication attempt deserves careful consideration. Bayesian approaches allow to incorporate uncertainty and prior information into the analysis of the replication attempt by their design. The Replication Bayes factor, introduced by Verhagen and Wagenmakers (2014 Verhagen, J., and Wagenmakers, E.-J. (2014), “Bayesian Tests to Quantify the Result of a Replication Attempt,” Journal of Experimental Psychology: General, 143, 1457–1475. DOI: 10.1037/a0036731.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), provides quantitative, relative evidence in favor or against a successful replication. In previous work by Verhagen and Wagenmakers (2014 Verhagen, J., and Wagenmakers, E.-J. (2014), “Bayesian Tests to Quantify the Result of a Replication Attempt,” Journal of Experimental Psychology: General, 143, 1457–1475. DOI: 10.1037/a0036731.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), it was limited to the case of t-tests. In this article, the Replication Bayes factor is extended to F-tests in multigroup, fixed-effect ANOVA designs. Simulations and examples are presented to facilitate the understanding and to demonstrate the usefulness of this approach. Finally, the Replication Bayes factor is compared to other Bayesian and frequentist approaches and discussed in the context of replication attempts. R code to calculate Replication Bayes factors and to reproduce the examples in the article is available at https://osf.io/jv39h/.