A clinical application of expert system methodology

In recent years, several expert systems have been developed for practical applications in applied statistical methodologies. Existing expert systems in statistics have explored several areas, e.g. the determination of appropriate statistical tests, regression analysis, and determination of the ‘best’ experimental design for industrial screening experiments. We present here the DESIGN EXPERT which is a prototype expert system for the design of complex statistical experiments. It is intended for scientific investigators and statisticians who must design and analyze complex experiments, e.g. multilevel medical experiments with nested factors, repeated measures, and both fixed and random eflects. This system is ‘expert’ in the sense that it is capable of the following:(i) recognize specific types of complex experimental designs, based on the application of inference rules to non-technical information supplied by the user; (ii) encode the obtained and inferred information in a flexible general-purpose internal representation, for use by other program modules; (iii) generate analysis of variance tables for the recognized design and an appropriate BMDP runfile for data analysis, using the encoded information. DESIGN EXPERT is capable of recognizing randomized block designs, including lattice designs within embedded Latin squares, cross-over designs, split plots, nesting, repeated measures and covariates. It is written in an experimental programming language developed specifically for research in artificial intelligence.     

ON THE OPTIMAL ASYMPTOTIC TESTS FOR THE EFFECTS OF CLOUD SEEDING ON RAINFALL (1) THE CASE OF FIXED EFFECTS

In this paper we consider a sequence of experimental units {u_n} which are t o be treated according to some random scheme. A general randomized design is suggested for the purpose. Asymptotic tests, optimal in some sense, are derived for testing the absence of the effects of the treatment. These tests are applicable in various situations, for example, when the treatment effects are additive or when they are multiplicative. Based on the asymptotic power of the tests obtained, optimality of various designs is discussed. The randomized designs discussed here have a wide range of applicability, e.g. in weather modification experiments and bio-assay.     

Analyzing Hybrid Randomized Response Data with a Binomial Selection Procedure

The operating characteristics (OCs) of an indifference-zone ranking and selection procedure are derived for randomized response binomial data. The OCs include tables and figures to facilitate tradeoffs between sample size and a stated probability of a correct selection, i.e., correctly identifying the binomial population (out of k ≥ 2) characterized by the largest probability of success. Measures of efficiency are provided to assist the analyst in selection of an appropriate randomized response design for the collection of the data. A hybrid randomized response model, which includes the Warner model and the Greenberg et al. model, is introduced to facilitate comparisons among a wider range of statistical designs than previously available. An example comparing failure rates of contraceptive methods is used to illustrate the use of these new results.     

Analysis of a supersaturated design using Entropy Prior Complexity for binary responses via generalized linear models

A supersaturated design is a factorial design in which the number of effects to be estimated is greater than the available number of experimental runs. It is used in many experiments for screening purposes, i.e., for studying a large number of factors and then identifying the active ones. The goal with such a design is to identify just a few of the factors under consideration, that have dominant effects and to do this at minimum cost. While most of the literature on supersaturated designs has focused on the construction of designs and their optimality, the data analysis of such designs remains still at an early stage. In this paper, we incorporate the parameter model complexity into the supersaturated design analysis process, by assuming generalized linear models for a Bernoulli response, for analyzing main effects designs and discovering simultaneously the effects that are significant.     

Estimating standard error of intra-class correlation coefficients up to three level unbalanced nested clinical trials

ABSTRACT

Very often researchers plan a balanced design for cluster randomization clinical trials in conducting medical research, but unavoidable circumstances lead to unbalanced data. By adopting three or more levels of nested designs, they usually ignore the higher level of nesting and consider only two levels, this situation leads to underestimation of variance at higher levels. While calculating the sample size for three-level nested designs, in order to achieve desired power, intra-class correlation coefficients (ICCs) at individual level as well as higher levels need to be considered and must be provided along with respective standard errors. In the present paper, the standard errors of analysis of variance (ANOVA) estimates of ICCs for three-level unbalanced nested design are derived. To conquer the strong appeal of distributional assumptions, balanced design, equality of variances between clusters and large sample, general expressions for standard errors of ICCs which can be deployed in unbalanced cluster randomization trials are postulated. The expressions are evaluated on real data as well as highly unbalanced simulated data.     

A method for obtaining randomized block designs in preclinical studies with multiple quantitative blocking variables

A method is proposed for block randomization of treatments to experimental units that can accommodate both multiple quantitative blocking variables and unbalanced designs. Hierarchical clustering in conjunction with leaf‐order optimization is used to block experimental units in multivariate space. The method is illustrated in the context of a diabetic mouse assay. A simulation study is presented to explore the utility of the proposed randomization method relative to that of a completely randomized approach, both in the presence and absence of covariate adjustment. An example R function is provided to illustrate the implementation of the method. Copyright © 2010 John Wiley & Sons, Ltd.     

Designing field experiments which are subject to representation bias

The term 'representation bias' is used to describe the disparities that exist between treatment effects estimated from field experiments, and those effects that would be seen if treatments were used in the field. In this paper we are specifically concerned with representation bias caused by disease inoculum travelling between plots, or out of the experimental area altogether. The scope for such bias is maximized in the case of airborne spread diseases. This paper extends the work of Deardon et al. (2004), using simulation methods to explore the relationship between design and representation bias. In doing so, we illustrate the importance of plot size and spacing, as well as treatment-to-plot allocation. We examine a novel class of designs, incomplete column designs, to develop an understanding of the mechanisms behind representation bias. We also introduce general methods of designing field trials, which can be used to limit representation bias by carefully controlling treatment to block allocation in both incomplete column and incomplete randomized block designs. Finally, we show how the commonly used practice of sampling from the centres of plots, rather than entire plots, can also help to control representation bias.     

Hypothesis Testing in Multivariate Linear Models with Randomly Missing Data

Tests for mean equality proposed by Weerahandi (1995) and Chen and Chen (1998), tests that do not require equality of population variances, were examined when data were not only heterogeneous but, as well, nonnormal in unbalanced completely randomized designs. Furthermore, these tests were compared to a test examined by Lix and Keselman (1998), a test that uses a heteroscedastic statistic (i.e., Welch, 1951) with robust estimators (20% trimmed means and Winsorized variances). Our findings confirmed previously published data that the tests are indeed robust to variance heterogeneity when the data are obtained from normal populations. However, the Weerahandi (1995) and Chen and Chen (1998) tests were not found to be robust when data were obtained from nonnormal populations. Indeed, rates of Type I error were typically in excess of 10% and, at times, exceeded 50%. On the other hand, the statistic presented by Lix and Keselman (1998) was generally robust to variance heterogeneity and nonnormality.     

Application of PBIB designs in CDC Method IV

In this paper we propose the use of some partially balanced incomplete block designs for blocking in complete diallel cross Method IV (Griffing, 1956) to deal with the situation when it is not desirable for all crosses to be accommodated in the block of a traditional randomized block design. A method is also proposed to analyse the MatingEnvironment designs for estimating the general combining ability effect of lines.     

Comparison of unweighted and weighted rank based tests for an ordered alternative in randomized complete block designs

In randomized complete block designs, a monotonic relationship among treatment groups may already be established from prior information, e.g., a study with different dose levels of a drug. The test statistic developed by Page and another from Jonckheere and Terpstra are two unweighted rank based tests used to detect ordered alternatives when the assumptions in the traditional two-way analysis of variance are not satisfied. We consider a new weighted rank based test by utilizing a weight for each subject based on the sample variance in computing the new test statistic. The new weighted rank based test is compared with the two commonly used unweighted tests with regard to power under various conditions. The weighted test is generally more powerful than the two unweighted tests when the number of treatment groups is small to moderate.     

A scenario for sequential experimentation

This tutorial emphasizes the role of differecnt types of experimental design in a multi–stage investigation. In the initial phase group–screeningo can reveal the really important factors among hundreds of factors. Resooulution III designs are useful immediately after the screening phase, to investigate firstorder effects, provided higher–order effects are unimportants, i.e., validation is necessary. Resulotion IV designs may explain why a first–order model is not valid, i.e., they may yield unbiased estimators of sums of interactions. Resolution V designs yield unbiased estimators of the individual two–factor interactions. They can be easily extended to central composite designs to estimate pure quadratic effects of quantitative factors. Smaller steps are also possible, e.g. one run at a time, for model discrimination and calibration.     

Estimation of Missing Cells in Randomized Block and Latin Square Designs

Classical missing cell formulas for the randomized block design and Latin square design are derived using the modified cell means model. The role of the assumptions of no interaction for these designs is made clear in the development. Examples are given for the randomized block and Latin square.     

Optimum covariate designs in partially balanced incomplete block (PBIB) design set-ups

The use of covariates in block designs is necessary when the covariates cannot be controlled like the blocking factor in the experiment. In this paper, we consider the situation where there is some flexibility for selection in the values of the covariates. The choice of values of the covariates for a given block design attaining minimum variance for estimation of each of the parameters has attracted attention in recent times. Optimum covariate designs in simple set-ups such as completely randomised design (CRD), randomised block design (RBD) and some series of balanced incomplete block design (BIBD) have already been considered. In this paper, optimum covariate designs have been considered for the more complex set-ups of different partially balanced incomplete block (PBIB) designs, which are popular among practitioners. The optimum covariate designs depend much on the methods of construction of the basic PBIB designs. Different combinatorial arrangements and tools such as orthogonal arrays, Hadamard matrices and different kinds of products of matrices viz. Khatri–Rao product, Kronecker product have been conveniently used to construct optimum covariate designs with as many covariates as possible.     

A case study comparing a randomized withdrawal trial and a double-blind long-term trial for assessing the long-term efficacy of an antidepressant

Assessing long-term efficacy in psychiatric drugs involves a number of complex questions, and the priaority of these questions is different for different disorders and for different stakeholders. Therefore, it is essential that we not adopt a one-method-fits-all approach, but rather adapt the specific details of the designs and analysis of data from long-term trials to individual disease states. Randomized withdrawal (RW) designs, even though addressing a specific question of particular interest, face some difficult methodological and ethical challenges. A less common alternative design, termed the double-blind long-term efficacy (DBLE) design, is logistically similar to traditional responder extension designs. However, use of an analytic approach that includes all randomized patients rather than only the selected subset that continued beyond acute treatment avoids the major criticism of the extender design. The present paper illustrates the attributes of the RW and DBLE designs by analyzing data from trials adopting these designs. The RW and DBLE designs address different questions, and are thus not directly comparable. Potential benefits of the DBLE design include: (1) the parsimonious use of patients and the resultant reduced exposure to placebo as each patient can contribute to multiple developmental objectives; (2) the results are generalizable to actual clinical practice as the design matches treatment guidelines; and, (3) results of safety assessments are meaningful as they involve all randomized patients. Our case study suggests that the DBLE design can provide definitive answers to important questions and may be a useful design for assessing long-term treatment effects.     

On selecting the best treatment in a generalized linear model

The problem of selecting the best treatment is studied under generalized linear models. For certain balanced designs, it is shown that simple rules are Bayes with respect to any non-informative prior on the treatment effects under any monotone invariant loss. When the nuisance parameters such as block effects are assumed to follow a uniform (improper) prior or a normal prior, Bayes rules are obtained for the normal linear model under more suitable balanced designs, keeping the generality of the loss and the generality of the non-informativeness on the prior of the treatment effects. These results are extended to certain types of informative priors on the treatment effects. When the designs are unbalanced, algorithms based on the Gibbs sampler and the Laplace method are provided to compute the Bayes rules.     

Short confidence intervals for variance components

Four approximate methods are proposed to construct confidence intervals for the estimation of variance components in unbalanced mixed models. The first three methods are modifications of the Wald, arithmetic and harmonic mean procedures, see Harville and Fenech (1985), while the fourth is an adaptive approach, combining the arithmetic and harmonic mean procedures. The performances of the proposed methods were assessed by a Monte Carlo simulation study. It was found that the intervals based on Wald's method maintained the nominal confidence levels across all designs and values of the parameters under study. On the other hand, the arithmetic (harmonic) mean method performed well for small (large) values of the variance component, relative to the error variance component. The adaptive procedure performed rather well except for extremely unbalanced designs. Further, compared with equal tails intervals, the intervals which use special tables, e.g., Table 678 of Tate and Klett (1959), provided adequate coverage while having much shorter lengths and are thus recommended for use in practice.     

Estimation with unbalanced panel data having covariate measurement error

Panel data with covariate measurement error appear frequently in various studies. Due to the sampling design and/or missing data, panel data are often unbalanced in the sense that panels have different sizes. For balanced panel data (i.e., panels having the same size), there exists a generalized method of moments (GMM) approach for adjusting covariate measurement error, which does not require additional validation data. This paper extends the GMM approach of adjusting covariate measurement error to unbalanced panel data. Two health related longitudinal surveys are used to illustrate the implementation of the proposed method.     

Optimal Experiments for Time-Dependent Mineral Processes

Time dependence is an important characteristic of mineral processing plant data. This paper finds that the time dependence in the recovery data for an experiment at Bougainville Copper Limited (BCL) (Napier-Munn, 1995) can be described by an autoregressive-one process. The paper investigates the optimum form of experimental design for such data. Two intuitive approaches for the design of experiments involving time-dependent data have been disproved recently. Cheng & Steinberg (1991) showed that in some circumstances systematic experiments are preferable to replicated randomized block designs, and Saunders & Eccleston (1992) showed that rather than sampling at a frequency which ensures independent data, in some circumstances sampling intervals should be as small as possible. A third issue, raised in this paper, concerns the use of standard statistical tests when the data are serially correlated. It is shown that the simple paired t -test, suitably modified for time dependence, is appropriate and easily adapted to allow for a covariate and a sequential analysis. The results are illustrated using the BCL data and are already being used to design major experiments involving another mineral process.     

A useful approximation for planning block designs with potential missing data

Many empirical studies are planned with the prior knowledge that some of the data may be missed. This knowledge is seldom explicitly incorporated into the experiment design process for lack of a candid methodology. This paper proposes an index related to the expected determinant of the information matrix as a criterion for planning block designs. Due to the intractable nature of the expected determinantal criterion an analytic expression is presented only for a simple 2x2 layout. A first order Taylor series approximation function is suggested for larger layouts. Ranges over which this approximation is adequate are shown via Monte Carlo simulations. The robustness of information in the block design relative to the completely randomized design with missing data is discussed.     

The mad estimator: when is it non-linear? applications to two-way design models

The mean absolute deviation (MAD) estimator has recently received a great deal of attention as applied to full-rank linear regression models. This paper provides a necessary and sufficient condition for the MAD estimator to be a non-linear estimator, in which case conditions for the variance of the MAD estimator to be larger or smaller than those for OLS are, in general, unknown. The non-linearity of the MAD estimator is examined for several two-way designs; in particular (1) randomized block design (2) two-way nested design (3) two-way classification with interaction and (4) partially balanced incomplete block design