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PubMed2002

Now you see it, now you don't: statistical and methodological considerations in fMRI.

We illustrate the effects of statistical threshold, spatial clustering, voxel size, and two approaches to multiple comparison correction on fMRI results. We first analyzed fMRI images obtained from a single subject during a noun-verb matching task. Data were analyzed with Statistical Parametric Mapping (SPM) using two different voxel sizes, and results were displayed at three different levels of statistical significance. At each statistical threshold, results were first uncorrected for multiple comparisons and spatial extent and then presented using a spatial extent cluster of 20 voxels. We then statistically controlled the Type I error rate associated with multiple comparisons by using the false discovery rate and by the random field adjustment for false-positive rate used by SPM. We also examined group results from language and graphesthesia paradigms at three levels of statistical significance. In all circumstances, apparent random activations decreased as more conservative statistical approaches were employed, but activation in areas considered to be functionally significant was also reduced. These issues are important in the choice of analytic approach and interpretation of fMRI results, with clear implications for the surgical management of individual patients when fMRI results are used to delineate specific areas of eloquent cortex.

Journal Article↗
PubMed2002

Application of an adjusted chi2 statistic to site-specific data in observational dental studies.

BACKGROUND: When a binary response is observed on teeth from each subject belonging to 2 or more exposure groups, application of the usual Pearson chi2 tests is invalid, since such responses within the same subject are not independent. Consequently, special statistical methods are needed to control for the correlation among teeth (sites) within the same subject. A simple adjustment to the Pearson chi2 statistic has been proposed for comparing proportions in site-specific data. However, the required assumptions for this statistic have not yet been thoroughly addressed. These assumptions are guaranteed to hold in experimental comparisons, but may be violated in some observational studies. METHOD: We investigate the conditions under which the adjusted chi2 statistic is valid and examine the performance of the adjusted chi2 statistic when these conditions are violated. RESULTS: Our simulation study shows that the adjusted chi2 statistic generally produces good empirical type I errors under the assumption of a common intracluster correlation coefficient. Even if the intracluster correlations are different, the adjusted statistic performs well when the groups have equal numbers of clusters (subjects). CONCLUSION: The discussion is illustrated using an observational study of caries on the roots of teeth.

Analysis of Variance↗
PubMed2003

Statistically relevant conserved quantities for truncated quasigeostrophic flow.

Systematic applications of ideas from equilibrium statistical mechanics lead to promising strategies for assessing the unresolved scales of motion in many problems in science and engineering. A scientific debate over more than the last 25 years involves which conserved quantities among the formally infinite list are statistically relevant for the large-scale equilibrium statistical behavior. Here this important issue is addressed by using suitable discrete numerical approximations for geophysical flows with many conserved quantities as a numerical laboratory. The results of numerical experiments are presented here for these truncated geophysical flows with topography in a suitable regime. These experiments establish that the integrated third power of potential vorticity besides the familiar constraints of energy, circulation, and enstrophy (the integrated second power) is statistically relevant in this regime for the coarse-grained equilibrium statistical behavior at large scales. Furthermore, the integrated higher powers of potential vorticity larger than three are statistically irrelevant for the large-scale equilibrium statistical behavior in the examples studied here.

Journal Article↗
PubMed2000

Scan statistics to scan markers for susceptibility genes.

Scan statistics are applied to combine information on multiple contiguous genetic markers used in a genome screen for susceptibility loci. This information may be, for example, allele sharing proportions for sib pairs or logarithm of odds (lod) scores in general small families. We focus on a dichotomous outcome variable, for example, case and control individuals or affected-affected versus affected-unaffected siblings, and suitable single-marker statistics. A significant scan statistic based on the single-marker statistics represents evidence of the presence of a susceptibility gene. For a given length of the scan statistic, we assess its significance by Monte Carlo permutation tests. Comparing P values for varying lengths of scan statistics, we treat the smallest observed P value as our statistic of interest and determine its overall significance level. We applied this method to a genome screen with autism families. The result was informative and surprising: A susceptibility region was found (genome-wide significance level, P = 0.038), which is missed with conventional approaches.

Alleles↗
PubMed2002

Statistical mechanics in the context of special relativity.

In Ref. [Physica A 296, 405 (2001)], starting from the one parameter deformation of the exponential function exp(kappa)(x)=(sqrt[1+kappa(2)x(2)]+kappax)(1/kappa), a statistical mechanics has been constructed which reduces to the ordinary Boltzmann-Gibbs statistical mechanics as the deformation parameter kappa approaches to zero. The distribution f=exp(kappa)(-beta E+betamu) obtained within this statistical mechanics shows a power law tail and depends on the nonspecified parameter beta, containing all the information about the temperature of the system. On the other hand, the entropic form S(kappa)= integral d(3)p(c(kappa) f(1+kappa)+c(-kappa) f(1-kappa)), which after maximization produces the distribution f and reduces to the standard Boltzmann-Shannon entropy S0 as kappa-->0, contains the coefficient c(kappa) whose expression involves, beside the Boltzmann constant, another nonspecified parameter alpha. In the present effort we show that S(kappa) is the unique existing entropy obtained by a continuous deformation of S0 and preserving unaltered its fundamental properties of concavity, additivity, and extensivity. These properties of S(kappa) permit to determine unequivocally the values of the above mentioned parameters beta and alpha. Subsequently, we explain the origin of the deformation mechanism introduced by kappa and show that this deformation emerges naturally within the Einstein special relativity. Furthermore, we extend the theory in order to treat statistical systems in a time dependent and relativistic context. Then, we show that it is possible to determine in a self consistent scheme within the special relativity the values of the free parameter kappa which results to depend on the light speed c and reduces to zero as c--> infinity recovering in this way the ordinary statistical mechanics and thermodynamics. The statistical mechanics here presented, does not contain free parameters, preserves unaltered the mathematical and epistemological structure of the ordinary statistical mechanics and is suitable to describe a very large class of experimentally observed phenomena in low and high energy physics and in natural, economic, and social sciences. Finally, in order to test the correctness and predictability of the theory, as working example we consider the cosmic rays spectrum, which spans 13 decades in energy and 33 decades in flux, finding a high quality agreement between our predictions and observed data.

Journal Article↗
PubMed2003

Active and passive fields in turbulent transport: the role of statistically preserved structures.

We have recently proposed that the statistics of active fields (which affect the velocity field itself) in well-developed turbulence are also dominated by the statistically preserved structures of auxiliary passive fields which are advected by the same velocity field. The statistically preserved structures are eigenmodes of eigenvalue 1 of an appropriate propagator of the decaying (unforced) passive field, or equivalently, the zero modes of a related operator. In this paper we investigate further this surprising finding via two examples of shell models, one akin to turbulent convection in which the temperature is the active scalar, and the other akin to magnetohydrodynamics in which the magnetic field is the active vector. In the first example, all the even correlation functions of the active and passive fields exhibit identical scaling behavior. The second example appears at first sight to be a counterexample: the statistical objects of the active and passive fields have entirely different scaling exponents. We demonstrate, nevertheless, that the statistically preserved structures of the passive vector dominate again the statistics of the active field, except that due to a dynamical conservation law the amplitude of the leading zero mode cancels exactly. The active vector is then dominated by the subleading zero mode of the passive vector. Our work thus suggests that the statistical properties of active fields in turbulence can be understood with the same generality as those of passive fields.

Journal Article↗
PubMed1999

A global goodness-of-fit statistic for Cox regression models.

In this paper, a global goodness-of-fit test statistic for a Cox regression model, which has an approximate chi-squared distribution when the model has been correctly specified, is proposed. Our goodness-of-fit statistic is global and has power to detect if interactions or higher order powers of covariates in the model are needed. The proposed statistic is similar to the Hosmer and Lemeshow (1980, Communications in Statistics A10, 1043-1069) goodness-of-fit statistic for binary data as well as Schoenfeld's (1980, Biometrika 67, 145-153) statistic for the Cox model. The methods are illustrated using data from a Mayo Clinic trial in primary billiary cirrhosis of the liver (Fleming and Harrington, 1991, Counting Processes and Survival Analysis), in which the outcome is the time until liver transplantation or death. The are 17 possible covariates. Two Cox proportional hazards models are fit to the data, and the proposed goodness-of-fit statistic is applied to the fitted models.

Biometry↗
PubMed1998

Clinical significance not statistical significance: a simple Bayesian alternative to p values.

OBJECTIVES: To take the common "Bayesian" interpretation of conventional confidence intervals to its logical conclusion, and hence to derive a simple, intuitive way to interpret the results of public health and clinical studies. DESIGN AND SETTING: The theoretical basis and practicalities of the approach advocated is at first explained and then its use is illustrated by referring to the interpretation of a real historical cohort study. The study considered compared survival on haemodialysis (HD) with that on continuous ambulatory peritoneal dialysis (CAPD) in 389 patients dialysed for end stage renal disease in Leicestershire between 1974 and 1985. Careful interpretation of the study was essential. This was because although it had relatively low statistical power, it represented all of the data that were available at the time and it had to inform a critical clinical policy decision: whether or not to continue putting the majority of new patients onto CAPD. MEASUREMENTS AND ANALYSIS: Conventional confidence intervals are often interpreted using subjective probability. For example, 95% confidence intervals are commonly understood to represent a range of values within which one may be 95% certain that the true value of whatever one is estimating really lies. Such an interpretation is fundamentally incorrect within the framework of conventional, frequency-based, statistics. However, it is valid as a statement of Bayesian posterior probability, provided that the prior distribution that represents pre-existing beliefs is uniform, which means flat, on the scale of the main outcome variable. This means that there is a limited equivalence between conventional and Bayesian statistics, which can be used to draw simple Bayesian style statistical inferences from a standard analysis. The advantage of such an approach is that it permits intuitive inferential statements to be made that cannot be made within a conventional framework and this can help to ensure that logical decisions are taken on the basis of study results. In the particular practical example described, this approach is applied in the context of an analysis based upon proportional hazards (Cox) regression. MAIN RESULTS AND CONCLUSIONS: The approach proposed expresses conclusions in a manner that is believed to be a helpful adjunct to more conventional inferential statements. It is of greatest value in those situations in which statistical significance may bear little relation to clinical significance and a conventional analysis using p values is liable to be misleading. Perhaps most importantly, this includes circumstances in which an important public health or clinical decision must be based upon a study that has unavoidably low statistical power. However, it is also useful in situations in which a decision must be based upon a large study that indicates that an effect that is highly statistically significant seems too small to be of practical relevance. In the illustrative example described, the approach helped in making a decision regarding the use of CAPD in Leicestershire during the latter half of the 1980s.

Bayes Theorem↗
PubMed2005

Selecting genes by test statistics.

Gene selection is an important issue in analyzing multiclass microarray data. Among many proposed selection methods, the traditional ANOVA F test statistic has been employed to identify informative genes for both class prediction (classification) and discovery problems. However, the F test statistic assumes an equal variance. This assumption may not be realistic for gene expression data. This paper explores other alternative test statistics which can handle heterogeneity of the variances. We study five such test statistics, which include Brown-Forsythe test statistic and Welch test statistic. Their performance is evaluated and compared with that of F statistic over different classification methods applied to publicly available microarray datasets.

Journal Article↗
PubMed2006

Revision of visual impairment definitions in the International Statistical Classification of Diseases.

BACKGROUND: The existing definitions of visual impairment in the International Statistical Classification of Diseases are based on recommendations made over 30 years ago. New data and knowledge related to visual impairment that have accumulated over this period suggest that these definitions need to be revised. DISCUSSION: Three major issues need to be addressed in the revision of these definitions. First, the existing definitions are based on best-corrected visual acuity, which exclude uncorrected refractive error as a cause of visual impairment, leading to substantial underestimation of the total visual impairment burden by about 38%. Second, the cut-off level of visual impairment to define blindness in the International Statistical Classification of Diseases is visual acuity less than 3/60 in the better eye, but with increasing human development the visual acuity requirements are also increasing, suggesting that a level less than 6/60 be used to define blindness. Third, the International Statistical Classification of Diseases uses the term 'low vision' for visual impairment level less than blindness, which causes confusion with the common use of this term for uncorrectable vision requiring aids or rehabilitation, suggesting that alternative terms such as moderate and mild visual impairment would be more appropriate for visual impairment less severe than blindness. We propose a revision of the definitions of visual impairment in the International Statistical Classification of Diseases that addresses these three issues. According to these revised definitions, the number of blind persons in the world defined as presenting visual acuity less than 6/60 in the better eye would be about 57 million as compared with the World Health Organization estimate of 37 million using the existing International Statistical Classification of Diseases definition of best-corrected visual acuity less than 3/60 in the better eye, and the number of persons in the world with moderate visual impairment defined as presenting visual acuity less than 6/18 to 6/60 in the better eye would be about 202 million as compared with the World Health Organization estimate of 124 million persons with low vision defined as best-corrected visual acuity less than 6/18 to 3/60 in the better eye. CONCLUSION: Our suggested revision of the visual impairment definitions in the International Statistical Classification of Diseases takes into account advances in the understanding of visual impairment. This revised classification seems more appropriate for estimating and tracking visual impairment in the countries and regions of the world than the existing classification in the International Statistical Classification of Diseases.

Biometry↗
PubMedDate not supplied

Consideration of media fill tests for evaluation and control of aseptic processes: a statistical approach to quality criteria.

The concept of upper and lower statistical confidence limits has been introduced to the current media fill tests used for the assurance of aseptic operation. Results of media fill tests can be evaluated with rationale and interpreted more clearly by introducing the upper and lower limits for the number of observed positive units. Quality criteria derived by the misuse of statistics should be reconsidered. Media fill tests are one of the most useful methods for the evaluation of aseptic filling processes, and acceptance criteria have been issued in various official compendia. In some official compendia, various combinations of the number of media fills and the number of detected allowable contaminated units have been indicated based on the misuse of statistics. This study has statistically revealed that the larger number of fills allows for the worse average accepted quality. This study has shown that media fill tests can be used for the evaluation of aseptic operation with fully scientific and statistical rationale by evaluating the statistical lower limit for the number of positive units observed. This study proposed that the new criteria should be simply expressed as the process should be in a controlled state and can manufacture product whose sterility can be statistically assured with 95% confidence level.

Asepsis↗
PubMed2003

[Statistical correlation between a transference test and embryonic transference in an assisted reproduction program].

OBJECTIVE: Determining if a statistical correlation can be established between those variables observed during the transference test performed before ovarian stimulation and those obtained during the real embryo transference. TYPE OF STUDY: Clinical retrospective. MATERIALS AND METHODS: Ninety four female patients included in the IVF-ET were studied and a transference test previous to ovarian stimulation was performed. The following parameters were considered in this test: hysterometry, type of catheter, degree of difficulty, and person performing it. A total of 117 embryonic transferences were carried out, and the same parameters observed during the test were measured. The chi square test was used for the statistical analysis. RESULTS: The most commonly used kind of catheter was the Cook Soft Pass (n = 92), and a statistically significant correlation was observed with the one used during the real transference (n = 94). Concerning the degree of difficulty, the transference test resulted complicated in 4.2% of the cases, difficult in 31.6% of them, and easy in 64.2% of them, presenting a statistical correlation with the real transference, where the procedure resulted complicated in 1.7% of the patients, difficult in 32.4% of them, and easy in 65.8%. In addition, and with the intention of ruling out the medical factor, we tried to have the same person performing the transference test and the real procedure, and a statistically significant correlation was also observed. Pregnancy rate per transference was 27.4%. When an association between the difficulty of a real transference and pregnancy rates was tried, no statistical association between an easy or a difficult transference was observed. CONCLUSIONS: Embrionic transference is a fundamental phase for IVF-ET programs. However, a variety of factors can influence this procedure, some are medical and others are mechanical. Our results allow us to conclude that there is a statistical correlation between those variables observed during the real embryonic transference and the test, so the latter can be considered as a very useful element in the integral in vitro fertilization process, which prevents the real transference from becoming a blind procedure.

Adult↗
PubMed2003

The effect of revised populations on mortality statistics for the United States, 2000.

OBJECTIVES: This report presents revised mortality statistics for the year 2000 based on April 1, 2000, population figures from the 2000 census. Death rates are presented by race, Hispanic origin, sex, age, and cause of death. Life expectancies are presented by race (white and black), sex, and age. The revised statistics are compared with previously published statistics that used July 1, 2000, postcensal population estimates based on the 1990 census. METHODS: Data in this report are based on information from all death certificates filed in the 50 States and the District of Columbia. The statistics presented in this report are computed on the basis of two sets of population figures provided by the U.S. Census Bureau. The first set includes July 1, 2000, postcensal population estimates based on the 1990 decennial census. The second set includes April 1, 2000, populations from the 2000 decennial census bridged to single race categories. RESULTS: Crude death rates were lower for all groups using the April 1, 2000, populations. Age-specific death rates were generally lower for most age groups, except for infants and the very old for which death rates were higher. Age-specific death rates for males were lower for most age groups, except infants and those 75 years and over. For females, with the exception of infants, age-specific death rates were lower. Race-specific pattems by age for the white and black populations were similar to all races combined. For the American Indian population, age-specific death rates were substantially lower for ages under 75 years. For ages 75 years and over, American Indian death rates were dramatically higher. Age-specific death rates for the Asian or Pacific Islander (API) population were higher for ages under 15 years; lower for ages 15-84 years, especially for the 15-34 year age group; and higher for those 85 years and over. For the Hispanic population, age-specific death rates were substantially lower for those age 15-34 years and higher for those age 55 years and over, especially for those age 85 years and over. For the total white and total black populations, the age-adjusted death rate was somewhat higher for males and lower for females. For API the pattern was reversed. For the American Indian and Hispanic populations, age-adjusted death rates were higher for both males and females. For the 15 leading causes of death, age-adjusted death rates based on the April 1, 2000, population figures were lower for heart disease, cancer, chronic liver disease, septicemia, diabetes, chronic lower respiratory diseases, unintentional injuries, homicide, suicide, and hypertension. Age-adjusted death rates were higher for pneumonitis, Alzheimer's disease, and stroke. Rates were unchanged for influenza and pneumonia and nephritis, nephrotic syndrome and nephrosis. Life expectancy at birth was higher for the entire population and both the white and black populations using the April 1, 2000, population figures. It was 0.1 year higher for the whole population as well as for the total white and total black populations. For the total male population, life expectancy at birth was 0.1 year higher while it was 0.2 years higher for the female population. The increase in life expectancy at birth was 0.1 year for both sexes within the white and black populations. This observed gain in life expectancy at birth based on the revised population figures is reversed for life expectancy at the oldest age groups for the whole population and for males. A similar pattern is observed for both white and black males; however, the magnitude of the decline in life expectancy at older ages is much greater among black males. Among females of both race groups and the total population, there is either no change or an increase in life expectancy in the oldest age groups. CONCLUSIONS: Revised death rates and life expectancies are, in many cases, significantly different from previously published mortality statistics calculated using 1990-based postcensal estimates for 2000. Thus, previously published mortality statistics for 2000 using the 1990-based populations will not be comparable to the corresponding statistics that will be published for 2001. The data in this report will provide comparable 2000 data. Efforts are also underway to revise previously published mortality tables for 2000 as well as previously published data for 1991-99.

Adolescent↗
PubMed2006

"Statistical evidence" for the investigation of international crimes.

Statistics are widely applied throughout scientific research disciplines but 'statistical evidence' sounds surely an unhappy term rather avoided. In International Criminal Law the term seems to stress the value that statistical methods have for the analysis of large-scale victimisation and describes rather the tools used to support the evidence. However, statistics is required for valid, reliable and objective results that would otherwise be left in the dusty political sphere of the warring parties and their actors. But what are the concepts to do so? Today's presentation shows two widely known cases from the International Criminal Tribunal for the Former Yugoslavia (ICTY) where statisticians analysed the Crime Scenes in Srebrenica and Kosovo. The cases introduce two different analytical approaches. Firstly, in Srebrenica the analysts focussed on civilians that were killed during the take over of the enclave. Thus the findings are descriptive, summarizing observations and presenting results based on simple statistical tools. Secondly, in Kosovo the researchers asked what caused the killings and refugee migration during the NATO air campaign in springtime 1999. Here, in a complex environment statistical methods are exercised to determine causal relations. Hypotheses are tested to be consistent with huge data sets collected from a broad field of sources, to finally end up with Statistical Evidence.

Crime↗
PubMed1988

Descriptive occupational morbidity statistics.

In spite of their value to indicate the magnitude of occupational health problems, descriptive occupational morbidity statistics tend to be neglected. The accuracy of occupational morbidity statistics depends on counting the morbid condition as well as the occupational element. At present, there is no clearcut model for counting the occupational element. The International Conferences of Labour Statisticians have contributed greatly to the development of statistics on employment injuries. Such statistics are a by-product of the provision of compensation to workers with occupational injuries and diseases. Statistics which are a by-product of investigation into occupational injuries and diseases followed by intervention seem to have received much less attention. Comments are made on the present situation regarding national statistics on occupational injuries and pneumoconiosis. The statistical issues with respect to work-related diseases and sickness absence are also examined and discussed.

Absenteeism↗
PubMed1977

The statistical distribution of colony counts in the spleen colony assay.

The statistical distribution of colony counts in the spleen colony assay was determined in C57BL/6 and C3H mice under varying conditions of the assay procedure. Assay mice were given syngeneic bone marrow cells from normal or irradiated donors. The mice were injected intravenously with marrow cells either immediately or 3 days after irradiation. Eight days after engraftment, spleen colonies were counted and the statistical distribution of colony counts was determined using a mean to variance ratio criterion. Analysis of the data indicated that the statistical distribution of colony counts was different in the two strains of mice. In addition, delaying time of injection of mice with bone marrow cells or injecting bone marrow cells form irradiated donors also changed the statistical distribution. The significance of this work lies in the fact that modification of the usual assay procedure can alter the statistical distribution of colony counts, thus changing the statistical accuracy of the assay. Modification in the assay procedure, such that an increase occurs in the variance of the distribution of colony counts, must be compensated for by increasing the number of spleens counted in order to maintain a constant level of statistical accuracy in experiments.

Animals↗
PubMed2001

A study comparing precision of the maximum multipoint heterogeneity LOD statistic to three model-free multipoint linkage methods.

This study compared the performance of the maximum lod (MLOD), maximum heterogeneity lod (MHLOD), maximum non-parametric linkage score (MNPL), maximum Kong and Cox linear extension (MKC(lin)) of NPL, and maximum Kong and Cox exponential extension (MKC(exp)) of NPL as calculated in Genehunter 1.2 and Genehunter-Plus. Our performance measure was the distance between the marker with maximum value for each linkage statistic and the trait locus. We performed a simulation study considering: 1) four modes of transmission, 2) 100 replicates for each model, 3) 58 pedigrees (with 592 subjects) per replicate, 4) three linked marker loci each having three equally frequent alleles, and 5) either 0% unlinked families (linkage homogeneity) or 50% unlinked families (linkage heterogeneity). For each replicate, we obtained the Haldane map position of the location at which each of the five statistics is maximized. The MLOD and MHLOD were obtained by maximizing over penetrances, phenocopy rate, and risk-allele frequencies. For the models simulated, MHLOD appeared to be the best statistic both in terms of identifying a marker locus having the smallest mean distance from the trait locus and in terms of the strongest negative correlation between maximum linkage statistic and distance of the identified position and the trait locus. The marker loci with maximum value of the Kong and Cox extensions of the NPL statistic also were closer to the trait locus than the marker locus with maximum value of the NPL statistic.

Bias↗
PubMed1988

Statistical properties of randomization in clinical trials.

This is the first of five articles on the properties of different randomization procedures used in clinical trials. This paper presents definitions and discussions of the statistical properties of randomization procedures as they relate to both the design of a clinical trial and the statistical analysis of trial results. The subsequent papers consider, respectively, the properties of simple (complete), permuted-block (i.e., blocked), and urn (adaptive biased-coin) randomization. The properties described herein are the probabilities of treatment imbalances and the potential effects on the power of statistical tests; the permutational basis for statistical tests; and the potential for experimental biases in the assessment of treatment effects due either to the predictability of the random allocations (selection bias) or the susceptibility of the randomization procedure to covariate imbalances (accidental bias). For most randomization procedures, the probabilities of overall treatment imbalances are readily computed, even when a stratified randomization is used. This is important because treatment imbalance may affect statistical power. It is shown, however, that treatment imbalance must be substantial before power is more than trivially affected. The differences between a population versus a permutation model as a basis for a statistical test are reviewed. It is argued that a population model can only be invoked in clinical trials as an untestable assumption, rather than being formally based on sampling at random from a population. On the other hand, a permutational analysis based on the randomization actually employed requires no assumptions regarding the origin of the samples of patients studied. The large sample permutational distribution of the family of linear rank tests is described as a basis for easily conducting a variety of permutation tests. Subgroup (stratified) analyses, analyses when some data are missing, and regression model analyses are also discussed. The Blackwell-Hodges model for selection bias in the composition of the study groups is described. The expected selection bias associated with a randomization procedure is a function of the predictability of the treatment allocations and is readily evaluated for any sequence of treatment assignments. In an unmasked study, the potential for selection bias may be substantial with highly predictable sequences. Finally, the Efron model for accidental bias in the estimate of treatment effect in a linear model is described. This is important because the potential for accidental bias is equivalent to the potential for a covariate imbalance.(ABSTRACT TRUNCATED AT 400 WORDS)

Clinical Trials as Topic↗