## References

On the Mode of Communication of Cholera. 2nd edn. Churchill Livingstone London, 1854. 2. Pickle L, Mungiole M, Jones G, White A. Exploring spatial patterns of mortality the new atlas of united states mortality. Statistics in Medicine 1999 18 3211-3220. 3. MacEachren AM. How Maps Work Representation, Visualisation, and Design. Guildford Press New York, 1995. 4. Monmonier M. How to Lie with Maps. 2nd edn. University of Chicago Press London, 1996. 5. Pickle LW, Hermann DJ. Cognitive...

## Genetic Terminology And Linkage Concepts

Simple genetic models are derived from Mendelian laws of inheritance. Each individual has two sets of 23 chromosomes, one maternal and one paternal in origin. One of the 23 pairs of chromosomes are the sex chromosomes, and we shall concern ourselves with the remaining 22 pairs of autosomal chromosomes in this tutorial. Each chromosome consists of a long strand of DNA, a linear molecule with units known as base pairs. A chromosomal location (which may be a single base pair or a collection of...

## Model Specifications

In two-level hierarchical models, separate level 1 models are developed for each of the J level 2 units. Consider the case of a continuous outcome or dependent variable, Y (for example, patient satisfaction), and a single, continuous level 1 predictor or covariate X (for example, patient's age). The level 1 models are of the form where Yy is the dependent variable measured on the ith level 1 unit (for example, patient) nested within the j'th level 2 unit (for example, physician), poj is the...

## W

The level 2 (physician) covariate or predictor Level 2 identifier (for example physician identification number) i)0j,Uij BVN (0,0, T0o> T11 > P) X and W variables can be modelled in their original, untransformed metric or centred (about respective grand means, or X about respective group means). Model. One-way ANOVA with random effects class phys model y s random int s Model 2. Means as outcomes regression model class phys model y w s random int s Model 3. One-way ANCOVA with random effects...

## Proc Mixed

Proc mixed data fev method ml class id rage model lnfev agel age 2 ht s p random int type un subject id g repeated local r subject id type sp (pow) (agel) make 'SolutionF' out fixl make 'Predicted' out predl title 'Spline model (Diggle Covariance)' next line gives alternate REPEATED repeated rage local r subject id type AR(1) METHOD ML indicates that maximum likelihood estimation is used. The CLASS statement declares classification variables so that SAS can create a set of dummy variables that...

## Survival Models

Several different formulations for survival data modelling are available to illustrate how these can be extended to multilevel structures, where they are often referred to as frailty models 38 , we consider the proportional hazards (Cox) model and a piecewise discrete time model. Goldstein 18 gives other examples. Consider a simple two-level model with, say, patients within hospitals or occasions within subjects. As in the standard single-level case we consider each time point in the data as...

## In Conclusion

The models that we have described in this paper represent a powerful set of tools available to the data analyst for exploring complex data structures. They are being used in many areas, including health, with great success in providing insights that are unavailable with more conventional methods. There is a growing literature extending these models, for example to multilevel structural equation models, and especially to the application of the multiple membership models in areas such as...

## Gg241

Level-2 unit is collapsed to a few data points, thus losing both statistical power and information about intra-individual variation. Further, to have comparable equations using OLS methods, each level-2 unit should have the same number of observations based on the same times of observations with no missing data values. While highly desirable, this is often not feasible for many clinical studies. Finally, OLS estimation is based on the assumption that the residual from the prediction of each...

## Statistical Approaches To Human Brain Mapping By Functional Magnetic Resonance Imaging

National Institutes of Health, Federal Building, Room 7C04, Bethesda, MD 20892-9135, U.S.A. Proper use of functional neuro-imaging through effective experimental design and modern statistical analysis provides new insights in current brain research. This tutorial has two aims to describe aspects of this technology to applied statisticians and to provide some statistical ideas to neuroscientists unfamiliar with quantitative analytic methods that accommodate randomness. Introductory background...

## Ovarian Steroid Secretion Data

A total of 175 women were recruited for the study between 1985 and 1988 from the family planning clinics of the King County Hospital Center and the State University Hospital in Brooklyn, New York 4 . Among these, 118 women were seeking tubal ligation and 57 women were fertile women using a variety of contraceptive methods and not seeking tubal ligation. Women were eligible for the study if they were between 21 and 36 years of age, had experienced at least one pregnancy, were not pregnant or...

## Info

Difference in LOS Days (Specialist - Routine) Figure 2. Stroke example, x-axis displays xj xqi, the difference in average length of stay, measured in days, for each of the nine studies and their corresponding 95 per cent confidence intervals (sj s (+ where Shorter lengths of stay are assumed to reflect better care management only source of uncertainty is that resulting from the sampling of people into studies. This type of variation may be characterized as within-study variation that is a...

## N V 0009 0025 J

The results are identical to those of Berkey et al. 50 with the random-effects multiple outcomes that were estimated with the method named by Berkey as the multivariate maximum likelihood (MML) method. Our presentation concentrates on dichotomous outcomes. Much of it carries over to other effect measures that are measured on a different scale. For instance, our methods apply if the outcome variable is continuous and an estimate of the average outcome and its standard error is available in both...

## Example Data

A pharmaceutical example experiment will be used to illustrate the methodology. Objectives of the study were to compare effects of two drugs (A and B) and a placebo (P) on a measure of Figure 1. FEV1 repeated measures for each patient. Table I. REML covariance and correlation estimates for FEV1 repeated measures data. Figure 1. FEV1 repeated measures for each patient. Table I. REML covariance and correlation estimates for FEV1 repeated measures data. 0.893 0.880 0.784 0. 88 0. 75 0.5l 0. 42

## Fev1 Definitiom Biostatistics

Variances on diagonal, covariances above diagonal, correlations below diagonal. respiratory ability, called FEV1. Twenty-four patients were assigned to each of the three treatment groups, and FEV1 was measured at baseline (immediately prior to administration of the drugs), and at hourly intervals thereafter for eight hours. Data were analysed using PROC MIXED of the SAS System, using baseline FEV1 as a covariable. An SAS data set, named FEV1UN1, contained data with variables DRUG, PATIENT, HR...

## Using The Mixed Procedure To Fit Linear Mixed Models

We now turn to PROC MIXED for analyses of the FEV1 data which fit the mean model (3) and accommodate structures defined on the covariance matrix. We assume the reader has some familiarity with the SAS System, and knows how to construct SAS data sets and call SAS procedures. The general linear mixed model (5) may be fit by using the MODEL, CLASS, RANDOM and REPEATED statements in the MIXED procedure. The MODEL statement consists of an equation which specifies the response variable on the left...

## Analysing Onedimensional Treatment Effects

The analysis under homogeneity makes the assumption that the unknown parameter is exactly the same in all studies, that is 1 2 n . The log-likelihood for is given by ' E ' -1 E - 7s2 ln s2 ln 2T Maximization is straightforward and results in the well-known estimator of the common effect Confidence intervals for can be based on normal distributions, since the s2 terms are assumed to be known. Assuming the s2 terms to be known instead of to be estimated has little impact on the results 14 . This...

## Metaregression

In case of substantial heterogeneity between the studies, it is the statistician's duty to explore possible causes of the heterogeneity 15,37-39 . In the context of meta-analysis that can be done by covariates on the study level that could 'explain' the differences between the studies. The term meta-regression to describe such analysis goes back to papers by Bashore et al. 40 , Jones 41 , Greenland 42 and Berlin and Antman 37 . We consider only analyses at the aggregated meta-analytic level....