EGRET review - University of Bristol
Contents
1. BoXo B3Xs By Xa BsXsi OUy 5 and the expression in EGRET is egret doc 5 use Fixed random Fixed GM LC AGE Urban Random SCL For a model with different random effects for urban and rural districts the model is logit y Bot Biri ByX2i B3 3i By Xai BsX5i OU 6 and o 6 6 x EGRET uses the model use Fixed random Fixed GM LC AGE Urban Random SCL Urban In 6 o is fitted as a function of the intercept and the Urban group In fitting the three models above EGRET produces a Likelihood Ratio Test LRT statistic to test the significance of the random intercept term SCL in Model 5 compared to the single level model 4 and a LRT for the random effect associated with the variable Urban in 6 compared to 5 Two steps are required to fit a model defining the model and analysing it Options DefineModel and Analyze in the menu carry out the steps as shown below egret doc 6 Figure 1 The DefineModel window Figure 2 The Analyze window for Model 5 Logistic Binomial for Distinguishable Data z m Available variables List of variable s Match variable Select transformation m Regression term 4 Jasia SS None X IV Include constant term m Group size variable _ Fixed fi Variable 7 m Outcome variable 4 Juse m Repetition count variable Weight 4 2 OK Canc2. terms by variable names weighting variable denominator response variable and level 2 identifier This is a read only window In the original MS DOS version of EGRET simple commands in two groups called DEF and PECAN were required Commands under DEF were for data manipulation and defining models and commands under PECAN were for fitting models and model diagnostics In the window version these commands are made redundant and replaced by Window options with dialog boxes 2 Standard modelling tools for multilevel analysis egret doc 3 2 1 A brief check of model list EGRET has window screens with dialog boxes for defining and fitting Logistic Regression Poisson Regression Cox Proportional Hazards Regression and Parametric Regressions for Failure Time However as it is designed for analysing categorical data it has no suitable tool for modelling Normal response data For binary and binomial outcomes with a 2 level clustering structure EGRET fits logistic models with random The estimation algorithms are Modified Newton default or Newton Raphson or Quasi Newton or Nelder Mead method with marginal maximum likelihood estimates provided Covariates are allowed in the fixed part of the models The random effect at level 2 can be modelled as a linear function of level 2 covariates Random effect models are also known as two parameter models in EGRET We review here models for binary and binomial outcomes EGRET terms data with covaria
3. window to enable one to evaluate the significance of the new variable s added in any part of the existing model However this tool does not apply to the situation when one wants to remove parameter s from the existing model For model diagnostics EGRET has Post Fit tools in a table and a graph to report predicted numerator Fitted values and predicted proportion Fitted proportion as well as residuals for each observed unit A graph of fitted values against case number for each unit by y 1 the case in Epidemiology and y 0 control is presented One can change settings of the graph for example a graph of fitted proportion against residual or against other covariate A click on any point in the graph will highlight the case record in the table and vice versa A summary of these tools is given in Table 1 egret doc 4 3 Model specifications Basic models 3 1 Two level Logistic binomial models for distinguishable data A th ste Using the standard notation for the 7 case in the y cluster the probability of response zz for the 7 covariate pattern is related to the covariates by where x 2 xj 8 Xip Is the linear predictor in the fixed part O is a positive scalar and is used to model over dispersion in the data The distributional assumptions for the random effects are that u is a standard Normal random variable Note that EGRET also allows for the response proportion to have a Beta binomial distrib
4. A review of random effects models in EGRET for Windows Version 2 0 3 Min Yang Centre for Multilevel Modelling Institute of Education University of London m yang ioe ac uk 1 Introduction 1 1 Background EGRET was originally developed at the School of Public Health of University of Washington USA Mauritsen R H 1984 Designed for analysing data from Biomedical and Epidemiology studies EGRET stands for Epidemiological GRaphics Estimation Testing It fits generalised linear models with and without random effects and survival models It concentrates on models for categorical data collected from Epidemiology and Biomedical studies including cohort data cross sectional data case control data clinical trial data and survival data It is widely used by Epidemiologists and Biostatisticians EGRET for Windows was developed based from an early MS DOS platform Released in 1999 the current Window version was developed by a team in CYTEL Software Corporation of Cambridge MA in the USA 1 2 Software and hardware requirements The recommended hardware and software requirements for the window version 2 0 3 October 2000 include A system running MS Windows 95 98 or MS Windows NT A Pentium II 200MHz processor 32 MB or more of RAM A hard disk with at least 32 MB of available disk space The on line user s manual can be browsed using Acrobat Reader 1 3 Data input output functionality EGRET for Windows can read data files as f
5. Match variable LC p3 2 Group size variable fixed as 1 Bs OPE 00079 Age B H ane a variable 9 797 0 105 Urban B Choose from the menu D 2 456 73 df 1 928 Random Analyze None New In the dialog box 1 Add LC Age and Urban to the Model Terms 2 Tick off the random effect term SCL 3 Click on OK Random Fixed Choose from the menu Bo 1 694 0 148 10 intercept GM Bo Analyze Extend P 1 109 0 158 LC 2 B In the dialog box of Random effect term B 1 378 0 175 1 Tick the box of Include Scale LC 3 B gt Click on OK 3 1 347 0 180 Lc 4 B 24 0 027 0 0079 Age pa B 9 730 0 120 Urb B O 0 455 0 071 rban Random D 2 412 9 df 1 927 SCL O re eae Random Fixed Choose from the menu Bo 1 706 0 156 10 effect GM Bo Analyze different Extend i 1 103 0 158 between LC 2 B In the dialog box By 1 372 0 175 Urban and 1 Add Urban to the Random effect term rural Le 3 B 2 Click on OK B3 1 346 0 180 groups Loe B B4 0 027 0 0079 3 Age pa f 0 805 0 126 iba 8 0 0 582 0 099 gt P5 Padon 02 0 314 0 138 0 Be D 2 407 69 df 1 926 Urban gt LRT 5 28 df 1 10 Table 2 EGRET specifications for 2 level Logistic models indistinguishable data Model Fixed amp random Machine steps to run models Estimates SE Seconds to effects Ests convergence Logistic normal Fix
6. ed Choose from the menu B 0 843 0 118 3 GM B DefineModel Quasi Newton Logistic regression with random effects P 1 224 0 328 0 rai Raphson Urban 2 Logistic Normal regression 0 434 0 132 algorithm Random In the dialog box select i i 0 078 0 363 SCL Q 1 Group size variable Denom 02 Urban gt 2 Outcome variable TN 3 Click on OK Choose from the menu Analyze New In the dialog box 1 Add Urban to the Model Terms 2 Add Urban to the Random effect term 3 Click on OK D 113 3 df 56 l1
7. el Reset m Random effect term IV Include Scale Cancel Advanced Outcome Variable use Group size 1 Repetition count Variable Matching district From the DefineModel window the information about the cluster response denominator and weight are specified In the Analyze window Model 5 is set up Model 4 is fitted by excluding the Scale from the Random effect term In the Advanced dialog box one out of four estimation algorithms can be selected Estimates for models 4 6 are presented in Table 2 The run time has been converted for a Pentium II 433 Mhz processor under Windows 2000 3 2 Two level Logistic models for indistinguishable data We first fit a model with different random effects for urban and rural logit y By 25X5 A1 O2 s 7 In this review we fit a logistic Normal model The model specification and results are in Tables 1 and 2 egret doc 7 Figure 3 The DefineModel window Figure 4 The Analyze window for Model 7 Random Effects Logistic normal regression x List of variable s Regression Model lt Logistic Regression with Normal Random Effect se r Available variables Select transformation m Regression term None X IV Include constant term 3 urban Group size variable ban C Fixed fT Variable 4 fe r Qutcome variable 4 fm m Repetit
8. ion count variable weight fal OK Cancel Reset urban gt Random effect term IV Include Scale Model Outcome Variable TN Group size denom Repetition count Variable Cancel Advanced if 4 Documentation and user support The User Manual EGRET for Windows is well organised and well written with clear detail Part I deals with installation data input output menus windows and tutorial Part II describes how to define and run regressions Part III is about nonparametric procedures IV is about assessing goodness of fit and V has appendices on special topic such as modelling strategies and troubleshooting example datasets and program limits It has a chapter bridging EGRET DOS use with the Windows version and has a list of Beta version testers The full document is available also through the on line help in the program In the package is included free technical support and new product announcements Summary EGRET for Windows is very easy to use with a user friendly environment for data handling model definition and fitting and reporting Being dedicated to binomial and count data as well as survival data and being unable to fit Normal response models it has limited functionality and those from outside the medical sciences some of the terminology may be unfamiliar Furthermore Poisson models with random effects cannot be fitted EGRET for Windo
9. nalysis and model fitting EGRET has four windows for review and output Log Result Desc Stats and Current Model Info Log window stores the history of analysis or operations and fitted models including estimation procedure deviance value by iteration final parameter estimates and their standard errors in table form They can be either copied partly and pasted into other files or saved wholly as a text file using Save Log option in the File drop down list Result workbook window keeps details of the current model definition number of observations number of parameters fixed random coefficients deviance parameter estimates in table form and timings The whole window can be output as an Excel xls or htm file via the Save Output option One can also use the Scratch tool in the same window to organise any information piece by piece into an Excel spreadsheet for presentation or graphing Other results such as Fitted values proportion and Residuals can be copied into the Results window to be saved via the Save Output option A residual here refers to the difference between the observed and the Fitted value at a data point Desc Stats window stores histogram of single variable or scatter plot of two variables as part of the descriptive statistics They can be output as Windows Bitmap file bmp or JPEG file jpg using Export Graph option Current Model Info window shows text information including model name fixed and random
10. ollows Dos Egret hdr LOGXACT cy1 STATXACT cy3 ASCII txt Text data dat Excel 5 0 or 7 0 xls Excel CSV SPSS scv SYSTAT syd and SAS xpt The same types of data files can be exported from EGRET for Windows except for SPSS SYSTAT and SAS files Data file input is by means of the Import option in the dropdown list of the File window and output is by the Save Save As options in the same list For opening a saved EGRET system file cy1 or hdr the Open option should be used Once a dataset is imported in EGRET there is a standard procedure for naming transforming and defining variables see window below For a categorical covariate the factor box should be ticked The reference category either at the ow end of the high end of the category range is selected in the box next to the factor box egret doc 2 Yariable Properties a i xj List of variable s Variable detail women district Name ic rtrt i i SCC Description Number of living children in the househol Type Numeric gt Factor V Low lt lt Previous Next gt gt Restore Cancel Copying a segment of the data into another file can be done by highlighting it in the Case Editor window then clicking on copy button and paste in other files Data types EGRET accepts can be String Numeric and Date 1 4 Other interface features For keeping information on data a
11. tes varying within cluster as distinguishable data and data with constant covariates within cluster as indistinguishable In a two level structure of individuals nested within cluster if the response is binary with individual level covariates the data are distinguishable For a proportion response if it is nested within a higher level cluster with covariates at the response level the data are also distinguishable Where the proportion response is at the cluster level the term indistinguishable is used Some other terms in EGRET different from the conventional ones are as follows Conventional description EGRET terms Level 2 cluster Level 2 identifier Match variable Denominator Group size variable Weight Repetition count variable Response variable numerator denominator Outcome variable numerator Intercept GM Grand mean Random effect associated with the intercept SCL Scalar 2 2 Tools for statistical inference and model diagnostics After fitting each new model EGRET reports in the Result window an overall deviance and the tail probability of y distribution using a Wald test statistic for each parameter estimate except for the variance For each fixed parameter estimate a 95 confidence interval CI for the estimated odds ratio is reported too When adding further variables to an existing model the Extend option in the DefineModel window can be used After the model runs a likelihood ratio test statistic is reported in the Result
12. ution with mean given by the fixed part and a scale parameter or alternatively a binomial binomial distribution The level 2 variation is effectively modelled by the scalar O which can be a function of cluster specific covariates as O 21j0it 2G 2 where Z zj1 z jq represent a vector of q cluster specific covariates 0 is the coefficient for zq This allows complex variation at cluster level to be fitted The example data for illustration purpose are from the 1988 Bangladesh Fertility Survey Steele et ct A sub sample of 1 934 women grouped in 60 districts had response on the contraceptive use status at time of survey y 1 using or y 0 not using Three background variables of each woman are number of living children at time of survey LC coded as none 1 2 3 with three dummy variables xij 2 X3 age of woman in years AGE x centred at the mean age and type of region of residence URBAN xs Urban 1 and Rural 0 The data are distinguishable and only Logistic binomial random effect models can be fitted See web site data set descriptions For a single level logistic model with all three covariates fitted we have logit y By Bix Born 3X3 4X4 B5 Xs 4 The model expression in EGRET is use GM LC AGE Urban where LC and Urban are two category variables or factors termed in EGRET For a variance component or random intercept model there is logit y By By y
13. ws is nevertheless good at what it does and a useful package for teaching Epidemiological modelling The current prices of EGRET for Windows are 395 per copy for academic users and 795 for commercial Shipping and handling costs are 75 to abroad and 15 domestic The program is currently distributed by Cytel Statistical Software CYTEL Software Corporation 675 Massachusetts Avenue Cambridge MA 02139 USA www cytel com products egret egret doc 8 Email Sales cytel com References Mauritsen R H 1984 Logistic regression with random effects Ph D thesis Department of Biostatistics University of Washington Cytel Software Corporation 2000 EGRET for Windows User manual Cambridge USA Steele F Diamond I amp Amin S 1996 Immunization uptake in rural Bangladesh a multilevel analysis Journal of the Royal Statistical Society Series A 159 289 299 egret doc 9 Table 1 EGRET specifications for single level and 2 level models distinguishable data Model Fixed parameter Machine steps to run models Estimates SE amp Seconds to and random Deviance convergence effects Ests Single Fixed Choose from the menu Bo 1 568 0 126 7 level GM Bo DefineModel model Logistic regression with random effects 1 1 059 0 152 Lc 2 p Logistic binomial regression for B 1 288 0 167 distinguishable data LC 3 VA In the dialog box select P 1 216 0 171 i 1 District as
Download Pdf Manuals
Related Search