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We consider modelling and testing for `interaction' between a continuous covariate X and a categorical covariate C in a regression model. Here C represents two treatment arms in a parallel-group clinical trial and X is a prognostic factor which may influence response to treatment. Usually X is categorised into groups according to cut-point(s) and the interaction is analysed in a model with main effects and multiplicative terms. A trend test of the effect of C over the ordered categories from X may be performed and is likely to have better power. The cut-point approach raises several well-known and difficult issues for the analyst, including dependency of the results on the choice of cut-point, loss of power due to categorisation, and the danger of `over-fitting' if several cut-points are considered in a search for `optimality' (Altman et al., 1994).

We will describe an approach to avoid such problems based on fractional polynomial (FP) modelling of X, without categorisation, overall and at each level of C (Royston and Sauerbrei, 2002). The first step is to construct a multivariable adjustment model which may contain binary covariates and FP transformations of continuous covariates other than X. The second step involves FP modelling of X within the adjustment model.

Stata software to fit the models will be demonstrated using example datasets, mainly from cancer studies. The examples show the power of the approach in detecting and displaying interactions in real data from randomised controlled trials with a survival-time outcome.

References

Altman, D. G., B. Lausen, W. Sauerbrei, M. Schumacher. 1994.

The dangers of using `optimal' cutpoints in the evaluation of prognostic factors. Journal of the National Cancer Institute 86: 829–835.

Royston, P. and W. Sauerbrei. 2002.

A new approach to modelling interactions between treatment and continuous covariates

in clinical trials by using fractional polynomials. Statistics in Medicine, to be submitted.

Hand-outs/slides
royston.pdf

It is commonplace to compute various flavours of residual and predicted values after fitting many different kinds of model. This allows production of a great variety of diagnostic graphics, used to examine the general and specific fit between data and model and to seek possible means of improving the model. Several different graphs may be inspected in many modelling exercises, partly because each kind may be best for particular purposes, and partly because in many analyses a variety of models — in terms of functional form, choice of predictors, and so forth — may be entertained, at least briefly. It is therefore helpful to be able to produce such graphs very rapidly.

Official Stata supplies as built-ins a bundle of commands originally written for use after regress: avplot, avplots, cprplot, acprplot, lvr2plot, rvfplot and rvpplot. These were introduced in Stata 3.0 in 1992 and are documented at [R] regdiag. More recently, in an update to Stata 7.0 on 6 September 2001, all but the first two have been modified so that they may be used after anova. Despite their many uses, this suite omits some very useful kinds of plot, while none of the commands may be used after other modelling commands.

The presentation focuses on a new set of commands, which are biased to graphics useful for models predicting continuous response variables. The ideal, approachable asymptotically, is to make minimal assumptions about which modelling command has been issued previously. The down-side for users is that if the data and the previous model results do not match the assumptions, it is possible to get either bizarre results or an error message.

The commands which have been written include

anovaplot shows fitted or predicted values from an immediately previous one-, two-, or three-way anova. By default the data for the response are also plotted. In particular, anovaplot can show interaction plots.

indexplot plots estimation results (by default whatever predict produces by default) from an immediately previous regress or similar command versus a numeric index or identifier variable, if that is supplied, or observation number, if that is not supplied. Values are shown, by default, as vertical spikes starting at 0.

ovfplot plots observed vs fitted or predicted values for the response from an immediately previous regress or similar command, with by default a line of equality superimposed.

qfrplot plots quantile plots of fitted values, minus their mean, and residuals from the previous estimation command. Fitted values are whatever predict produces by default and residuals are whatever predict, res produces. Comparing the distributions gives an overview of their variability and some idea of their fine structure. By default plots are side-by-side. Quantile plots may be observed vs normal (Gaussian).

rdplot graphs residual distributions. The residuals are, by default, those calculated by predict, residuals or (if the previous estimation command was glm) by predict, response. The graph by default is a single or multiple dotplot, as produced by dotplot: histograms or box plots may be selected by specifying either the histogram or the box option.

regplot plots fitted or predicted values from an immediately previous regress or similar command. By default the data for the response are also plotted. With one syntax, no varname is specified. regplot shows the response and predicted values on the y axis and the covariate named first in the regress or similar command on the x axis. Thus with this syntax the plot shown is sensitive to the order in which covariates are specified in the estimation command. With another syntax, a varname is supplied, which may name any numeric variable. This is used as the variable on the x axis. Thus in practice regplot is most useful when the fitted values are a smooth function of the variable shown on the x axis, or a set of such functions given also one or more dummy variables as covariates. However, other applications also arise, such as plotting observed and predicted values from a time series model versus time.

rvfplot2 graphs a residual-versus-fitted plot, a graph of the residuals versus the fitted values. The residuals are, by default, those calculated by predict, residuals or (if the previous estimation command was glm) by predict, response. The fitted values are those produced by predict by default after each estimation command. rvfplot2 is offered as a generalisation of rvfplot in official Stata.

Hand-outs/slides
diag.pdf
diag.html — graphs covered in the meeting

outdat is a Stata program to transfer data from Stata to other statistical packages. outdat writes data to a disk file in ASCII format and makes a dictionary to read the data into SPSS, Stata, or Limdep. The presentation shows how outdat works and how to expand outdat to other data formats.

Hand-outs/slides
kohler.pdf
outdat.zip

Models for handling sample selection or informative missingness have been developed for both cross-sectional and longitudinal or panel data. For cross-sectional data, Heckman (1979) suggested a joint model for the response and sample selection processes where the disturbances of the processes are correlated. For longitudinal data, Hausman and Wise (1979) and Diggle and Kenward (1994) developed a model in which the continuous response (observed or unobserved), and possibly the lagged response, is a predictor of attrition or dropout. The Heckman model can be estimated using the heckman command in Stata and the Diggle–Kenward model is available in the Oswald package running in S-PLUS. Both models can also be estimated using gllamm with the advantage that the following three generalisations are possible. First, the models can be extended to multilevel settings where there may be unobserved heterogeneity between the clusters at the different levels in both the substantive and selection processes and where selection may operate at several levels. Second, the Heckman model can be modified for nonnormal response processes. Third, both the Heckman and Diggle–Kenward models can be extended to situations where the substantive response is a latent variable measured by a number of indicators. I will show how the standard Heckman and Diggle–Kenward models are estimated in gllamm and give a examples of all three types of generalisation of these standard models. The research was carried out jointly with Anders Skrondal and Andrew Pickles.

Hand-outs/slides
select.pdf

Correct data are crucial for any analysis. For example, the date of randomization in a clinical trial should never preceed the date of diagnosis, and treatment should always start at the date of randomization or thereafter. You could easily list patients with f laws in the data using:

     . l patnr ddiag drand if ddiag>drand, nod noo 
     . l patnr drand dsttreat if drand>dsttreat, nod noo 

However, when the number of variables and the number of data checks are large, the errors in the data of a certain patient may be found anywhere in your output, which will hamper easy admission of the data. To overcome these problems, the program qd.ado was developed. All errors are now neatly grouped by patient; moreover, additional comments to facilitate the admission of the data can easily be defined. We will demonstrate the program and show some examples. To get more information about this program, you should type findit qd in Stata. You will find the relevant ado-files and also a PowerPoint presentation.

Hand-outs/slides
qd.ppt

The program adoinf.ado is useful for an overview of your ado-files in your site or personal directory. If the number of ado-files grows, you easily forget the meaning of certain ado-files and whether they are still necessary or not. You also easily forget which subroutines are used in a file and/or where the file is called by other ado-files. This can especially be important when you publish ado-files on the web. Furthermore, for each file is tried to search for the author, oneliner describing the file, date last saved, date last help version, and so on. The get more information about this program, you type findit adoinf in Stata, where the files and also the PowerPoint presentation is available.

Hand-outs/slides
adoinf.ppt

In this talk, I discuss Pearson's X² as a measure of goodness of fit for quantal response models, including binary outcome models (logit, probit, gompit), multinomial logistic regression (mlogit) and conditional logistic regression (clogit). Large sample results for X² have been derived by a.o. McCullagh and Windmeijer. A Stata implementation of the test will be illustrated.

Hand-outs/slides
pearsonx2.pdf

Classification and Regression Tree analysis can be applied for the identification and assessment of prognostic factors in clinical research. It involves repeated subdivisions of a group of subjects on the basis of the choice of optimal cut-points of binary, ordinal, or continuous covariates, which maximizes a certain split criterion. I will describe a specific implementation of CART as Stata ado-file cart.ado for failure time data with as split criterion an adjusted p-value. The p-value is associated with the chisquare logrank statistic based on residuals. The adjustment is for the multiple testing associated with the search for the optimal cutpoint with the maximum chisquare value (Lausen, 1997). Examples of applications are given. CART has a serious risk of overfitting. However, it can be a useful exploratory tool in addition to more standard regression type techniques.

Reference

Lausen, B. et. al. 1997.

The regression tree method and its application in nutritional epidemiology. Informatik, Biometrie und Epidemiologie in Medizin und Biologie 28(1): 1–13.

Hand-outs/slides
cart.pdf
cart.ppt

With the release of Stata 7, the capabilities of glm were greatly enhanced. Among the improvements was the ability for users to program their own custom link and variance functions. Whereas previously glm was used primarily as a platform on which to compare the results of standard regression models (such as the logistic, probit, and Poisson), it may now be utilised to perform generalized maximum pseudo-likelihood estimation in any framework. Thus far, this has been an ability that for the most part has not been exploited.

The method by which user-defined links and variance functions may be incorporated is quite straightforward, as demonstrated in the companion text to glm by Hardin and Hilbe (2001). In this talk, I present a few examples of case studies from the literature where the science dictated the fitting of a generalized linear model with special (non-standard) link and/or variance function. I demonstrate how these models (which were typically fit using SAS's GENMOD procedure) may be fit using Stata.

Reference

Hardin, J. and J. Hilbe. 2001.

Generalized linear models and extensions. Stata Press, College Station, TX.

A set of Stata routines to help analysis of `income mobility' are presented and illustrated. Income mobility is taken here as the pattern of income change from one time period to another within an income distribution. Multiple approaches have been advocated to assess the magnitude of income mobility. The macros presented provide tools for estimating several measures of income mobility; e.g., the Shorrocks (JET 1978) or King (Econometrica 1983) indices or summary statistics for transition matrices.

Hand-outs/slides
vankerm.pdf

Bill Gould, who is President of StataCorp, and more importantly for this meeting, the head of development, will ruminate about work at Stata over the last year and about ongoing activity.