Stata User Meeting presentations by Roger Newson

These were given at Stata User Meetings, and are summarized here with their abstracts and downloadables. Stata User Meetings are a principal opportunity for face-to-face networking within the Stata user community, and are also an opportunity to feed ideas and wishes for further development back to Stata Corporation, the makers of Stata statistical software. These user meetings take place in many locations all over the world, but the largest ones are usually in London, UK, where a large concentration of Stata users is based at locations mutually accessible by train, bus or bicycle. This page contains all my own presentations given at these meetings, in reverse order of presentation date.

To find out more about Stata User Meetings, click here for the official Stata versions of the proceedings, or click here for the Boston College of Economics versions maintained by Kit Baum and listed with RePEc. To find out more about Stata Statistical Software, click here.

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List of presentations

Presentation yearPresentation title
2016The role of Somers' D in propensity modelling
2015Somers' D: A common currency for associations
2014Easy-to-use packages for estimating rank and spline parameters
2013Creating factor variables in resultssets and other datasets
2012Scenario comparisons: How much good can we do?
2011Sensible parameters for polynomials and other splines
2010Post-parmest peripherals: fvregen, invcise, and qqvalue
2009Homoskedastic adjustment inflation factors in model selection
2008parmest and extensions
2007Robust confidence intervals for Hodges-Lehmann median differences
2006On the central role of Somers' D
2006Resultssets, resultsspreadsheets and resultsplots in Stata
2005Generalized confidence interval plots using commands or dialogs
2004From datasets to resultssets in Stata
2003Multiple test procedures and smile plots
2002Creating plots and tables of estimation results using parmest and friends
2001Splines with parameters that can be explained in words to non-mathematicians
2000Confidence intervals for rank order statistics: Somers' D, Kendall's tau-a and their differences

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The role of Somers' D in propensity modelling. Presented at the 22nd UK Stata User Meeting, 8–9 September, 2016.

The Rubin method of confounder adjustment, in its 21st-century version, is a two-phase method for using observational data to estimate a causal treatment effect on an outcome variable. It involves first finding a propensity model in the joint distribution of a treatment variable and its confounders (the design phase), and then estimating the treatment effect from the conditional distribution of the outcome, given the treatments and confounders (the analysis phase). In the design phase, we want to limit the level of spurious treatment effect that might be caused by any residual imbalance between treatment and confounders that may remain, after adjusting for the propensity score by propensity matching and/or weighting and/or stratification. A good measure of this is Somers' D(W|X), where W is a confounder or a propensity score, and X is the treatment variable. The SSC package somersd calculates Somers' D for a wide range of sampling schemes, allowing matching and/or weighting and/or restriction to comparisons within strata. Somers' D has the feature that, if Y is an outcome, then a higher-magnitude D(W|X) cannot be secondary to a lower-magnitude D(W|X), implying that D(W|X) can be used to set an upper bound to the size of a spurious treatment effect on an outcome. For a binary treatment variable X, D(W|X) gives an upper bound to the size of a difference between the proportions, in the two treatment groups, that can be caused for a binary outcome. If D(W|X) is less than 0.5, then it can be doubled to give an upper bound to the size of a difference between the means, in the two treatment groups, that can be caused for an equal-variance Normal outcome, expressed in units of the common standard deviation for the two treatment groups. We illustrate this method using a familiar dataset, with examples using propensity matching, weighting and stratification. We use the SSC package haif in the design phase, to check for variance inflation caused by propensity adjustment, and use the SSC package scenttest (an addition to the punaf family) to estimate the treatment effect in the analysis phase.

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Somers' D: A common currency for associations. Presented at the 21st UK Stata User Meeting, 10–11 September, 2015.

Somers' D(Y|X) is an asymmetric measure of ordinal association between two variables Y and X, on a scale from -1 to 1. It is defined as the difference between the conditional probabilities of concordance and discordance between two randomly-sampled (X,Y)-pairs, given that the two X-values are ordered. The somersd package enables the user to estimate Somers' D for a wide range of sampling schemes, allowing clustering and/or sampling-probability weighting and/or restriction to comparisons within strata. Somers' D has the useful feature that a larger D(Y|X) cannot be secondary to a smaller D(W|X) with the same sign, enabling us to make scientific statements that the first ordinal association cannot be caused by the second. An important practical example, especially for public-health scientists, is the case where Y is an outcome, X an exposure, and W a propensity score. However, an audience accustomed to other measures of association may be culture-shocked, if we present associations measured using Somers' D. Fortunately, under some commonly-used models, Somers' D is related monotonically to an alternative association measure, which may be more clearly related to the practical question of how much good we can do. These relationships are nearly linear (or log-linear) over the range of Somers' D values from -0.5 to 0.5. We present examples with X and Y binary, with X binary and Y a survival time, with X binary and Y conditionally Normal, and with X and Y bivariate Normal. Somers' D can therefore be used as a common currency for comparing a wide range of associations between variables, not limited to a particular model.

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Easy-to-use packages for estimating rank and spline parameters. Presented at the 20th UK Stata User Meeting, 11–12 September, 2014.

So-called non-parametric methods are in fact based on estimating and testing parameters, usually either rank parameters or spline parameters. Two comprehensive packages for estimating these are somersd (for rank parameters) and bspline (for spline parameters). Both of these estimate a wide range of parameters, but both are frequently found to be difficult to use by casual users. This presentation introduces rcentile, an easy-to-use front end for somersd, and polyspline, an easy-to-use front end for bspline. rcentile estimates percentiles with confidence limits, optionally allowing for clustered sampling and sampling-probability weights. The confidence intervals are saved in a Stata matrix, with one row per percentile, which the user can save to a resultsset using the xsvmat package. polyspline inputs an X- variable and a user-defined list of reference points and outputs a basis of variables for a polynomial or for another unrestricted spline. This basis can be included in the covariate list for an estimation command, and the corresponding parameters will be values of the polynomial or spline at the reference points, or differences between these values. By default, the spline will simply be a polynomial, with a degree one less than the number of reference points. However, if the user specifies a lower degree, then the spline will have knots interpolated sensibly between the reference points.

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Creating factor variables in resultssets and other datasets. Presented at the 19th UK Stata User Meeting, 12–13 September, 2013.

Factor variables are defined as categorical variables with integer values, which may represent values of some other kind, specified by a value label. We frequently want to generate such variables in Stata datasets, especially resultssets, which are output Stata datasets produced by Stata programs, such as the official Stata statsby command and the SSC packages parmest and xcontract. This is because categorical string variables can only be plotted after conversion to numeric variables, and because these numeric variables are also frequently used in defining a key of variables, which identify observations in the resultsset uniquely in a sensible sort order. The sencode package is downloadable, and frequently downloaded, from SSC, and is a “super” version of encode, which inputs a string variable and outputs a numeric factor variable. Its added features include a replace option allowing the output numeric variable to replace the input string variable, a gsort() option allowing the numeric values to be ordered in ways other than alphabetical order of the input string values, and a manyto1 option allowing multiple output numeric values to map to the same input string value. The sencode package is well–established, and has existed since 2001. However, some tips will be given on ways of using it that are not immediately obvious, but which the author has found very useful over the years when mass–producing resultssets. These applications use sencode with other commands, such as the official Stata command split and the SSC packages factmerg, factext and fvregen.

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Scenario comparisons: How much good can we do? Presented at the 18th UK Stata User Meeting, 13–14 September, 2012.

Applied scientists, especially public health scientists, frequently want to know how much good can be caused by a proposed intervention. For instance, they might want to estimate how much we could decrease the level of a disease, in a dream scenario where the whole world stopped smoking, assuming that a regression model fitted to a sample is true. Alternatively, they may want to compare the same scenario between regression models fitted to different datasets, as when disease rates in different subpopulations are standardized to a common distribution of gender and age, using the same logistic regression model with different parameters in each subpopulation. In statistics, scenarios can be defined as alternative versions of a dataset, with the same variables, but with different values in the observations, or even with non–corresponding observations. Using regression methods, we may estimate scenario means of a Y–variable in scenarios with specified X–values, and compare these scenario means. In Stata Versions 11 and 12, the standard tool for estimating scenario means is margins. A suite of packages is introduced for estimating scenario means and their comparisons, using margins, together with nlcom to implement Normalizing and variance–stabilizing transformations. margprev estimates scenario prevalences for binary variables. marglmean estimates scenario arithmetic means for non–negative valued variables. regpar estimates 2 scenario prevalences, together with their difference, the population attributable risk (PAR). punaf estimates 2 scenario arithmetic means from cohort or cross–sectional data, together with their ratio, the population unattributable fraction (PUF), which is subtracted from 1 to give the population attributable fraction (PAF). punafcc estimates an arithmetic mean between–scenario rate ratio for cases or non–survivors in case–control or survival data, respectively. This mean rate ratio, also known as a PUF, is also subtracted from 1 to estimate a PAF. These packages use the log transformation for arithmetic means and their ratios, the logit transformation for prevalences, and the hyperbolic arctangent or Fisher’s z transformation for differences between prevalences. Examples are presented for these packages.

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Sensible parameters for polynomials and other splines. Presented at the 17th UK Stata User Meeting, 15-16 September, 2011.

Splines, including polynomials, are traditionally used to model non-linear relationships involving continuous predictors. However, when they are included in linear models (or generalized linear models), the estimated parameters for polynomials are not easy for non–mathematicians to understand, and the estimated parameters for other splines are often not easy even for mathematicians to understand. It would be easier if the parameters were values of the polynomial or spline at reference points on the X–axis, or differences or ratios between the values of the spline at the reference points and the value of the spline at a base reference point. The bspline package can be downloaded from SSC, and generates spline bases for inclusion in the design matrices of linear models, based on Schoenberg B–splines. The package now has a recently added module flexcurv, which inputs a sequence of reference points on the X–axis, and outputs a spline basis, based on equally–spaced knots generated automatically, whose parameters are the values of the spline at the reference points. This spline basis can be modified by excluding the spline vector at a base reference point and including the unit vector. If this is done, then the parameter corresponding to the unit vector will be the value of the spline at the base reference point, and the parameters corresponding to the remaining reference spline vectors will be differences between the values of the spline at the corresponding reference points and the value of the spline at the base reference point. The spline bases are therefore extensions, to continuous factors, of the bases of unit vectors and/or indicator functions used to model discrete factors. It is possible to combine these bases for different continuous and/or discrete factors in the same way, using product bases in a design matrix to estimate factor–value combination means and/or factor–value effects and/or factor interactions.

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Post-parmest peripherals: fvregen, invcise, and qqvalue. Presented at the 16th UK Stata User Meeting, 9-10 September, 2010.

The parmest package is used with Stata estimation commands to produce output datasets (or resultssets) with one observation per estimated parameter, and data on parameter names, estimates, confidence limits, P-values, and other parameter attributes. These resultssets can then be input to other Stata programs to produce tables, listings, plots, and secondary resultssets containing derived parameters. Three recently-added packages for post-parmest processing are fvregen, invcise, and qqvalue. fvregen is used when the parameters belong to models containing factor variables, introduced in Stata Version 11. It regenerates these factor variables in the resultsset, enabling the user to plot, list, or tabulate factor levels with estimates and confidence limits of parameters specific to these factor levels. invcise calculates standard errors inversely from confidence limits produced without standard errors, such as those for medians and for Hodges-Lehmann median differences. These standard errors can then be input, with the estimates, into the metaparm module of parmest, to produce confidence intervals for linear combinations of medians or of median differences, such as those used in meta-analysis or interaction estimation. qqvalue inputs the P-values in a resultsset, and creates a new variable containing the frequentist q-values, calculated by inverting a multiple-test procedure designed to control the familywise error rate (FWER) or the false discovery rate (FDR). The frequentist q-value for each P-value is the minimum FWER or FDR for which that P-value would be in the discovery set, if the specified multiple-test procedure was used on the full set of P-values. fvregen, invcise, qqvalue, and parmest can be downloaded from SSC.

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Homoskedastic adjustment inflation factors in model selection. Presented at the 15th UK Stata User Meeting, 10-11 September, 2009.

Insufficient confounder adjustment is viewed as a common source of "false discoveries", especially in the epidemiology sector. However, adjustment for "confounders" that are correlated with the exposure, but which do not independently predict the outcome, may cause loss of power to detect the exposure effect. On the other hand, choosing confounders based on "stepwise" methods is subject to many hazards, which imply that the confidence interval eventually published is likely not to have the advertized coverage probability for the effect that we wanted to know. We would like to be able to find a model in the data on exposures and confounders, and then to estimate the parameters of that model from the conditional distribution of the outcome, given the exposures and confounders. The haif package, downloadable from SSC, calculates the homoskedastic adjustment inflation factors (HAIFs), by which the variances and standard errors of coefficients for a matrix of X-variables are scaled (or inflated), if a matrix of unnecessary confounders A is also included in a regression model, assuming equal variances (homoskedasticity). These can be calculated from the A- and X-variables alone, and can be used to inform the choice of a set of models eventually fitted to the outcome data, together with the usual criteria involving causality and prior opinion. Examples are given of the use of HAIFs and their ratios.

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parmest and extensions. Presented at the 14th UK Stata User Meeting, 8-9 September, 2008.

The parmest package creates output datasets (or resultssets) with one observation for each of a set of estimated parameters, and data on the parameter estimates, standard errors, degrees of freedom, t- or z-statistics, P-values, confidence limits, and other parameter attributes specified by the user. It is especially useful when parameter estimates are "mass-produced", as in a genome scan. Versions of the package have existed on SSC since 1998, when it contained the single command parmest. However, the package has since been extended with additional commands. The metaparm command allows the user to mass-produce confidence intervals for linear combinations of uncorrelated parameters. Examples include confidence intervals for a weighted arithmetic or geometric mean parameter in a meta-analysis, or for differences or ratios between parameters, or for interactions, defined as differences (or ratios) between differences (or ratios). The parmcip command is a lower-level utility, inputting variables containing estimates, standard errors, and degrees of freedom, and outputting variables containing confidence limits and P-values. As an example, we may input genotype frequencies and calculate confidence intervals for geometric mean homozygote/heterozygote ratios for genetic polymorphisms, measuring the size and direction of departures from Hardy-Weinberg equilibrium.

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Robust confidence intervals for Hodges-Lehmann median differences. Presented at the 13th UK Stata User Meeting, 10-11 September, 2007.

The cendif module is part of the somersd package, and calculates confidence intervals for the Hodges-Lehmann median difference between values of a variable in two subpopulations. The traditional Lehmann formula, unlike the formula used by cendif, assumes that the two subpopulation distributions are different only in location, and that the subpopulations are therefore equally variable. The cendif formula therefore contrasts with the Lehmann formula as the unequal-variance t-test contrasts with the equal-variance t-test. In a simulation study, designed to test cendif to destruction, the performance of cendif was compared to that of the Lehmann formula, using coverage probabilities and median confidence interval width ratios. The simulations involved sampling from pairs of Normal or Cauchy distributions, with subsample sizes ranging from 5 to 40, and between-subpopulation variability scale ratios ranging from 1 to 4. If the sample numbers were equal, then both methods gave coverage probabilities close to the advertized confidence level. However, if the sample numbers were unequal, then the Lehmann coverage probabilities were over-conservative if the smaller sample was from the less variable population, and over-liberal if the smaller sample was from the more variable population. The cendif coverage probability was usually closer to the advertized level, if the smaller sample was not very small. However, if the sample sizes were 5 and 40, and the two populations were equally variable, then the Lehmann coverage probability was close to its advertized level, while the cendif coverage probability was over-liberal. The cendif confidence interval, in its present form, is therefore robust both to non-Normality and to unequal variablity, but may be less robust to the possibility that the smaller sample size is very small. Possibilities for improvement are discussed.

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On the central role of Somers' D. Presented at the 12th UK Stata User Meeting, 11-12 September, 2006.

Somers' D and Kendall's tau-a are parameters behind rank or "non-parametric" statistics, interpreted as differences between proportions. Given two bivariate data pairs (X_1,Y_1) and (X_2,Y_2), Kendall's tau-a is the difference between the probability that the two pairs are concordant and the probability that the two pairs are discordant, and Somers' D is the difference between the corresponding conditional probabilities, given that the X-values are ordered. The somersd package computes confidence intervals for both parameters. The Stata 9 version of somersd uses Mata, and greatly extends the definition of Somers' D, allowing the X- and/or Y-variables to be left- or right-censored, and allowing multiple versions of Somers' D for multiple sampling schemes for pairs of X,Y-pairs. In particular, we may define stratified versions of Somers' D, in which we only compare pairs from the same stratum. The strata may be defined by grouping a Rubin-Rosenbaum propensity score, based on the values of multiple confounders for an association between an exposure variable X and an outcome variable Y. Therefore, rank statistics can have not only confidence intervals, but confounder-adjusted confidence intervals. Usually, we either estimate D(Y|X) as a measure of the effect of X on Y, or estimate D(X|Y) as a measure of the performance of X as a predictor of Y, compared to other predictors. Alternative rank-based measures of the effect of X on Y include the Hodges-Lehmann median difference and the Theil-Sen median slope, both of which are defined in terms of Somers' D and estimated using the somersd package.

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Resultssets, resultsspreadsheets and resultsplots in Stata. Presented at the 4th German Stata User Meeting, 31 March, 2006.

Most Stata users make their living producing results in a form accessible to end users. Most of these end users cannot immediately understand Stata logs. However, they can understand tables (in paper, PDF, HTML, spreadsheet or word processor documents) and plots (produced using Stata or non-Stata software). Tables are produced by Stata as resultsspreadsheets, and plots are produced by Stata as resultsplots. Sometimes (but not always), resultsspreadsheets and resultsplots are produced using resultssets. Resultssets, resultsspreadsheets and resultsplots are all produced, directly or indirectly, as output by Stata commands. A resultsset is a Stata dataset, which is a table, whose rows are Stata observations and whose columns are Stata variables. A resultsspreadsheet is a table in generic text format, conforming to a TeX or HTML convention, or to another convention with a column separator string and possibly left and right row delimiter strings. A resultsplot is a plot produced as output, using a resultsset or a resultsspreadsheet as input. Resultsset-producing programs include statsby, parmby, parmest, collapse, contract, xcollapse and xcontract. Resultsspreadsheet-producing programs include outsheet, listtex, estout and estimates table. Resultsplot-producing programs include eclplot and smileplot. There are two main approaches (or dogmas) for generating resultsspreadsheets and resultsplots. The resultsset-central dogma is followed by parmest and parmby users, and states: "Datasets make resultssets, which make resultsplots and resultsspreadsheets". The resultsspreadsheet-central dogma is followed by estout and estimates table users, and states: "Datasets make resultsspreadsheets, which make resultssets, which make resultsplots". The two dogmas are complementary, and each dogma has its advantages and disadvantages. The resultsspreadsheet dogma is much easier for the casual user to learn to apply in a hurry, and is therefore probably preferred by most users most of the time. The resultsset dogma is more difficult for most users to learn, but is more convenient for users who wish to program everything in do-files, with little or no manual cutting and pasting.

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Generalized confidence interval plots using commands or dialogs. Presented at the 11th UK Stata User Meeting, 17-18 May, 2005.

Confidence intervals may be presented as publication-ready tables or as presentation-ready plots. eclplot produces plots of estimates and confidence intervals. It inputs a dataset (or resultsset) with one observation per parameter and variables containing estimates, lower and upper confidence limits, and a fourth variable, against which the confidence intervals are plotted. This resultsset can be used for producing both plots and tables, and may be generated using a spreadsheet or using statsby, postfile or the unofficial Stata parmest package. Currently, eclplot offers 7 plot types for the estimates and 8 plot types for the confidence intervals, each corresponding to a graph twoway subcommand. These plot types can be combined to produce 56 combined plot types, some of which are more useful than others, and all of which can be either horizontal or vertical. eclplot has a plot() option, allowing the user to superimpose other plots to add features such as stars for P-values. eclplot can be used either by typing a command, which may have multiple lines and sub-suboptions, or by using a dialog, which generates the command for users not fluent in the Stata graphics language. This presentation includes a demonstration of eclplot, using both commands and dialogs.

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From datasets to resultssets in Stata. Presented at the 10th UK Stata User Meeting, 28-29 June, 2004.

A resultsset is a Stata dataset created as output by a Stata program. It can be used as input to other Stata programs, which may in turn output the results as publication-ready plots or tables. Programs that create resultssets include xcontract, xcollapse, parmest, parmby and descsave. Stata resultssets do a similar job to SAS output data sets, which are saved to disk files. However, in Stata, the user typically has the options of saving a resultsset to a disk file, writing it to the memory (overwriting any pre-existing data set), or simply listing it. Resultssets are often saved to temporary files, using the tempfile command. This lecture introduces programs that create resultssets, and also programs that do things with resultssets after they have been created. listtex outputs resultssets to tables that can be inserted into a Microsoft Word, HTML or LaTeX document. eclplot inputs resultssets and creates confidence interval plots. Other programs, such as sencode and sdecode, process resultssets after they are created and before they are listed, tabulated or plotted. These programs, used together, have a power not always appreciated if the user simply reads the on-line help for each package. This lecture is a survey lecture, and is based on a handout and a set of example do-files, which can be downloaded with or without the presentation.

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Multiple test procedures and smile plots. Presented at the 9th UK Stata User Meeting, 19-20 May, 2003.

Scientists often have good reasons for wanting to calculate multiple confidence intervals and/or P-values, especially when scanning a genome. However, if we do this, then the probability of not observing at least one "significant" difference tends to fall, even if all null hypotheses are true. A sceptical public will rightly ask whether a difference is "significant" when considered as one of a large number of parameters estimated. This presentation demonstrates some solutions to this problem, using the unofficial Stata packages parmest and smileplot. The parmest package allows the calculation of Bonferroni-corrected or Sidak-corrected confidence intervals for multiple estimated parameters. The smileplot package contains two programs, multproc (which carries out multiple test procedures) and smileplot (which presents their results graphically by plotting the P-value on a reverse log scale on the vertical axis against the parameter estimate on the horizontal axis). A multiple test procedure takes, as input, a set of estimates and P-values, and rejects a subset (possibly empty) of the null hypotheses corresponding to these P-values. Multiple test procedures have traditionally controlled the family-wise error rate (FWER), typically enabling the user to be 95% confident that all the rejected null hypotheses are false, and that all the corresponding "discoveries" are real. The price of this confidence is that the power to detect a difference of a given size tends to zero as the number of measured parameters becomes large. Therefore, recent work has concentrated on procedures that control the false discovery rate (FDR), such as the Simes procedure and the Yekutieli-Benjamini procedure. FDR-controlling procedures attempt to control the number of false discoveries as a proportion of the number of true discoveries, typically enabling the user to be 95% confident that some of the discoveries are real, or 90\% confident that most of the discoveries are real. This less stringent requirement causes power to "bottom out" at a non-zero level as the number of tests becomes large. The smileplot package offers a selection of multiple test procedures of both kinds. This presentation uses data provided by the ALSPAC Study Team at the Institute of Child Health at Bristol University, UK.

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Creating plots and tables of estimation results using parmest and friends. Presented at the 8th UK Stata User Meeting, 20-21 May, 2002.

Statisticians make their living mostly by producing confidence intervals and P-values. However, the ones supplied in the Stata log are not in any fit state to be delivered to the end user, who usually at least wants them tabulated and formatted, and may appreciate them even more if they are plotted on a graph for immediate impact. The parmest package was developed to make this easy, and consists of two programs. These are parmest, which converts the latest estimation results to a data set with one observation per estimated parameter and data on confidence intervals, P-values and other estimation results, and parmby, a "quasi-byable" front end to parmest, which is like statsby, but creates a data set with one observation per parameter per by-group instead of a data set with one observation per by-group. The parmest package can be used together with a team of other Stata programs to produce a wide range of tables and plots of confidence intervals and P-values. The programs descsave and factext can be used with parmby to create plots of confidence intervals against values of a categorical factor included in the fitted model, using dummy variables produced by xi or tabulate. The user may easily fit multiple models, produce a parmby output data set for each one, and concatenate these output data sets using the program dsconcat to produce a combined data set, which can then be used to produce tables or plots involving parameters from all the models. For instance, the user might tabulate or plot unadjusted and adjusted regression parameters side by side, together with their confidence limits and/or P-values. The parmest team is particularly useful when dealing with large volumes of results derived from multiple multi-parameter models, which are particularly common in the world of epidemiology. This version of the presentation is a post-publication update, made in response to changes in the parmest package suggested by Bill Gould of StataCorp after seeing the original presentation.

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Splines with parameters that can be explained in words to non-mathematicians. Presented at the 7th UK Stata User Meeting, 14 May, 2001.

Splines are traditionally used to model non-linear relationships involving continuous predictors, usually confounders. One example is in asthma epidemiology, where splines are used to model a seasonal and longer-term time trend in asthma-related hospital admissions, which must be eliminated in a search for shorter-term epidemics caused by pollution episodes. Usually, the spline is included in a regression model by defining a basis of splines, and including this basis amongst the X-variates, together with the predictors of interest. The basis is typically a plus-function basis, a truncated-power basis, or a Schoenberg B-spline basis. With either of these options, the parameters estimated by the regression model will not be easy to explain in words to non-mathematicians. An STB insert (sg151 in STB-57) presented two programs for generating spline bases. One of these (bspline) generates Schoenberg B-splines. The other program (frencurv, short for "French curve") generates an alternative spline basis, whose parameters are simply values of the spline at reference points along the horizontal axis. In the example from asthma epidemiology, these parameters might be the expected hospital admissions counts on the first day of each month, in the absence of a pollution episode. The expected pollution-free admissions counts on other days of the month are interpolated between the parameters, using the spline. These parameters can be presented, with their confidence limits, to non-technical people. Confidence limits can also be computed for differences and/or ratios between expected values at different reference points, using lincom.

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Confidence intervals for rank order statistics: Somers' D, Kendall's tau-a and their differences. Presented at the 6th UK Stata User Meeting, 15 May, 2000.

So-called "non-parametric" methods are in fact based on population parameters, which are zero under the null hypothesis. Two of these parameters are Kendall's tau-a and Somers' D. both of which measure ordinal correlation between two variables X and Y. If X is a binary variable, then Somers' D(Y|X) is the parameter tested by a Wilcoxon rank-sum test. It is more informative to have confidence limits for these parameters than P-values alone, for three main reasons. First, it might discourage people from arguing that a high P-value proves a null hypothesis. Second, for continuous data, Kendall's tau-a is often related to the classical Pearson correlation by Greiner's relation, so we can use Kendall's tau-a to define robust confidence limits for Pearson's correlation. Third, we might want to know confidence limits for differences between two Kendall's tau-a or Somers' D parameters, because a larger Kendall's tau-a or Somers' D cannot be secondary to a smaller one. The program somersd calculates confidence intervals for Somers' D or Kendall's tau-a, using jackknife variances. There is a choice of transformations, including Fisher's z, Daniels' arcsine, Greiner's rho, and the z-transform of Greiner's rho. A cluster option is available, intended for measuring intra-class correlation (such as exists between measurements on pairs of sisters). The estimation results are saved as for a model fit, so that differences can be estimated using lincom.

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Roger B. Newson
Email: r.newson@imperial.ac.uk
Text written: 16 October 2015. (Papers and presentations may have been revised since then.)
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