help glst-------------------------------------------------------------------------------

Title

glst-- Generalized Least Squares for trend estimation of summarized dose-response data

Syntax

glstdepvardose[indepvars] [if] [in],se(varname)cov(n cases)[options]

optionsDescription ------------------------------------------------------------------------- Modelse(varname)variable containing estimate of standard error.cov(n cases)variables containing the information required to fit the covariances.cccase-control data.irincidence rate data.cicumulative incidence data.vwlsvariance-weighted least squares estimation.crudescrude relative risks and correlations.pfirst(id study)pool-first method.tstage({f|r})two-stage fixed or random effects meta-analysis.sseststudy-specific linear trend estimates.randomrandom-effects for thedosecoefficient in an aggregate analysis.Reporting

level(#)set confidence level; default islevel(95)eformgeneric label;exp(b); the default------------------------------------------------------------------------- where

depvarcontains log relative risks;doseis the main covariate of interest and contains the exposure levels;indepvarsmay contain other covariates (for instance, polynomial terms ofdoseor interaction terms)

Description

glstestimates log-linear dose-response regression model using generalized least squares for trend estimation of single or multipe summarized dose-response epidemiological studies, namely case-control, incidence-rate, and cumulative incidence data. It differs from variance weighted least squares (help vwls) in thatglstestimates a variance-covariance matrix of the beta coefficients, as proposed by Greenland and Longnecker (1992).

Options+-------+ ----+ Model +------------------------------------------------------------

se(varname)specifies an estimate of the standard error ofdepvar, log relative risks. All values ofvarnamemust be > 0.

cov(n cases)specifies variables containing the information required to fit the covariances among the beta coefficients. At each exposure level,nis the number of subjects (controls plus cases) for case-control data (cc); or the total person-time for incidence rate data (ir); or the total number of persons (cases plus non-cases) for cumulative incidence data (ci). The variablecasescontains the number of cases at each exposure level.

ccspecifies case-control data. It's required for trend estimation of a single study unless the optionpfirst(id study)is specified.

irspecifies incidence rate data. It's required for trend estimation of a single study unless the optionpfirst(id study)is specified.

cispecifies cumulative incidence data. It's required for trend estimation of a single study unless the optionpfirst(id study)is specified.

vwlsspecifies variance-weighted least squares (help vwls) estimation which assume zero covariances among series of log relative risks; the default is generalized least squares.

crudesspecifies to calculate the vector of crude relative risks, and its variance-covariance and correlation matrix. This option provides also the relative differences (as percentages) between crude and adjusted relative risks and their correlation matrix.

randomspecifies the iterative generalized least squares method to estimate a random-effect meta-regression model (aggregate analysis). Between-study variability of thedosecoefficient is estimated with the moment estimator. This option can be specified only ifpfirst(idstudy)is specified.

pfirst(id study)specifies the pool-first method with multiple summarized studies. The variableidis an indicator variable that assumes the same value across correlated parameters within a study. The variablestudymust take value 1 for case-control, 2 for incidence rate, and 3 for cumulative incidence study. Within each group of parameters the first observation is assumed to be the referent. This option allows the estimation either fixed or random-effects meta-regression model.

tstage({f|r})specifies the two-stage fixed (f) (inverse variance-weighted least squares) or random (r) effects meta-analysis of dose-response linear trends (using the method of moments to estimate the between-study variance tau2). This option can be specified only ifpfirst(id study)is also specified, and if only one covariate, namely thedosevariable, is included in the linear predictor.

ssestdisplays study-specific linear trend estimates. This option can be specified only ifpfirst(id study)is also specified.+-----------+ ----+ Reporting +--------------------------------------------------------

level(#)specifies the confidence level, as a percentage, for confidence intervals. The default islevel(95)or as set byset level.

eformreports coefficient estimates as exp(b) rather than b. Standard errors and confidence intervals are similarly transformed.

Example* input data from Table 1. page 1302 of Greenland and Longnecker (1992) . use http://nicolaorsini.altervista.org/stata/data/dose.dta, clear * to go from 95% CI of OR to 95% CI of log OR

. gen double logor = log(adjor) . gen double logorlb = log(lb) . gen double logorub = log(ub) . gen double se = ((logorub - logorlb)/(2*invnorm(.975)))

* trend estimation without correction for covariance of odds ratios

. vwls logor dose in 2/4, sd(se) nocons . mat list e(V)

* trend estimation with correction for covariance of log odds ratios

. glst logor dose, se(se) cov(N case) cc

* check the variance-covariance matrix of log odds ratios

. mat list e(Sigma)

ReferenceOrsini N., Bellocco R., Greenland S. 2006. Generalized least squares for trend estimation of summarized dose-response data,

Stata Journal, 6(1): 40-57.Greenland S. and Longnecker M. P. 1992. Methods for trend estimation from summarized dose-reponse data, with applications to meta-analysis,

American Journal Epidemiology, 135(11), pp.1301-1309.AuthorsNicola Orsini, Division of Nutritional Epidemiology, Institute of Environmental Medicine, Karolinska Institutet, Sweden

Rino Bellocco, Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Sweden

Sander Greenland, Department of Epidemiology, UCLA School of Public Health, USA

Supporthttp://nicolaorsini.altervista.org nicola.orsini@ki.se

Also see

[R] vwlsOn-line: help for vwls