help glst


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


glst depvar dose [indepvars] [if] [in] , se(varname) cov(n cases) [ options ]

options Description ------------------------------------------------------------------------- Model se(varname) variable containing estimate of standard error. cov(n cases) variables containing the information required to fit the covariances. cc case-control data. ir incidence rate data. ci cumulative incidence data. vwls variance-weighted least squares estimation. crudes crude relative risks and correlations. pfirst(id study) pool-first method. tstage({f|r}) two-stage fixed or random effects meta-analysis. ssest study-specific linear trend estimates. random random-effects for the dose coefficient in an aggregate analysis.

Reporting level(#) set confidence level; default is level(95) eform generic label; exp(b); the default

------------------------------------------------------------------------- where depvar contains log relative risks; dose is the main covariate of interest and contains the exposure levels; indepvars may contain other covariates (for instance, polynomial terms of dose or interaction terms)


glst estimates 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 that glst estimates a variance-covariance matrix of the beta coefficients, as proposed by Greenland and Longnecker (1992).


+-------+ ----+ Model +------------------------------------------------------------

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

cov(n cases) specifies variables containing the information required to fit the covariances among the beta coefficients. At each exposure level, n is 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 variable cases contains the number of cases at each exposure level.

cc specifies case-control data. It's required for trend estimation of a single study unless the option pfirst(id study) is specified.

ir specifies incidence rate data. It's required for trend estimation of a single study unless the option pfirst(id study) is specified.

ci specifies cumulative incidence data. It's required for trend estimation of a single study unless the option pfirst(id study) is specified.

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

crudes specifies 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.

random specifies the iterative generalized least squares method to estimate a random-effect meta-regression model (aggregate analysis). Between-study variability of the dose coefficient is estimated with the moment estimator. This option can be specified only if pfirst(id study) is specified.

pfirst(id study) specifies the pool-first method with multiple summarized studies. The variable id is an indicator variable that assumes the same value across correlated parameters within a study. The variable study must 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 if pfirst(id study) is also specified, and if only one covariate, namely the dose variable, is included in the linear predictor.

ssest displays study-specific linear trend estimates. This option can be specified only if pfirst(id study) is also specified.

+-----------+ ----+ Reporting +--------------------------------------------------------

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

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


* input data from Table 1. page 1302 of Greenland and Longnecker (1992) . use, 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)


Orsini 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. Authors

Nicola 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


Also see

[R] vwls

On-line: help for vwls