Fixed and random effects meta-analysis


glst Generalized Least Squares for Trend… para estudios de tendencias de análisis de dosis-respuesta Syntax



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glst
Generalized Least Squares for Trend… para estudios de tendencias de análisis de dosis-respuesta
Syntax
glst depvar dose [indepvars] [if] [in], se(varname) cov(n cases) {cc

| ir | ci} [options]


options description

-------------------------------------------------------------------------

* 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


level(#) set confidence level; default is level(95)

eform generic label; exp(b); the default

-------------------------------------------------------------------------

* se() and cov() are required.

+ One of cc, ir, or ci is required for trend estimation.

depvar contains log relative-risks; dose is the main covariate of

interest and contains the exposure levels; and indepvars may contain

other covariates, such as polynomial terms of dose or interaction

terms.

Description
glst estimates log-linear dose-response regression models using

generalized least squares for trend estimation of single or multiple

summarized dose-response epidemiological studies, namely, case-control,

incidence-rate, and cumulative incidence data. It differs from

variance-weighted least squares (see [R] vwls) in that glst estimates a

variance-covariance matrix of the beta coefficients, as proposed by

Greenland and Longnecker (1992).

Options
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 noncases) for

cumulative incidence data (ci). The cases variable contains the

number of cases at each exposure level.
cc specifies case-control data. It is required for trend estimation of

one study unless the pfirst() option is specified.


ir specifies incidence-rate data. It is required for trend estimation of

one study unless the pfirst() option is specified.


ci specifies cumulative incidence data. It is required for trend

estimation of one study unless the pfirst() option is specified.


vwls specifies variance-weighted least-squares (see [R] vwls) estimation,

which assumes zero covariances among a 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 matrices. This option also

provides the relative differences (as percentages) between crude and

adjusted relative risks and their correlation matrix.


pfirst(id study) specifies the pool-first method with multiple summarized

studies. The id variable is an indicator variable that assumes the

same value across correlated parameters within a study. The study

variable must take value 1 for case-control data, 2 for

incidence-rate data, and 3 for cumulative incidence data. Within each

group of parameters, the first observation is assumed to be the

referent. This option allows the estimation either a fixed- or

random-effects meta-regression model.


tstage(f|r) specifies the two-stage fixed-effects (f) (inverse

variance-weighted least squares) or random-effects (r) 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() 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() is also specified.


random specifies the iterative generalized least-squares method to fit a

random-effects 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()

is specified.
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.



Example
Input data from table 1, page 1302 of Greenland and Longnecker (1992)
. use http://nicolaorsini.altervista.org/stata/data/dose.dta, clear

Go from 95% CI of odds ratios to 95% CI of log odds-ratios


. 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)

Reference
Greenland S. and M. P. Longnecker. 1992. Methods for trend estimation

from summarized dose-reponse data, with applications to

meta-analysis. American Journal of Epidemiology 135: 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


Support
http://nicolaorsini.altervista.org

nicola.orsini@ki.se



Also see
Article: Stata Journal, volume 9, number 2: st0096_2

Stata Journal, volume 9, number 1: st0096_1



Stata Journal, volume 6, number 1: st0096
Manual: [R] vwls
Online: [R] vwls
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