help drmeta

Title

drmeta -- Dose-response meta-analysis of summarized data

Syntax

drmeta depvar dose_vars [if] [in] , [ options ]

options

Model
se(varname) standard error of depvar

data(varname1 varname2) crude data

id(varname) study-specific contrasts

type(varname) type of depvar

or odds ratio

rr risk ratio

hr hazard ratio

md mean difference

smd standardized mean difference

vwls variance-weighted least squares estimation

2stage two-stage dose-response meta-analysis

ml maximum likelihood method

reml restricted maximum likelihood method

fixed fixed-effects method

hamling Hamling's method for the covariances

acov(varname) passes average covariance as variable

mcov(matrix_list) passes var/cov as matrices

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

eform generic label; exp(b); the default

noretable suppress random-effects table

stddeviations show random-effects and residual-error parameter estimates as standard deviations and correlations

nolrt suppress likelihood-ratio test for random-effects

where depvar contains empirical estimates of contrasts in responses;
dose_vars specifies what are the variables to model the dose (polynomials, splines).

After drmeta, the command drmeta_graph can be useful to plot the estimated dose-response model.
The predict command saves different types of predicted values (fixed, random, fixed plus random).
The drmeta_gof provides tools to evaluate the goodness-of-fit of the model.
Standard post-estimation commands such as testparm and predictnl can be used.

Description

drmeta estimates parametric dose-response models based on summarized data. It can be used to investigate linear and non-linear
dose-response relationships. It fits fixed-effects and random-effects model using
a one-stage or a two-stage approach. Effect measures include odds ratios, risk ratios, hazard ratios, mean differences, and standardized mean differences.

Options

Model

se(varname) specifies an estimate of the standard error of depvar. It is a required option.

data(varname1 varname2) specifies variables containing the information required to reconstruct the covariances of depvar.
It is a required option. At each exposure level, varname1 is the number of subjects (controls plus cases) for case-control data (or);
or the total person-time for incidence rate data (hr); the total number of persons (cases plus non-cases) for cumulative incidence data (rr).
The variable varname2 contains the number of cases at each exposure level.
In case depvar are mean differences and standardized mean differences total, the variable varname1 indicates the total number of persons
and the variable varname2 contains the standard deviation of the outcome at each exposure level.
Any missing values in either of the two variables set to zero the covariances.

or specifies odds ratio data. It's required for trend estimation of a single study unless the option type(varname) is specified.

hr specifies hazard ratio data. It's required for trend estimation of a single study unless the option type(varname) is specified.

rr specifies risk ratio data. It's required for trend estimation of a single study unless the option type(varname) is specified.

md specifies mean difference data. It's required for trend estimation of a single study unless the option type(varname) is specified.

smd specifies standardized mean difference data. It's required for trend estimation of a single study unless the option type(varname) is specified.

vwls sets to zero the covariances of depvar within each study.

hamling specifies the Hamling's method to estimate the covariances in case depvar is a log relative risk (Stat Med. 2008. 27(7):954-70).
The default is the Greenland and Longnecker's method (AJE. 1992. 135(11), pp.1301-1309). In case depvar is a mean difference or a standardized mean
difference, the method used for the covariance is described by Crippa and Orsini (BMC Med Res Methodol. 2016 Aug 2;16:91).

2stage specifies the two-stage approach for dose-response meta-analysis. It is calling the
mvmeta command. The default is the one-stage approach.

id(varname) specifies the variable identyfing study-specific contrasts. The reference dose is the row with a value of 0 for the standard error.
This option is required with multiple studies.

type(varname) specifies the variable indicating the type of measure used to contrast dose levels. It can take on value 1 for odds ratio,
2 for hazard ratio, 3 for risk ratio, 4 for mean difference, and 5 for standardized mean difference.

acov(varname) passes average covariance as variable.

mcov(matrix_list) passes a list of variance/covariance matrices, one for each study. It is an advanced option where the order of the matrix list matters.
The first matrix is supposed to be related to the first set of contrasts and so on. It can be useful when empirical contrasts and related variance/covariance
matrices are available directly from fitting a model on primary data. So this option allows the user to skip the specification of the data() option.

ml fit random-effects model via maximum likelihood (ML); the default. All variances and covariances of the random-effects are allowed to be distinct.
So if dose_vars includes p variables, then an additional p(p+1)/2 random-effects parameters are estimated.

reml fit random-effects model via restricted maximum likelihood (REML). All variances and covariances of the random-effects are allowed to be distinct.
So if dose_vars includes p variables, then an additional p(p+1)/2 random-effects parameters are estimated.

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.

noretable suppress the random-effects parameter estimates.

stddeviations displays the random-effects parameter estimates as standard deviations and correlations.

nolrt suppress the likelihood-ratio test for the unstructured variance/covariance components. It assesses whether all random-effects parameters
of the dose-response model are simultaneously zero. Of note, the likelihood-ratio test is conservative.

Example 1 - Observational cohort studies on alcohol consumption and colorectal cancer risk

* Read data described by Orsini et al. AJE 2012

use http://www.stats4life.se/data/ex_alcohol_crc.dta, clear

* Model 1. One-stage random-effects dose-response model assuming a linear trend

drmeta logrr dose , data(peryears cases) id(study) type(type) se(se) reml
lincom dose*12, eform
drmeta_graph , dose(0(1)60) ref(10) equation(d) eform

* Model 2. One-stage random-effects dose-response model using restricted cubic splines

mkspline doses = dose, nk(3) cubic
mat knots = r(knots)
drmeta logrr doses1 doses2 , data(peryears cases) id(study) type(type) se(se) reml
drmeta_graph , dose(0(1)60) ref(10) matk(knots) eform

* Model 3. Two-stage random-effects dose-response model using restricted cubic splines

drmeta logrr doses1 doses2 , data(peryears cases) id(study) type(type) se(se) reml 2stage
`"drmeta_graph , dose(0(1)60) ref(10) matk(knots) eform ytitle("Relative Risk") xtitle("Alcohol consumption (g/day)")"'

Example 2 - Randomized trials on effectiveness of aripiprazole in schizoaffective patients

* Read data described by Crippa & Orsini. BMC Med Res Methodol. 2016 Aug 2;16:91.

use http://www.stats4life.se/data/aripanss, clear

* Model 1. One-stage random-effects dose-response model assuming a quadratic trend

drmeta md dose dosesq , se(se_md) data(n sd) id(id) type(type_md)
`"drmeta_graph , d(0(1)30) ref(0) eq(d d^2) ytitle("Mean difference") xtitle("Ariprazole (mg/day)") "'

References

Crippa A, Discacciati A, Bottai M, Spiegelman D, and Orsini N. One-stage dose–response meta-analysis for aggregated data. Stat Methods Med Res. 2019 May;28(5):1579-1596.

Crippa A, Orsini N. Dose-response meta-analysis of differences in means. BMC Med Res Methodol. 2016 Aug 2;16(1):91.

Orsini N, Ruifeng L, Wolk A, Khudyakov P, Spiegelman D. Meta-analysis for linear and non-linear dose-response relationships: examples, an evaluation of approximations, and software. American Journal Epidemiology. 2012 Jan 1;175(1):66-73.

Hamling J, Lee P, Weitkunat R, Ambühl M. Facilitating meta-analyses by deriving relative effect and precision estimates for alternative comparisons from a set of estimates presented by exposure level or disease category.
Statistics in Medicine. 2008 Mar 30;27(7):954-70.

Stored results

drmeta stores the following in e():

Scalars

e(N) number of observations

e(k) number of parameters

e(k_f) number of fixed-effects parameters

e(k_r) number of random-effects parameters

e(N_s) number of sets of contrasts

e(df_m) model degrees of freedom

e(chi2) chi-squared

e(p) p-value for model test

e(ll) log likelihood

e(ll_c) log likelihood, comparison model

e(lrt_c) likelihood ratio test, comparison test

e(df_c) degrees of freedom, comparison test

e(p_c) p-value for comparison test

e(r2) overall coefficient of determination (R-squared)

e(D) overall deviance statistic

e(p_D) p-value of the overall deviance statistic

e(Q) Cochran Q-test for heterogeneity (Two-stage)

e(Q_df) degrees of freedom of the Q-test

e(Q_p) p-value of the Q-test

Macros

e(cmd) drmeta

e(cmdline) command as typed

e(depvar) name of dependent variable

e(idname) name of sets of contrasts

e(id) values of the sets of contrasts

e(se) name of standard errors of contrasts

e(dm) names specified in dose_vars

e(method) ml or reml

e(mtype) fixed or random

e(proc) One-stage or Two-stage

e(properties) b V

e(predict) program used to implement predict

Matrices

e(b) coefficient vector of fixed effects

e(V) variance-covariance matrix of fixed effects

e(Psi) variance-covariance matrix of random effects

e(PsiC) correlation matrix of random effects

e(Sigma) variance-covariance matrices of all sets of contrasts

e(bs#) coefficient vector for the # set of contrasts (GLS) in e(id)

e(vs#) variance-covariance matrix for the # set of contrasts (GLS) in e(id)

e(X#) design matrix used for the # set of contrasts in e(id)

e(Sigma#) variance-covariance matrix for the # set of contrasts in e(id)

e(xbu#) coefficient vector (fixed+BLUP) for the # set of contrasts in e(id)

e(blup#) predicted random-effects (BLUP) for the # set of contrasts in e(id)

Functions

e(sample) marks estimation sample

Author

Nicola Orsini, Biostatistics Team,
Department of Public Health Sciences, Karolinska Institutet, Sweden

Support

http://www.stats4life.se

nicola.orsini@ki.se

Also see

glst, drmeta_graph, predict, drmeta_gof