Treasure Island (FL): StatPearls Publishing; 2023 Jan. Associations between an exposure X t and outcome Y t measured longitudinally, with, MeSH The analysis under model iii based on a nonindependence working correlation structure would nonetheless be subject to confounding bias and GEE bias when that working correlation structure is misspecified, as is likely when the outcome model is nonlinear. Dziak JJ, Li R, Tan X, Shiffman S, Shiyko MP. Cannabis Use Is Associated With Decreased Antiretroviral Therapy Adherence Among Older Adults With HIV. SR Google Scholar, Conneely, K.N., Boehnke, M.: So many correlated tests, so little time! PubMedGoogle Scholar. Stat. Wiley Series in Probability and Statistics. Data from the Comprehensive Dialysis Study motivate the proposed methods. Interestingly, this holds even if the functional form of the propensity score used in the SCMM is misspecified, provided the exposure effect is the same across all levels of the propensity score and the remaining predictors in the model (12). We define. One possible model for the propensity score is: This approach is also based on regression. Soc. Biometrics 54, 638645 (1998), CrossRef A practical data example is presented along with example programs for both SAS and R. These keywords were added by machine and not by the authors. In practice, bias can also occur due to lack of positivity, which requires both exposed and unexposed individuals at every level of the confounders (13). 3pm}^9F%]pL7. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. In linear models without interactions, the conditional and unconditional effects coincide but are otherwise different. Disclaimer. When incorporated into the survival model as a time-varying covariate, the joint model, called a shared parameter model is estimated using the NLMIXED procedure. SCMMs including the propensity score estimate a different conditional effect. 2023 Feb 7. Patients' self-management of adverse events and patient-reported outcomes in advanced renal cell carcinoma treated with targeted therapies: A prospective, longitudinal, observational study. MSM 2 is correctly specified, and the estimates are unbiased using either stabilized weights or unstabilized weights. Time-varying ATS use, a categorical variable measuring number of days respondents used ATS in the previous 28-day period (variable atsFactor ). However, the bias is eliminated by using an unstructured working correlation matrix. JM (eds) Innovative Statistical Methods for Public Health Data. HHS Vulnerability Disclosure, Help Online ahead of print. , Hernn MA. . Estimation of causal effects of time-varying exposures using longitudinal data is a common problem in epidemiology. In: Seeber, G.U.H., et al. . 1 0 obj , Glymour M, Weuve J, et al. 2023 Feb 16;23(4):2221. doi: 10.3390/s23042221. -. There is some small finite sample bias using unstabilized weights. 13 0 obj Provided by the Springer Nature SharedIt content-sharing initiative, Over 10 million scientific documents at your fingertips, Not logged in : Feasibility of text messaging for ecologocial momentary assessment of marijuana use in college students. Modeling Time-Dependent Covariates in Longitudinal Data Analyses. VanderWeele Vansteelandt It has been suggested that weights could be truncated to improve precision (13). 330., NBER Technical Working Paper 2006. In linear models, our propensity score adjusted estimates are equivalent to efficient g-estimates in a SNMM for short-term effects (27). 16 0 obj The site is secure. Goetgeluk S, Vansteelandt S, Goetghebeur E. Estimation of controlled direct effects. However, in this paper we show how standard regression methods can be used, even in the presence of time-dependent confounding, to estimate the total effect of an exposure on a subsequent outcome by controlling appropriately for prior exposures, outcomes, and time-varying covariates. Estimation of the causal effects of time-varying exposures. If we had a video livestream of a clock being sent to Mars, what would we see? Constructing inverse probability weights for continuous exposures: a comparison of methods. % i8/T:y%^FN>lEF1;Jsgg'1BqZztvVp.Bw$'bSKM$ Q 95xfxwA[^mjs; }OcZ0',]B&W?FW\j:&A. Bookshelf Harvard University Press, Cambridge (1985), MATH This is a preview of subscription content, access via your institution. Statistical analysis of longitudinal data requires methods that can properly account for the intra-subject cor-relation of response measurements. The 5. , Vansteelandt S, Goetghebeur E. Naimi Data file structures Time-varying and time-invariant covariates Modeling nonlinearity and interactions Modeling treatment effects Error covariance structures Models with random coefficients Comparison of Traditional and Modern Methods Traditional Methods paired-samplest-test andrepeatedmeasuresANOVA MANOVA/MANCOVA trendanalysis Advantages : Longitudinal data analysis for discrete and continuous outcomes. : A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data. endstream <> Conditional effects may be more realistic for interpretation, in particular when the exposed and unexposed have quite different covariate histories. endobj Prev Sci. Model iii, fitted using an independence working correlation matrix, fails to account for confounding by Yt1, resulting in bias. endobj For linear models X1, X1, and X1 all represent the same estimand, provided the MSMs and SCMM are correctly specified. . In theory, IPW estimation of MSMs extends to continuous exposures by specifying a model for the conditional distribution of the continuous exposure in the weights. A 95% confidence interval for Y was estimated using 1,000 bootstrap samples, using the percentile method (22, 23). Unlike SCMMs, MSMs do not accommodate control for outcome history via regression adjustment; hence GEE bias cannot be avoided by adjustment for the outcome history (14, 15). xzt1@psu.edu PMID: 22103434 PMCID: PMC3288551 DOI: 10.1037/a0025814 Abstract I am working through Chapter 15 of Applied Longitudinal Data-Analysis by Singer and Willett, on Extending the Cox Regression model, but the UCLA website here has no example R code for this chapter. (3) for an overview), which have not been used extensively in practice (2426). Epidemiology. 2014;25(2):292299. , Joffe M. Vansteelandt B 69(1), 7999 (2007), Lalonde, T.L., Nguyen, A.Q., Yin, J., Irimate, K., Wilson, J.R.: Modeling correlated binary outcomes with time-dependent covariates. The propensity score for an individual at time. JM endobj . Functional data analysis for dynamical system identification of behavioral processes. FOIA The .gov means its official. New York, NY: John Wiley and Sons; 2002. [ 15 0 R] 9 0 obj SCMMs estimate conditional effects, whereas MSMs are typically used to estimate marginal effects. Left column: sample size, Intercept (left plot) and slope (right plot) function estimates for the empirical data., MeSH sharing sensitive information, make sure youre on a federal This would occur if Xt referred to a status during [t1,t) and Yt referred to a status during [t,t+1). doi: 10.35371/aoem.2022.34.e37. Federal government websites often end in .gov or .mil. Adding EV Charger (100A) in secondary panel (100A) fed off main (200A). By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. 19(2), 219228 (2004), Lee, Y., Nelder, J.A., Pawitan, Y.: Generalized Linear Models with Random Effects, 1st edn. Petersen Our approach, stemming from functional principal component analysis, calibrates the unobserved synchronized covariate values from the observed asynchronous and error-prone covariate values, and is broadly applicable to asynchronous longitudinal regression with time-invariant or time-varying coefficients. Please enable it to take advantage of the complete set of features! 2023 Jan 25;14:1051208. doi: 10.3389/fphys.2023.1051208. The three levels of this variable are no use (0 days used ATS in last 28 days), low use (0-12 days used ATS in last 28 days) and 'high' use (13-28 days used ATS in last 28 days). AI endobj However, I am happy to use Stata also. Did the Golden Gate Bridge 'flatten' under the weight of 300,000 people in 1987? We conducted a longitudinal survey to examine the temporal patterns of owner-pet relationship, stress, and loneliness during four phases of the pandemic: 1) pre-pandemic (February 2020), 2) lockdown (April to June 2020), 3) reopening (September to December 2020), and 4 . 12 0 obj Open Forum Infect Dis. Stat. If interest is only in a short-term treatment effect, it is sufficient to specify a MSM based only on the short-term effect, SCMMs can also be expressed in terms of counterfactuals; for example, model (, Both are marginal effects. KY Addresses the challenges that arise in analyzing longitudinal data, such as complex random-error structures, stochastic time-varying covariates, missing data, and attrition Presents contributions from some of the most prominent researchers in the field Includes an introductory chapter in each section to set the stage for subsequent chapters Methods such as inverse probability weighted estimation of marginal structural models have been developed to address this problem. . 2000;11(5):550560. Parabolic, suborbital and ballistic trajectories all follow elliptic paths. Am. Decomposition of time-dependent covariates into within and between components within each subject-specific model are discussed. endobj Wiley, Hoboken (2008), Neuhaus, J.M., Kalbfleisch, J.D. This is an area for further work. Biometrika 73, 1322 (1986), Liang, K.Y., Zeger, S.L., Qaqish, B.: Multivariate regression analyses for categorical data. The https:// ensures that you are connecting to the Our test, as described so far, assesses the presence of long-term direct effects when setting xt to 0; it will generally be a good idea to additionally assess whether there is evidence for long-term direct effects when setting xt to values other than zero. Careers. Econometrica 50, 569582 (1982), CrossRef However, HA-MSMs have not been much used in practice, and their validity remains in question (18). ILD offer unique opportunities to describe temporal behavioral changes in detail and identify related environmental and psychosocial antecedents and consequences. I am interested in looking at the relationship between cognition and taking ACE inhibitors in longitudinal data. : Between- and within-cluster covariate effects in the analysis of clustered data. Specific subject-specific models include random-intercept models and random-slopes models. 315324. Two MacBook Pro with same model number (A1286) but different year. J. Roy. Stat. Secondly, if follow-up was stopped at a time later than the last visit, then additional rows capturing the censoring time must be added to the dataset. 14 0 obj Epidemiology. We also present a new test of whether there are direct effects of past exposures on a subsequent outcome not mediated through intermediate exposures. We propose a multiscale adaptive generalized method of moments (MA-GMM) approach to estimate marginal regression models for imaging datasets that contain time-varying, spatially related responses and some time-varying covariates. UY and UX denote unobserved random effects affecting Yt and Xt respectively. eCollection 2023. Estimation of causal effects of time-varying exposures using longitudinal data is a common problem in epidemiology. 2014 Jun;19(2):175-87. doi: 10.1037/a0034035. R.H.K. 90(431), 845852 (1995), Fitzmaurice, G.M., Laird, N.M., Ware, J.H. Web Table 2 shows results for 10 study visits, when the efficiency of IPW estimation of MSMs compared with SCMMs is further reduced. TJ I am looking for some help with my analysis of longitudinal data with time-varying covariates. GEE bias can be avoided by using an independence working correlation matrix. Our method categorizes covariates into types to determine the valid moment conditions to combine during estimation. PMC Methods such as inverse probability weighted estimation of marginal structural models have been developed to address this problem. 15 0 obj Longitudinal Data Analysis. 11(1415), 18251839 (1992), Zeger, S.L., Liang, K.Y., Albert, P.S. The methods described in this paper are based on sequential conditional mean models (SCMMs) for the repeated outcome measures, fitted using generalized estimating equations (GEEs). : Hierarchical generalized linear models. b Bias in the estimated short-term causal effect of Xt on Yt averaged over 1,000 simulations. Google Scholar, Diggle, P.J., Heagerty, P., Liang, K.Y., Zeger, S.L. Associations between an exposure Xt and outcome Yt measured longitudinally, with random effects UX and UY (circles indicate that these are unobserved). We refer to the resulting estimation approach as sequential conditional mean models (SCMMs), which can be fitted using generalized estimating equations . xMK1N&n"E!`[jzBf23[89n!)% *DDX@A"itc+>|]F:U4K8)~t? Robins (21) proposed the direct effect g-null test, which is readily applicable to test for the presence of long-term direct effects. SCMMs and IPW estimation of MSMs can also be used to study short-term exposure effects in a survival analysis setting using Cox regression, using exposures and covariates measured at scheduled visits (20). This process is experimental and the keywords may be updated as the learning algorithm improves. Oxford University Press, Oxford (2002), Fitzmaurice, G.M. Stat. In addition to their simplicity and familiarity, SCMMs extend more easily to accommodate continuous exposures, drop-out, and missing data (see Web Appendix 5). Oxford University Press is a department of the University of Oxford. , Zeger S. Pepe The set of measures up to time t is indicated using a bar (e.g., Xt=(X1,,Xt1,Xt)). Ruth H Keogh, Rhian M Daniel, Tyler J VanderWeele, Stijn Vansteelandt, Analysis of Longitudinal Studies With Repeated Outcome Measures: Adjusting for Time-Dependent Confounding Using Conventional Methods, American Journal of Epidemiology, Volume 187, Issue 5, May 2018, Pages 10851092, https://doi.org/10.1093/aje/kwx311. Stata will estimate time-varying models, but Stata estimates models in which the time-varying regressors are assumed to be constant within intervals. The term "longitudinal data" refers to data that involve the collection of the same variables repeatedly over time. We refer to the resulting estimation approach as sequential conditional mean models (SCMMs), which can be fitted using generalized estimating equations. However, it is useful to understand whether earlier exposures directly affect a subsequent outcome other than via intermediate exposures. If anyone has any suggestions on how to model and analyse this type of data please let me know and thanks for your help. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. The .gov means its official. : Generalized Linear Models, 2nd edn. Often public health data contain variables of interest that change over the course of longitudinal data collection. Psychol. MathJax reference. endobj Model A: Predictors include birthyr and the time-invariant predictors earlymj and earlyod.. proc phreg data='c:aldafirstcocaine'; model cokeage*censor(1)= birthyr earlymj earlyod/ties = efron; run; <output omitted> Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 5525.059 . J. Roy. <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 10 0 R/Group<>/Tabs/S/StructParents 1>> We outline this approach and describe how including propensity score adjustment is advantageous. 8600 Rockville Pike Where can I find a clear diagram of the SPECK algorithm? There is a close connection between SCMMs and structural nested mean models (SNMMs) (26), in which a parametric model is specified for the causal effect of interest among people receiving a given level of treatment (e.g., g{E(Y(xt1,1)|Xt=xt,Lt)}g{E(Y(xt1,0)|Xt=xt,Lt)}). <> Simul. For example, to incorporate interactions between, Marginal structural models and causal inference in epidemiology, Methods for dealing with time-dependent confounding, Constructing inverse probability weights for continuous exposures: a comparison of methods, Effect of physical activity on functional performance and knee pain in patients with osteoarthritis: analysis with marginal structural models, Effects of physical activity and body composition on functional limitation in the elderly: application of the marginal structural model, Pillbox organizers are associated with improved adherence to HIV antiretroviral therapy and viral suppression: a marginal structural model analysis, Controlled direct and mediated effects: definition, identification and bounds, Longitudinal data analysis using generalized linear models, A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data, On regression adjustment for the propensity score, Constructing inverse probability weights for marginal structural models, On confounding, prediction and efficiency in the analysis of longitudinal and cross-sectional clustered data, History-adjusted marginal structural models for estimating time-varying effect modification, History-adjusted marginal structural models and statically-optimal dynamic treatment regimens, Invited commentary: effect modification by time-varying covariates, Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men, Bootstrap confidence intervals: when, which, what? These different types of effects are defined below. We recommend SCMM iv with an independence working correlation structure. E All of these effects may be viewed as causal. A conditional effect is sometimes of most realistic interest, in particular when the exposed and unexposed are very different in their covariate histories. B 54(1), 340 (1992), McCullagh, P., Nelder, J.A. For a binary outcome Yt, the SCMM (e.g., model (3)) can be replaced by a logistic model. Int. , Daniel RM. Med. In each simulated data set under scenario 1, we fitted SCMMs and MSMs using GEEs with independent and unstructured working correlation matrices. The propensity score model for Xt included Yt1 and Xt1. 5 0 obj We used simulation studies to compare SCMMs with IPW estimation of MSMs for the short-term effect of a binary exposure Xt on a continuous outcome Yt, and to assess the performance of the test for long-term direct effects. Wiley-Interscience, Hoboken (2006), Lai, T.L., Small, D.: Marginal regression analysis of longitudinal data with time-dependent covariates: a generalized method-of-moments approach. stream Why the obscure but specific description of Jane Doe II in the original complaint for Westenbroek v. Kappa Kappa Gamma Fraternity? Fitted linear regression lines demonstrate the directionality and the extent of the association between negative affect and smoking urges. In scenario 2, the mean estimate of Y was 0.012 (standard deviation, 1.102), and 5.2% of the 95% confidence intervals for Y excluded 0, demonstrating approximately correct type I errors. Careers. If interactions are present, MSMs are, however, still valid because they estimate marginal effects. SCMMs give better precision even than stabilized weights in realistic scenarios. : Generalized Estimating Equations. Tchetgen Tchetgen For full access to this pdf, sign in to an existing account, or purchase an annual subscription. We therefore propose using bootstrapping. outcomes, and time-varying covariates. I think i understand but it would be great to have your expertise. Bookshelf A practical guide for medical statisticians, Implementation of G-computation on a simulated data set: demonstration of a causal inference technique. . Why do men's bikes have high bars where you can hit your testicles while women's bikes have the bar much lower? , Brumback B, Robins JM. endobj Learn more about Stack Overflow the company, and our products. 10 0 obj With technological advances, intensive longitudinal data (ILD) are increasingly generated by studies of human behavior that repeatedly administer assessments over time. Construction of an anthropometric discriminant model for identification of elite swimmers: an adaptive lasso approach. <> %PDF-1.5 The most commonly used is marginal structural models (MSM) estimated using inverse probability of treatment weights . When the remaining long-term direct effects are of interest, estimation in linear SNMMs becomes more involved, but it is still feasible using standard software (27, 28). eCollection 2023. In SCMMs including the propensity score, interactions between the covariate and the propensity score should be included for every covariate-exposure interaction. : Applied Longitudinal Analysis, 2nd edn. Accessibility Trail JB, Collins LM, Rivera DE, Li R, Piper ME, Baker TB. ML Traditional analytical approaches impose strong parametric assumptions about the nature of change in the relationship between time-varying covariates and outcomes of interest. eCollection 2023 Jan. Ann Occup Environ Med. To illustrate the main points we considered four SCMMs: i) E(Yt|Xt,Yt1)=0+X1Xt; ii) E(Yt|Xt,Yt1)=0+X1Xt+YYt1; iii) E(Yt|Xt,Yt1)=0+X1Xt+X2Xt1; and iv) E(Yt|Xt,Yt1)=0+X1Xt+X2Xt1+YYt1. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. 6 0 obj Modeling options for time-dependent covariate data are presented in two general classes: subject-specific models and population-averaged models. B) With time-varying confounders. 2022 Dec 16;6(1):125. doi: 10.1186/s41687-022-00532-0. J. eCollection 2023 Mar. SCMMs easily handle continuous exposures Xt because they use standard regression. A major concern is that correct specification of the entire distribution is difficult, and slight misspecification of the tails could have a big impact on the weights. Innovative Statistical Methods for Public Health Data, https://doi.org/10.1007/978-3-319-18536-1_4, Tax calculation will be finalised during checkout. (2015). Examining Associations Between Negative Affect and Substance Use in Treatment-Seeking Samples: A Review of Studies Using Intensive Longitudinal Methods. , Wang Y, van der Laan MJ, et al. Results from additional simulation scenarios (see Web Figure 1) are given in Web Appendix 4 and Web Table 3. Unstabilized and stabilized weights were used and obtained using logistic regression models fitted across all 5 visits. , Deeks SG, Martin JN, et al. Cengage Learning, South Melbourne (2008), Zeger, S.L., Liang, K.Y. 8600 Rockville Pike Step 3. Weighted sum of two random variables ranked by first order stochastic dominance. (29) presented challenges arising in this setting in a causal context. Such total effects are useful for a doctor making a pragmatic decision about whether to start a patient on a treatment at a given time, accounting for the fact that the patient may subsequently naturally deviate from this treatment (or nontreatment) at a later visit. In our context, past exposure Xt1 can be considered a baseline variable and included in the numerator of the stabilized weights, provided the MSM also includes that variable (as in MSM (7)). MA 114. 14(3), 262280 (1996), Hardin, J.W., Hilbe, J.M. In survival analysis, timevarying covariates are covariates whose value can change during followup. Correspondence to Dr. Ruth H. Keogh, London School of Hygiene and Tropical Medicine, Department of Medical Statistics, Keppel Street, London WC1E 7HT, UK (e-mail: Search for other works by this author on: Division of Population Medicine, Cardiff University, Cardiff, United Kingdom, Department of Epidemiology, Harvard T.H. Econometrica 50(4), 10291054 (1982), Hansen, L.P.: Generalized Method of Moments Estimation, pp. S History-adjusted MSMs (HA-MSMs) have been described that accommodate interactions with time-dependent covariates; these assume a MSM at each time point and model the counterfactual outcome indexed by treatment that occurs after that time point, conditional on some subset of the observed history up to that time (16, 17). Unsynchronized longitudinal data refer to the timedependent response and covariate measurements for each individual measured at distinct time points. The site is secure. We set out the important considerations for securing results against bias due to model misspecification and compare the effects that can be estimated using SCMMs and IPW estimation of MSMs, as well as comparing the methods in simulation studies. Standard MSMs as described previously in this paper do not accommodate interactions between the exposure and time-dependent covariates because time-dependent confounders are handled in the weights rather than by adjustment. This site needs JavaScript to work properly. 2012 Jun;13(3):288-99. doi: 10.1007/s11121-011-0264-z. This will generally hold only approximately in an observational setting, and it is hoped that the most important confounders are measured. Several methods have been developed for estimating such effects by controlling for the time-dependent confounding that typically occurs. Goetgeluk IPW estimation of MSMs uses weighted regressions in which each individuals data at each time point receives a weight equal to the inverse of an estimated probability that that person had their observed exposures until that time, given their other covariates up to that time. The best answers are voted up and rise to the top, Not the answer you're looking for? Hypertension is the diagnosis of hypertension at each wave (timepoint) - once a person has been diagnosed they cannot go back to being non-hypertensive, the same is true for the variable diabetes. Several applications using IPW estimation of MSMs have in fact considered total, particularly short-term, effects (68) where simpler methods may have been suitable and more efficient. In the weight denominators, we used a logistic model for Xt with Xt1 and Yt1 as predictors. PeerJ. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. ML M The COVID-19 pandemic has affected us in numerous ways and may consequently impact our relationships with pet dogs and cats. Stabilized weights improve precision, but the empirical standard deviations remain larger than under SCMMs. A few points to consider: Thanks for contributing an answer to Cross Validated! Other methods for estimating joint effects include g-estimation and g-computation (see Daniel et al. We recommend adjustment for prior outcomes in the SCMM. Left column: sample size =50; right column: sample size =100. In the numerator of the stabilized weights, we used a logistic model for Xt with Xt1 as the predictor. -. Figure 1 depicts how variables may be related over time. It could be particularly informative to estimate the total effect of an exposure at a given time on outcomes at a series of future times. M : An overview of methods for the analysis of longitudinal data. An official website of the United States government. Google Scholar, Ziegler, A.: The different parametrizations of the gee1 and gee2. Example of repeated measurements That is, we provide a reminder that it is not always necessary to default to using IPW estimation of MSMs or g-methods when there are time-varying confounders. 33, 47564769 (2014), Lee, Y., Nelder, J.A. When there are time-varying confou . 26(3), 947957 (2014), Wooldridge, J.M. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. . : Longitudinal Data Analysis. 8 0 obj Data were simulated according to Figure 1A, using n=200 individuals observed at T=5 visits (simulation scenario 1). Dealing with time-varying covariates in mixed models but also in general is a challenging task. Soc. A) Without time-varying confounders. <> MP <> <>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> If the test provides no evidence for existence of long-term direct effects, this informs the investigator that joint exposure effects can be estimated without the need for complex methods. Bus. of time. I would differentiate between time-varying covariates, such as smoking, and intermediate events, such as hypertension in your example. . endobj When the time-varying covariate was forced to be mean balanced, GEE-Ind and GEE-Exch yielded almost identical results in all situations studied.