![]() Random-effects Parameters | Estimate Std. ![]() The following code simulates the data in R: expit chi2 = 0.0000 At each subsequent follow-up visit, dropout will be simulated among those still in the study dependent on the change in the outcome between the preceding visit and the visit before that. Specifically, we will simulate that some patients dropout before visit 1, dependent on their baseline covariate value. We will introduce some (monotone) dropout, leading to missing data, which will satisfy the missing at random assumption. To illustrate fitting the MMRM in the three packages, we will simulate a dataset with a continuous baseline covariate and three follow-up visits. First, we’ll simulate a dataset in R which we will then analyse in each package. In this post I’m going to review how to fit the MMRM model to clinical data in all three packages, which may be of use to those who similarly switch between these software packages and need to fit such models. I thus first learnt how to fit such models in Stata and SAS, and only later in R. My personal journey with statistical software started with Stata and SAS, with a little R. For a more in depth discussion of the model, see for example Molenberghs et al 2004 (open access). One can adjust for these as simple main effects, or additionally with an interaction with time, in order to allow for the association between the baseline variable(s) and outcome to potential vary over time. Often there are baseline covariates to be adjusted for. This implies a saturated model for the mean, or put another way, there is a separate mean parameter for each time point in each treatment group. ![]() This imposes no restriction on the form of the correlation matrix of the repeated measures.įor the so called ‘fixed effects’, one typically specifies effects of time (as a categorical or factor variable), randomised treatment group, and their interaction. In particular, to reduce the chances of model misspecification, commonly the residual errors are assumed to be from a multivariate normal distribution with a so called unstructured covariance matrix. Typically this model specifies no patient level random effects, but instead models the correlation within the repeated measures over time by specifying that the residual errors are correlated. Particularly within the pharmaceutical trials world, the term MMRM (mixed model repeated measures) is often used. Because of this a mixed model analysis has in many cases become the default method of analysis in clinical trials with a repeatedly measured outcome. In the context of randomised trials which repeatedly measure patients over time, linear mixed models are a popular approach of analysis, not least because they handle missing data in the outcome ‘automatically’, under the missing at random assumption. They extend standard linear regression models through the introduction of random effects and/or correlated residual errors. The rest of the guide presumes that the data is in long form.Linear mixed models are a popular modelling approach for longitudinal or repeated measures data. To change format from wide to long, or from long to wide, use the command reshape. Here we instead have few columns, but a lot of rows, but rows are easier to work with in Stata. The table above would look like this in long form: country But we also need a variable that shows which year the row represents. In long data each row represents one country one year, and each column represents one variable. In general it is more convenient to have the data in long form. But it is harder to do more advanced analyses, with many different variables (population, GDP, unemployment, and so on) we will need a lot of columns. It might seem intuitive at first glance, and it makes it easy to compare certain years to each other. For instance the population size of a country, a certain year. With wide data each row in the dataset stands for one country, and each column a variable at one point in time. To take an example, let's say we have data on countries, over time. ![]() Panel data can be structured in two ways: "long" or "wide". ![]()
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