Longitudinal meta-analysis

What longitudinal meta-analysis is

A standard meta-analysis takes one effect size per study and pools them. That works when each study gives one comparable number. Longitudinal evidence is different. A trial of an exercise program may report pain at six weeks, six months and two years. A cohort study of a diet may report weight at one, three and five years. Each study then contributes several estimates, and the estimates describe the same participants at different times.

Longitudinal meta-analysis is the set of methods for this situation. It can answer three kinds of question. What is the effect at a given time? How does the effect change as follow-up lengthens? And is the pattern over time the same across subgroups, doses or settings? The first question can be handled with ordinary methods if the time point is defined well. The second and third need approaches that respect the structure of the data.

The term is used loosely. Some authors mean meta-analysis of longitudinal studies, others mean pooling of growth curves or trajectories, and others mean any review that handles repeated outcomes. This page uses it in the first, practical sense: combining study results that were measured at multiple times.

Why time matters for the conclusion

An effect can be large early and fade. It can appear only after months. It can be positive in the short term and neutral or harmful later. A pooled estimate that mixes follow-up times hides these patterns, and a conclusion based on a single arbitrary window can mislead. Decision makers usually care about a specific horizon, such as one year, so the review should report that horizon directly.

Time also interacts with study quality. Long follow-up is where attrition accumulates, where participants cross over to other treatments and where blinding often fails. A review that reports only the longest follow-up may rely on a small, selected subset of the original participants. Reporting how many studies and participants contribute at each time is as important as the estimate itself.

Strategies for handling several time points

No single strategy is best. The choice depends on how many studies report each time, how consistent the time points are and what the question requires. The table summarizes the usual options.

The simplest defensible approach is to define windows in the protocol, to pick one estimate per study per window using a stated rule (the one closest to the window midpoint, for example), and to run a separate random-effects meta-analysis for each window. The rule matters. Choosing the most favorable time point from each study after looking at the data introduces bias, and the review should say how the rule was set.

Correlated estimates and why they matter

If a study contributes the three-month and the twelve-month result to the same meta-analysis as if they were independent, the study is counted twice and the pooled interval is too narrow. This is a unit-of-analysis error. The estimates from one study are correlated because they come from the same people, and the correlation is usually positive and sizeable.

There are three ways to avoid the error. The first is to include only one time point per study in any single analysis. The second is a multivariate model that estimates the effects at several times together and uses the correlations between them. The third is robust variance estimation, which gives valid standard errors for clustered estimates without needing the exact correlations. The multivariate model is more efficient when the correlations are known; robust variance estimation is more forgiving when they are not.

The difficulty is that primary studies rarely report the correlation between time points. Reviewers then assume a value, test several values in a sensitivity analysis and report how much the result depends on the assumption. If individual participant data are available, the correlations can be estimated directly, which is one reason that individual participant data meta-analysis is often attractive for longitudinal questions.

Modeling the effect as a function of time

When the question is how the effect changes over time, meta-regression on follow-up time is a natural tool. The model includes time as a moderator, with a linear term or a more flexible form such as a spline. Because each study may contribute several points, the model must account for clustering, through a random effect for study, through robust variance estimation or through a multivariate model.

The usual cautions for meta-regression apply. With few studies the model has little power and can overfit. Time is observed at the study level, so a trend across studies can differ from the trend within studies, which is the ecological problem. A trend that appears because short follow-up studies enrolled different populations from long follow-up studies is not a change in the effect over time. Where possible, the analysis should use within-study differences, comparing the early and late estimates from the same study.

For survival-type outcomes the time dimension is built into the data. Pooled hazard ratios, and in some cases restricted mean survival time differences, summarize the whole follow-up. When the hazard ratio is not constant, a single pooled number can be misleading, and the review should check the assumption and report alternatives.

Attrition, missing time points and bias

Longitudinal data are rarely complete. Participants drop out, and studies stop at different times. Two problems follow. First, the studies that report a late time point are not a random subset: they may be the larger, better funded or more successful studies. A change in the pooled effect from early to late may reflect which studies contribute, not a real change over time. Reporting the same analysis restricted to studies that report both times helps separate the two.

Second, the way a study handled missing data affects what its estimate means. A complete-case analysis, last observation carried forward and a model-based approach under a missing-at-random assumption answer slightly different questions and can give different numbers. Risk-of-bias tools, such as RoB 2 for randomized trials, include a domain on missing outcome data, and the review should apply it separately to each time point when attrition differs.

Selective reporting of time points is a related risk. A trial registered with outcomes at three and twelve months that publishes only the twelve-month result raises concern. Comparing registry entries and protocols with publications is the standard check.

A worked reading of results over time

Suppose a review of a behavioral program reports separate pooled standardized mean differences for three windows. The values are stated here only to show how the reading works; they are not data from a real review. In the first window of up to three months, twenty-two studies contribute and the estimate is moderate. In the second window of three to twelve months, fourteen studies contribute and the estimate is smaller. In the third window beyond twelve months, five studies contribute and the interval is wide and includes zero.

A careful reading does not conclude that the effect has vanished. It notes that the number of studies fell from twenty-two to five, that the late studies may differ in design, and that a wide interval is compatible with both a sustained and a lost effect. It checks whether the same pattern appears in the studies that report all three windows. It then reports the heterogeneity in each window and states the certainty of the evidence for each, which is usually lower for the late window because of imprecision and attrition.

Planning and reporting

The protocol should define the outcome, the time windows or the modeling approach, the rule for choosing among several time points in one study, the handling of correlation and the sensitivity analyses. These choices should be registered before data extraction. During extraction, record every reported time point, not only the one you plan to use, so that the rules can be checked and changed openly if needed.

The report should show how many studies and participants contribute at each time, include a figure that makes the pattern visible (a forest plot for each window, or a plot of the estimate against time), and describe the assumptions about correlation. PRISMA 2020 is the reporting standard for the review as a whole, and the multivariate and robust variance methods should be described in enough detail to be reproduced.

Software support is good. In R, the metafor package fits multivariate and multilevel models and robust variance estimation is available in the robumeta and clubSandwich packages. Stata and Bayesian software can fit similar models. The choice of software matters less than a clear description of the model.

Limitations

Longitudinal meta-analysis depends on what the primary studies report. Many report only a few time points, with differing definitions, and few report correlations. Assumptions about correlation can affect results, and a trend across studies is not always a trend within studies. Late time points often rest on few, selected studies. Multivariate and robust variance methods are more complex than standard pooling and need careful description to be reproduced. Results should be presented with their uncertainty, and the evidence for late windows is usually less certain than for early ones.

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