A dose-response meta-analysis pools studies to estimate how risk changes across the whole range of an exposure, rather than collapsing each study into a single high-versus-low comparison. It uses the multiple exposure categories a study already reports, each with its own relative risk against a common reference, to fit a trend, linear or curved, that describes the shape of the relationship. Where an ordinary meta-analysis answers “does more exposure raise risk?”, a dose-response model answers “by how much, and at which doses does the curve bend?”.
When a curve beats a high-versus-low contrast
The high-versus-low comparison is the crude default: take the top exposure category, take the bottom, and pool the contrast across studies. It is easy but wasteful and often misleading. It discards every intermediate category, so it ignores most of the information in the data, and the definition of “high” and “low” differs between studies, so you are averaging contrasts that are not comparable. Worst of all, it cannot detect a non-linear shape, a threshold below which nothing happens, a plateau, or a J-shaped curve where both low and high exposure carry risk. A dose-response meta-analysis keeps every category and models the trend, so it recovers the shape that a single contrast flattens. You reach for it whenever the exposure is continuous and reported in ordered bands, and whenever the clinical question is about the form of the relationship rather than a yes or no.
One-stage and two-stage approaches
There are two ways to assemble the analysis. The classic two-stage approach fits a dose-response curve within each study first, producing one trend per study, then pools those trends with a random-effects multivariate meta-analysis. This mirrors how most meta-analyses work and keeps each study’s internal correlation structure intact. The one-stage approach, sometimes called “pool first”, fits a single model to all the category data at once, which can be more efficient when studies have few categories and is more flexible for complex curves, at the cost of stronger assumptions about how studies relate. For most reviews the two-stage route is the workhorse and the one described in the standard tutorials, with the one-stage model reserved for sparse data or when you want to model the curve and the between-study variance jointly.
Linear and restricted cubic spline models
The simplest model fits a single linear trend, one slope that says risk rises (or falls) by a fixed amount per unit of exposure. It is interpretable and a sensible starting point, but it forces a straight line onto data that may curve. To let the relationship bend, the standard tool is the restricted cubic spline, a smooth curve built from piecewise cubic polynomials joined at fixed points called knots, with the tails constrained to be linear so the curve does not fly off at the extremes. A common default places three knots at the tenth, fiftieth, and ninetieth percentiles of the pooled dose distribution, which captures most realistic shapes with only two spline coefficients to estimate. You then test the spline terms for departure from linearity: if they are jointly significant, the relationship is genuinely non-linear and the curve, not the slope, is your headline result.
The Greenland and Longnecker method
The engine under most dose-response models is the Greenland and Longnecker method, published in 1992, which solved a subtle problem: the category-specific relative risks within one study are not independent, because they all share the same reference group. Ignore that correlation and your standard errors are wrong. Greenland and Longnecker showed how to reconstruct the covariance between the log relative risks from the numbers of cases and person-time in each category, so the within-study trend can be fitted by generalised least squares that respects the shared reference. This reconstruction is the reason a dose-response meta-analysis needs more than the relative risks alone; it needs the counts behind them. The method is the default in the standard software and is what makes the two-stage approach statistically honest.
A worked example of a curve
Suppose you are pooling cohort studies of coffee intake and a health outcome, each reporting relative risks for several intake bands against a non-drinking reference. A high-versus-low contrast would compare the heaviest drinkers with abstainers and report a single number, say a relative risk of 0.85. A dose-response meta-analysis instead fits the whole curve and reveals something the contrast hides: risk falls steadily up to around three cups a day, reaching a relative risk near 0.80, then flattens and begins to rise, so the benefit does not keep growing with dose. That non-linear shape, a U or J, is a genuine clinical finding with implications for guidance, and it is invisible to the two-category comparison. Reporting it means presenting the fitted curve with its confidence band, quoting the relative risk at a few reference doses, and stating the p-value for the test of non-linearity so the reader knows the bend is real rather than noise. This is the added value that justifies the extra modelling effort over a simple pooled effect size.
Fixed and random effects in the pooling stage
The two-stage dose-response model still has to combine the study-specific trends, and the same fixed-effect versus random-effects decision applies as in any meta-analysis, with a multivariate twist. Because each study contributes a trend described by more than one coefficient (an intercept-free slope for a linear model, or two spline coefficients for a cubic spline), the pooling is a multivariate random-effects meta-analysis that respects the correlation between those coefficients. A random-effects model is almost always the honest default, since dose-response relationships genuinely vary between populations and settings, and the between-study covariance matrix it estimates is what lets you draw a pooled curve with a valid confidence band. Ignoring that structure, or forcing a fixed-effect model onto clearly heterogeneous studies, produces confidence bands that are far too narrow and a curve that looks more certain than the evidence allows. A meta-regression on study-level characteristics can then probe whether the curve differs by, say, study region or follow-up length.
Extracting the data and the dosresmeta package
For each exposure category you must extract four things: the assigned dose (a single value representing the band, usually its midpoint or median), the relative risk and its confidence interval, and the number of cases and the total or person-years in that category. The counts are what let the Greenland and Longnecker reconstruction run, and reviews that record only the relative risks find they cannot fit the model. In R the dosresmeta package by Crippa and Orsini is purpose-built for this. You supply the dose, effect, variance, cases, and totals, choose a linear model or a restricted cubic spline through the rms package’s rcs() helper, and it returns the pooled trend and a test for non-linearity. Stata users reach for the drmeta or the older glst command. Plot the fitted curve against dose with a confidence band, and check the pooled inputs in our meta-analysis calculator as a sanity step.
Assigning a representative dose to each category
Every category in a study reports a range, not a point, so you must assign a single representative dose before modelling. For a closed band such as “10 to 20 units” the usual choice is the midpoint, or the median if the study reports the distribution within the band, which is preferable because exposure is often skewed. The hard cases are the open-ended categories at each end. For the top category (“more than 30 units”) a common convention assigns a value 1.2 times the lower bound, or better, uses the mean of that category if it is reported. For the bottom reference category, which is frequently “none” or “lowest”, you assign the midpoint of its range. These are judgement calls, and because the fitted curve can shift with them, a careful review runs a robustness check that repeats the model under alternative dose assignments and reports whether the shape of the relationship holds. Documenting exactly how each dose was assigned is part of a reproducible method, not an optional footnote.
Interpreting the pooled slope and the curve
For a linear model the headline output is a single slope, conventionally expressed as the change in relative risk per unit increment of exposure, for example a relative risk of 1.08 per additional daily serving. That figure is easy to communicate but assumes the effect per unit is constant across the whole range, which is precisely the assumption a restricted cubic spline relaxes. When the spline model wins the test for non-linearity, you should stop quoting a single slope and instead describe the curve in words tied to the plot: where risk rises fastest, where it plateaus, and whether there is a threshold below which no association is seen. Reporting a lone linear slope for a relationship that is genuinely curved is one of the most common ways a dose-response meta-analysis misrepresents its own data, so let the test for non-linearity, not convenience, decide which summary you present.
Heterogeneity and how to explore it
Like any synthesis, a dose-response model can show substantial between-study heterogeneity, and here it means the studies disagree about the shape or steepness of the curve, not just its height. The multivariate random-effects framework quantifies this with a between-study covariance matrix, and you can visualise it by overlaying the individual study trends on the pooled curve to see which studies pull it and where. When heterogeneity is high, the pooled curve is an average of genuinely different relationships and should be reported with a prediction band as well as a confidence band. A meta-regression on study characteristics can test whether the curve differs by exposure assessment method, outcome definition, or adjustment for confounders, turning unexplained heterogeneity into a structured secondary analysis. Software such as those compared in our guide to meta-analysis software handles the multivariate machinery, but the interpretation remains yours.
Reporting the curve and common data problems
Report the fitted curve with its confidence band, the dose at meaningful reference points (for example the relative risk at a doubling of exposure), the test for non-linearity, and the between-study heterogeneity. The recurring data problems are worth naming because they sink more analyses than the modelling does. Studies sometimes report an open-ended top category (“more than 20 units”) with no clear midpoint, which forces a judgement call about the assigned dose. Different studies use different reference categories, so you must be sure the contrasts share a consistent baseline before pooling. And the person-years or case counts needed for the covariance are often missing, incomplete, or reported only as totals, in which case approximations exist but should be flagged as a limitation. Because these decisions shape the curve, pre-specify them in your PRISMA 2020 reporting and test them in a sensitivity analysis, then carry the certainty judgement into the GRADE assessment. Done well, a dose-response curve is far more informative than the single effect size a high-versus-low contrast would have produced.