Multilevel network meta-regression for general likelihoods: synthesis of individual and aggregate data with applications to survival analysis

Making decisions about which medical treatments work best for a specific group of people is a complex puzzle. Doctors and health officials need to know how a new drug compares to existing options, but they rarely have a single study that tests every possible treatment against every other one. Instead, they must piece together evidence from many different trials, each comparing only a few treatments. To make sense of this patchwork, researchers use a technique called network meta-analysis, which connects these separate studies to estimate how treatments compare indirectly. However, this method relies on a critical assumption: that the people in all these different trials are similar enough that the results can be mixed together fairly. If the trials involve patients with different ages, disease severities, or other health characteristics, simply mixing the data can lead to misleading conclusions. The most reliable way to fix this is to have access to the detailed records of every single patient in every study, allowing researchers to adjust for these differences directly. But in the real world, detailed patient records are often missing; researchers usually only have summary statistics from many studies. This leaves a gap between the ideal way to analyze data and the reality of what is available.

A team of researchers has developed a new method to bridge this gap, allowing them to combine detailed patient records from some studies with summary data from others without losing accuracy. Their approach, an extension of a technique called multilevel network meta-regression, solves a long-standing problem that prevented these sophisticated adjustments from being used with time-to-event data, such as how long patients survive or remain free from disease. Previously, this method required the mathematical formulas for summary data to be simple and known in advance, which is rarely the case for survival data. The researchers found a way to bypass this requirement entirely. Instead of trying to force the summary data into a pre-existing mathematical box, they built a system that takes the detailed model of how individual patients respond to treatment and mathematically "averages" it over the known characteristics of the patients in the summary studies. This allows the model to learn from the detailed records while still making use of the broader, less detailed evidence, effectively creating a unified picture of treatment effectiveness that respects the differences between patient populations.

To test whether this new approach works, the researchers created a simulated scenario where they knew the true answers in advance. They generated fake data for a network of studies comparing three treatments, giving themselves full access to individual patient details for some studies but only summary information for others. When they applied their new method, the results matched the known true values almost perfectly, performing just as well as if they had been able to use the detailed records for every single study. The method successfully recovered the true differences between treatments, even when the summary studies had different patient characteristics than the detailed ones. Crucially, the precision of the estimates remained high, showing that the method did not lose valuable information by relying on the summary data. This simulation proved that the technique could handle the complex mathematics of survival data without needing the restrictive formulas that had previously blocked its use.

The researchers then applied their method to a real-world medical question: comparing maintenance treatments for newly diagnosed multiple myeloma, a type of blood cancer. They analyzed a network of five studies, three of which provided detailed patient records and two of which only offered summary data derived from published survival curves. In this analysis, they modeled the risk of disease progression over time using a flexible mathematical shape that could adapt to the data rather than forcing it into a rigid, pre-defined pattern. They adjusted for four key patient characteristics known to influence outcomes: age, disease stage, response to prior treatment, and sex. The results showed that two active drugs were consistently more effective than a placebo, but the size of the benefit varied depending on the specific patient population being considered. The method successfully produced estimates for a target population that matched the mix of patients in the summary studies, something that older methods could not do without making strong, untestable assumptions.

One of the most significant findings was that the new method could produce two different types of answers depending on what a decision-maker needed. It could calculate the average effect of a treatment for a patient with specific characteristics, or it could calculate the average effect for an entire population, regardless of individual differences. This distinction is vital because the two numbers are not the same and answer different questions. While older methods could only provide one type of answer or required complex workarounds that introduced bias, this new approach handles both naturally. The researchers also demonstrated that their method could detect when the assumption that treatment effects remain constant over time was violated, a common issue in survival analysis, and adjust for it by allowing the underlying risk to change shape over time. By using a flexible mathematical tool that could smooth out the data without overfitting, they ensured the model remained robust even when the data was complex.

The work confirms that it is possible to synthesize individual and aggregate data in a way that is both statistically rigorous and practically useful for survival outcomes. The method does not require the summary data to fit a specific mathematical form, removing a major barrier that had limited the application of population adjustment techniques. By integrating the individual-level model over the distribution of patient characteristics in the summary studies, the researchers created a framework that is general enough to handle almost any type of likelihood. This means the approach can be applied to a wide range of medical questions beyond just survival, including binary outcomes and other complex data types. The researchers have made the code for this method available in a software package, allowing other scientists to apply these techniques to their own networks of studies. The result is a more reliable way to compare treatments across diverse populations, ensuring that healthcare decisions are based on evidence that truly reflects the people who will receive the care.