# Meta-Analysis

# IPD meta-analysis of observational studies

For observational studies several arguments that meta-analysis from published data are in general insufficient to calculate a pooled estimate are discussed in Blettner et al (1999): Traditional reviews, meta-analyses and pooled analyses in epidemiology.

Provided that individual patient data are available, we have proposed A new strategy for meta-analysis of continuous covariates in observational studies (S&R 2011).

We ...provide a summary estimate of the functional relationship between a continuous covariate and the outcome in a regression model, adjusting for confounding factors. Our procedure comprises three steps. First, we determine a confounder model. Ideally, the latter should include the same variables across studies, but this may be impossible. Next, we estimate the functional form for the continuous variable of interest in each study, adjusted for the confounder model. Finally, we combine the individual functions by weighted averaging to obtain a summary estimate of the function. Fractional polynomial methodology and pointwise weighted averaging of functions are the key components.

Reproduced from the Abstract of S&R (2011) with permission from John Wiley & Sons Ltd. |

# IPD meta analysis of treatment effect functions from randomized trials

Beside of obvious applications in epidemiology such as the assessment of continuous risk factors our meta-analysis strategy can also be used to investigate continuous variables for potential treatment heterogeneity in randomized trials.

If IPD data from several RCTs are available, we can estimate continuous treatment effect functions in each of the trials and use the meta-analysis approach to derive an averaged continuous treatment effect function (TEF) for a potential treatment modifier. We propose using the MFPI approach to derive a TEF separately in each study and combine these TEFs by using our meta-analysis approach. Obviously, other approaches (for example splines) may be used to derive a continuous effect function and other approaches to combine functions across several studies may be used.

For more details about our first project combining MFPI with the meta-analysis approach see Kasenda et al (2014) Investigation of continuous effect modifiers in a meta-analysis on higher versus lower PEEP in patients requiring mechanical ventilation – protocol of the ICEM study.

The medical paper presenting results is published (Kasenda et al (2016) Multivariable fractional polynomial interaction to investigate continuous effect modifiers in a meta-analysis on higher versus lower PEEP for patients with ARDS) and a methodological paper is in preparation.