Advances in control risk regression

Meta-analysis is a long-established and widespread tool to summarize, aggregate and combine results from independent studies about the same issue of interest. As independent studies included in a meta-analysis differ in many ways, properly accounting for between-study heterogeneity is a relevant goal. The traditional meta-analysis model has a random-effect formulation, where between-study heterogeneity is accounted for through a variance component. When available, study-specific covariates can be inserted in the model, in order to better explain heterogeneity due to, for example, differences in studies’ design and characteristics of participants. The resulting model is a meta-regression model, where additional covariates represent information summarized at the study level, and thus can be affected by aggregation error. This thesis focuses on control risk regression, which is an example of meta-regression used in medical investigations to evaluate the effectiveness of a treatment in clinical trials comparing a treatment group and a control group. Control risk regression is characterized by the inclusion of a summarized measure of risk for the subjects in the control condition (control rate) as a covariate in the meta-regression model. Such a covariate represents a proxy for the underlying risk, that is, the measure of risk at the population level useful to describe unmeasurable sources of heterogeneity associated to a disease, as, for example, the severity of illness. Control rate is thus affected by measurement error. An appropriate analysis should correct for the presence of errors in order to provide reliable inference. The thesis focuses on two extensions of the classical control risk regression model. First, the model is extended to include additional study-specific covariates other than the control rate, as a way to provide a more accurate explanation of the heterogeneity. Likelihood-based inference is carried out by including measurement error corrections to prevent biases due to error in the control rate and errors in the additional covariates. Attention is paid to an approximate normal specification of the measurement error structure as well as to an exact, and more computationally involved, specification. The lack of information about within-study covariances between risk measures and the covariate components is overcome by deriving explicit expressions using Taylor expansion based on study-level covariate subgroup summary information. As an alternative, a more efficient solution based on a pseudo-likelihood solution is developed, under a working independence assumption between the observed error-prone measures. The methods are evaluated in a series of simulation studies under different specification for the sample size, the between-study heterogeneity, as well as the underlying risk distribution. The methods are applied to real meta-analyses about the association between COVID-19 and schizophrenia, and the association between COVID-19 and myocardial injury. A second extension of the classical control risk regression model intends to modify the linear relationship between the true treatment risk and the true control risk, which is motivated by convenience, although it is not always reasonable. The proposal is a U-shaped relationship between the risk measures, in this way allowing to describe treatments which have a positive effect and a negative effect. The price to pay is in terms of computational issues, since the likelihood function loses a closed-form expression, even under an approximate normal measurement error specification. The method is evaluated in a series of simulation studies, involving scenarios of different sample sizes and between-study heterogeneity, absence or presence of linear/quadratic relationships between the risk measures.