Background: Immune checkpoint inhibitors (ICIs) have reshaped the treatment landscape of metastatic melanoma. While combination regimens often demonstrate improved response and survival compared to monotherapy, they are also associated with a higher incidence of immune-related adverse events (irAEs). Understanding the balance between benefit and risk is essential for making informed treatment decisions, especially given the variability in reported outcomes across clinical trials. Methods: We conducted a systematic review and meta-analysis of 14 clinical trials (comprising 22 treatment arms and >5000 patients) comparing ICI monotherapy (nivolumab, ipilimumab, or pembrolizumab) and combination therapy (nivolumab + ipilimumab) in advanced melanoma. Treatment-related outcomes were synthesized using fixed-effects, random-effects, or generalized linear mixed models (GLMMs), depending on study variability. Survival data were extracted from published Kaplan–Meier curves and analyzed using longitudinal GLMMs to capture trends over time. Results: Compared to monotherapy, combination immunotherapy achieved higher clinical benefit, with an overall response of 52.2% (vs. 31.6%), a five-year overall survival of 55.7% (vs. 34.3%), and a five-year progression-free survival of 39.0% (vs. 17.2%). However, this benefit came with a higher risk of toxicity: immune-related adverse events occurred in 93.2% of patients receiving combination therapy versus in 81.9% receiving monotherapy. Differences were consistent across all individual severe toxicities. Conclusions: Combination immunotherapy offers greater long-term clinical benefit than monotherapy in metastatic melanoma but at the cost of increased toxicity. By applying models adapted to study variability, we provide more reliable estimates of treatment efficacy and risk. GLMMs provide the most robust estimates and enable the modeling of survival dynamics over time. These findings support evidence-based decision-making and highlight the value of model-informed meta-analysis in oncology.

The problem of determining the conditions under which a random rectangular matrix is of full rank is a fundamental question in random matrix theory, with significant implications for coding theory, cryptography, and combinatorics. In this paper, we study the probability of full rank for a $K\times N$ random matrix over the finite field ${\mathbb{F}}_q$, where q is a prime power, under the assumption that the rows of the matrix are sampled independently from a probability distribution $\mathcal{P}$ over ${\mathbb{F}}_q^N$. We demonstrate that the probability of full rank attains a local maximum when the distribution $\mathcal{P}$ is uniform over ${\mathbb{F}}_q^N\setminus \left\{0\right\}$, for any $K⩽N$ and prime power q. Moreover, we establish that this local maximum is also a global maximum in the special case where $K=2$. These results highlight the optimality of the uniform distribution in maximizing full rank and represent a significant step toward solving the broader problem of maximizing the probability of full rank for random matrices over finite fields.

Meta-analytic methods are essential for quantitative evidence synthesis, offering a statistical framework for model comparison and heterogeneity assessment. This paper revisits our previous work through a concise methodological review and model-comparison metaanalysis, illustrating adaptive model selection for binary outcomes. Thirteen studies (>6,000 patients) comparing monotherapy and combination regimens in metastatic melanoma immunotherapy were analyzed. Binary outcomes (benefit and risk rates) were pooled using fixed-effects (FEM), random-effects (REM), and generalized linear mixed models (GLMM), depending on heterogeneity. The results highlight how model choice influences pooled estimates and inference reliability, underscoring the importance of flexible statistical modeling in complex datasets.