The phenomenon of digital obituaries and posthumous identities is increasingly shaping the way contemporary society perceives death, remembrance, and the grieving process. Death no longer signifies the complete end of social presence, as digital profiles of the deceased remain active on social media platforms even after physical death, enabling a continuity of symbolic connection with them. This paper explores the emotional, psychological, social, ethical, and legal dimensions of digital memorialization, focusing on the impact of virtual spaces and algorithmic reminders on the grieving process and emotional resolution. A qualitative approach was employed in analyzing secondary sources, grounded in contemporary theories of identity, grief, and digital legacy. The paradoxes of digital mourning are analyzed, wherein memorial profiles and digital obituaries may offer a sense of presence and support, yet simultaneously prolong emotional attachment and hinder acceptance of loss. The paper also examines how the algorithmic functioning of digital platforms generates memories and reminders without sensitivity to the emotional state of users, potentially burdening the grieving process further. It raises critical ethical and legal questions surrounding the management of digital identities after death, including unclear ownership, control, and rights to content removal. The complexity of survivors’ emotional responses and the growing significance of digital legacy further reinforce the need for clear regulations aligned with the psychological dimensions of grief and ethical principles of dignity. In this context, digital memorialization emerges not only as a form of remembrance, but also as a challenge requiring thoughtful consideration within the frameworks of mental health, social practice, and legal accountability.

Intra-tumor heterogeneity (ITH) of somatic mutations is a hallmark of sporadic clear cell renal cell carcinoma (ccRCC). In contrast, the extent and nature of ITH in hereditary (VHL-associated) ccRCC remain poorly characterised, primarily due to the rarity of these tumors. This study aims to comprehensively characterise this heterogeneity and elucidate its evolutionary dynamics and biological relevance. To investigate intra- and inter-tumor heterogeneity in VHL-associated ccRCC, we performed multi-region whole-genome sequencing (WGS) of 23 primary tumor biopsies obtained from four spatially distinct regions of six small (≤3 cm) renal tumors across two patients carrying pathogenic germline VHL mutations. Somatic single-nucleotide variants (SNVs) and copy number alterations (CNAs) were analysed to reconstruct the genomic histories of these tumors. We found that all tumors were clonally independent, each harboring distinct sets of somatic variants and chromosomal copy number alterations, including the characteristic chromosome 3p loss. Within individual tumors, copy number profiles were homogeneous across regions, suggesting early acquisition of these events. Subclonal diversification of somatic SNVs was detected in all tumors. Notably, in one patient, two of the three analysed tumors displayed pronounced ITH, with most mutations being unique to a single region. Moreover, markedly distinct patient-specific molecular profiles emerged, characterised by divergent driver events and copy number landscapes that correlated with differences in their clinical grades. Although preliminary, these findings provide new insights into the genomic heterogeneity of VHL-associated ccRCC, advancing our understanding of how inherited kidney cancers develop and diversify, and potentially informing improved clinical management of patients with VHL disease. Francesca Corea, Husayn A. Pallikonda, Scott T. Shepherd, Isaline Rowe, Alessandro Larcher, Andrea Salonia, Samra Turajlic, Thomas J. Mitchell, Rosa Bernardi, Umberto Capitanio. Genomic evolution and heterogeneity of von Hippel-Lindau (VHL)-associated clear cell renal cell carcinoma revealed by multi-region whole-genome sequencing [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2026; Part 1 (Regular Abstracts); 2026 Apr 17-22; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2026;86(7 Suppl):Abstract nr 7507.

Clear Cell Renal Cell Carcinoma (ccRCC) is the most common and aggressive type of kidney cancer. ccRCC originates from proximal tubule (PT) epithelial cells in the nephron. Its initiation is characterised by a linear evolution from the loss of one copy of chromosome 3p to the inactivation of the second VHL allele on the remaining copy of 3p. Computational studies established that 3p loss occurs several decades before diagnosis. This offers an unprecedented window of opportunity for early detection, cancer prevention and for broader pan-cancer learning. However, the biological mechanisms driving the pre-cancerous expansion of PT cells harboring these events remain elusive. One of the major unmet needs in ccRCC initiation is the identification of molecular biomarkers for the initially quiescent tumor-initiating cell. Previous studies established that the putative ccRCC cell of origin (COO) is a subtype of PT cells characterized by VCAM1 expression, a marker of tubular injury in human kidneys. Therefore, we hypothesized that VCAM1 can be used as a marker to enrich for cells that have lost a copy of chromosome 3p. Preliminary single-cell whole genome sequencing (WGS) of VCAM1+ PT cells revealed a high incidence of aneuploidies, including chromosome 3-related aneuploidies, indicating that these cells represent a chromosomally unstable epithelial subpopulation within morphologically normal kidney tissue. Therefore, this data supports VCAM1 as a candidate marker for the study of ccRCC initiation in human kidneys.Despite its quasi-ubiquitous role in ccRCC initiation, several studies show that VHL inactivation is insufficient for tumorigenesis in mammalian kidneys. To study this, we used histological analysis of VHL patient-derived normal kidney tissues, where 3p loss occurs on the background of a germline VHL mutation. We demonstrated that VHL inactivation (marked by CAIX expression) occurs in all major cortical epithelial cell types. Surprisingly, only the proportion of CAIX+ distal tubule (DT) cells showed a significant correlation with the age of the patient at the time of tissue collection. In addition, there is a significantly higher proportion of multicellular DT CAIX+ foci compared to CAIX+ PT foci, suggesting clonal expansion after VHL inactivation is favored in DT cells. Only a minority of CAIX+ PT foci were multicellular, indicating that unknown cell-intrinsic or extrinsic factors are necessary for clonal expansion. Results from our cohort show a positive association between the density of VCAM1+ PT cells and CAIX+ PT in VHL patient-derived normal kidney tissues, indicating that tissue stress levels may potentiate the selection and expansion of VHL inactivation in the human kidney. Our data offers novel insight in the putative COO of ccRCC and the mechanisms driving the earliest stages of ccRCC. Moving forward, we plan to expand our cohort and molecularly profile VCAM1+ and CAIX+ cells using multi-omic approaches. Omar Bouricha, Daqi Deng, Anne-Laure Cattin, Matous Elphick, Scott Shepherd, Cathy D. Vocke, W. Marston Linehan, Samra Turajlic. Spatial and molecular profiling of tumor initiation in ccRCC [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2026; Part 1 (Regular Abstracts); 2026 Apr 17-22; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2026;86(7 Suppl):Abstract nr 3330.

Neoantigens from somatic tumor mutations are essential for effective anti-tumor immune responses. Frameshift insertions and deletions (fs-indels) represent a rare but highly immunogenic mutation subtype, as they create novel open reading frames (neoORFs) that generate peptides that are significantly distinct from self-antigens. Nevertheless, fs-indels often introduce premature termination codons, leading to transcript degradation via the nonsense-mediated mRNA decay (NMD) pathway, leading to loss of immunogenic neoantigen. For the first time, we pharmacologically inhibited SMG1, a core component of the NMD pathway, across a range of preclinical models, including human and mouse cancer cell lines, patient-derived tumor organoids (PDTOs), patient-derived tumor fragments (PDTFs), and syngeneic mouse xenografts. We analyzed the changes in transcriptome, proteome, and immunopeptidome following SMG1 inhibition (SMG1i) and peptide reactivity in in vitro priming experiments. We then combined tumor-T cell co-cultures and PDTFs to assess the anti-tumor immunogenicity induced by SMG1i. Ex vivo and in vivo immunological responses were assessed by high-dimensional flow cytometry, cytometric bead array, and single-cell RNA- and TCR-sequencing. Using multi-omic and checkpoint inhibitor (CPI) response data from over 1,000 patients, we show that decreased expression of the key NMD mediator, SMG1, correlates with improved CPI response. Inhibiting SMG1 ex vivo and in vivo activates and expands tumor-reactive T cells and sensitizes CPI efficacy. Mechanistically, SMG1 inhibition stabilizes frameshift-derived transcripts, increasing the abundance and surface presentation of immunogenic neoantigens. This results in an increase in neoepitope burden in tumors, similar to that seen in tumors with high tumor mutational burden (TMB), without inducing DNA damage. Co-culturing tumor cells and PDTOs with CD8+ T cells after SMG1i results in strong MHC class I antigen-dependent T cell activation and tumor cell killing. Our findings highlight SMG1 inhibition as a promising strategy to exploit an untapped source of highly immunogenic peptides. It enhances anti-tumor immunogenicity without introducing DNA mutations, regardless of tumor type or TMB status, providing translational evidence for sensitizing ICB responses. Hongchang Fu, Roberto Vendramin, Shanila Fernandez Patel, Yue Zhao, Danwen Qian, Lorena Ligammari, Osnat Bartok, Polina Greenberg, Ronen Levy, Andrea Castro, Krupa Thakkar, Jun Murai, Wei-ting Lu, Christopher C. Sng, Chen Weller, Gordon Beattie, Amandeep Bhamra, Roc Farriol-Duran, Despoina Karagianni, Marcellus Augustine, Krijn Djikstra, Christopher L. Pinder, Benjamin S. Simpson, Gordon Weng-Kit Cheung, TRACERx Consortium, Felipe Galvez Cancino, Petra Vlckova, Silvia Surinova, Manuel Rodriguez-Justo, Mansi Shah, Nicholas McGranahan, Jeremy G. Carlton, Eva Camilla Gronroos, Sergio Quezada, James Luke Reading, Samra Turajlic, Yardena Samuels, Charles Swanton, Kevin Litchfield. Nonsense-mediated mRNA decay inhibition augments in vitro, in vivo, and ex vivo anti-tumor immunity [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2026; Part 1 (Regular Abstracts); 2026 Apr 17-22; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2026;86(7 Suppl):Abstract nr 6742.

Multi-sample bulk DNA sequencing enables reconstruction of a tumor’s clonal history, but scalable methods often rely on heuristic search and provide no optimality guarantees. We present CITUP2, an integrative combinatorial optimization framework that reconstructs clonal trees from descendant cell fractions (DCFs) of mutational clusters. CITUP2 formulates tree inference as a mixed-integer quadratic program (MIQP) that jointly determines the tree topology and clone prevalences across samples. It minimizes a weighted discrepancy between observed and inferred DCFs, with options to prioritize trees exhibiting consistency in the presence-absence patterns of parent-child clones. Under this formulation, CITUP2 returns provably optimal solutions (with respect to the model) and avoids the combinatorial explosion of exhaustive topology enumeration used by existing methods with optimality guarantees. In addition, CITUP2 can report a user-specified number of best trees. In simulations and analyses of a large, recently published multi-sample TRACERx cohort, CITUP2 scales to trees with tens of clones (approximately 30) and matches or improves on the fit attained by state-of-the-art approaches, while providing clear optimality certificates. Salem Malikic, Hamza Iseric, Chih Hao Wu, Erin Molloy, S. Cenk Sahinalp. Reconstruction of Tumor Clonal Trees with Multi-Sample Bulk Sequencing Data by Integrative Combinatorial Optimization [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2026; Part 1 (Regular Abstracts); 2026 Apr 17-22; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2026;86(7 Suppl):Abstract nr 6905.

Understanding and comparing tumor evolutionary histories is fundamental to cancer genomics, with direct implications for tracking subclonal population dynamics, treatment resistance, and tumor heterogeneity. Clonal trees, widely used to model tumor progression, are rooted, unordered trees in which each node represents a subclone labeled by a set of distinct mutations. Various principled and efficient methods have been developed for inferring clonal trees from either bulk or single-cell sequencing data. However, no existing computational approach offers a method that is both efficient and principled to fully align clonal trees and to compare their subclonal architectures, which limits the robustness of any downstream analysis based on inferred clonal trees. We introduce omlta, the optimal multi-label tree alignment of two clonal trees, which removes the minimum number of mutation labels, so that the remaining trees are isomorphic. Computing omlta is NP-hard. Here, we present a fixed-parameter tractable algorithm to compute the omlta, with a running time of O(L^3 log L 2^k) where L is the number of mutation labels shared between the input trees and k is the minimum possible number of mutation labels that need to be removed for the alignment - which we call omltd, the optimal multi-label tree edit distance. Our approach provides an exponentially better (in k) asymptotic runtime than the state-of-the-art algorithm by Akutsu et al. for computing the classic tree alignment and edit distance, concepts similar to what omlta/omltd optimizes on clonal trees. We applied omlta to 126 multi-sample bulk-sequencing data from the TRACERx study on non-small cell lung cancers by comparing clonal trees inferred by CONIPHER and PairTree. Despite the theoretically exponential runtime, we could compute the tree alignment for each tumor quickly, often within seconds. The omltd between CONIPHER and PairTree clonal trees on the same tumor varies substantially across tumors and the distances are negatively associated with the mean cancer cell fraction among mutations. For the tumors characterized by mutations with low cancer cell fractions, it is thus advisable not to use a single tree, but rather the alignment of multiple alternative trees, so that downstream inferences are informed only by robustly placed mutations. We further evaluated our algorithm on an in-house melanoma sample with clonal trees inferred by PhISCS and ScisTree, highlighting the utility of omlta on trees inferred from single-cell sequencing data. On these datasets, our algorithm completed all analyses in practical wall-clock times and showed that it can identify common evolutionary trajectories among clonal trees representing (i) distinct tumors, (ii) distinct samples from the same tumor, (iii) distinct sequencing data from the same sample. Additional supplementary results demonstrate the robustness of our approach in comparison to alternatives on simulated data. Jacob Gilbert, Chih Hao Wu, Marina Knittel, Alejandro Schaffer, Salem Malikić, S. Cenk Sahinalp. Identifying robust subclonal structures through tumor progression tree alignment [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2026; Part 1 (Regular Abstracts); 2026 Apr 17-22; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2026;86(7 Suppl):Abstract nr 6898.

To support the high data rates for latency-critical applications, future wireless systems will employ fully digital beamforming multiple-input multiple-output (MIMO) architectures at millimeter wave (mmWave) frequencies. Moreover, mmWave MIMO deployments will coexist with conventional sub6 GHz MIMO systems, creating opportunities to exploit out-ofband sub- 6 GHz information to enhance channel estimation at mmWave frequencies. In this work, we analyze the pilot-aided channel estimation performance of mmWave MIMO systems under various pilot configurations in both static and dynamic environments. We evaluate the system performance in terms of spectral efficiency (SE) for line-of-sight and non-line-of-sight propagation conditions. Simulation results show that incorporating out-of-band sub- 6 GHz information yields notable SE gains in both static and dynamic scenarios.

Copy number alterations (CNA) is a phenomenon during cancer evolution where some regions of the genome may be amplified or deleted. This results in heterogeneous collections of cancer cells. Profiling and classification of CNA profiles play a vital role in understanding the cancer heterogeneity and evolution to better inform diagnosis and treatment. There are several short-reads haplotype-specific CNA profiling tools but short reads provide a limited phasing range. Long-reads facilitate the direct phasing of genomic variants into megabase-scale haplotypes, which supports the reconstruction of longer, up to chromosome-scale, CNA profiles. Here we present Wakhan, a tool to analyze haplotype-specific chromosome-scale somatic copy number aberrations using long reads. Leveraging high-quality genome assembly coverage profiles, we show that Wakhan significantly outperforms other common short- and long-read CNA callers in achieving chromosome-level CNA consistency. Wakhan uses tumor-normal long-read BAMs and phased germline SNP calls as input. It first extends the input phasing to be chromosome-scale by exploiting haplotype coverage imbalance. Wakhan detects those phase switch regions and corrects them by taking into consideration the changes in haplotype-specific coverage. Next, Severus utilizes this enhanced phasing to generate phased structural variant (SV) calls. Finally, Wakhan's integrated CNA algorithm uses the SV calls as boundaries and employs a haplotype coverage model to assign integer copy-number states to the resultant CNA regions. https://github.com/KolmogorovLab/Wakhan We sought to compare Wakhan's performance against several state-of-the-art haplotype-specific CNA calling tools. The tools selected for short-read analysis included: Purple, Hatchet, Battenberg and for long-read analysis Purple and Savana are included. As benchmarks for small variants and SV calling are available but no similar benchmarks for somatic CNA calls are available. We designed a CASTLE panel based CNA calling benchmark, consisting of 6 pairs of tumor/normal cell lines sequenced with multiple short- and long-read sequencing technologies. We define segment error (SE) as for each CNA segment, we calculate the haplotype-specific mean squared distance between expected and reference coverage at heterozygous SNPs. This is then used to compute a weighted chromosomal average, normalized by the tumor haplotype's mean coverage. Similarly, for chromosome error (CE), compare the phase of the whole chromosome against the reference coverage. In the five CASTLE datasets, Wakhan and PURPLE had the lowest SE50 and SE75, indicating high accuracy in reconstructing individual CNA segments. We also evaluated Wakhan on a tumor-only dataset. Both Wakhan and PURPLE handled the absence of normal samples well and accurately reflected the expected tumor/normal profiles. Tanveer Ahmad, Ayse Keskus, Mikhail Kolmogorov, Sergey Aganezov, Michael C. Dean, Midhat S. Farooqi, S. Cenk Sahinalp, Benedict Paten, Karen H. Miga, Salem Malikić, Yuelin Liu, Byunggil Yoo, Ataberk Ataberk Donmez, Anton Goretsky. Wakhan: Reconstruction of chromosome-scale copy number profiles of tumor genomes with long-read sequencing [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2026; Part 1 (Regular Abstracts); 2026 Apr 17-22; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2026;86(7 Suppl):Abstract nr 6900.

Tumor evolution is driven by various mutational processes, ranging from single nucleotide variants (SNVs) to large structural variants (SVs) to dynamic shifts in DNA methylation. Current short-read sequencing methods struggle to accurately capture the full spectrum of these genomic and epigenomic alterations, as well as their relations, due to inherent technical limitations. Here we used Nanopore long-read sequencing to profile 23 subclones, each derived from a single cell of a mouse melanoma cell line, for precise detection and evolutionary ordering of SNVs, SVs, copy number alterations (CNAs), and DNA methylation changes at subclonal level. Through phylogenetic analysis of these subclones, we reconstruct the timing of mutational processes and their contributions to diverse clonal phenotypes. The analysis reveals recurrent amplifications of putative driver genes, generated by independent SVs across different lineages, suggesting parallel evolution. Additionally, we described lineage-specific methylation changes associated with aggressive tumor subclones, highlighting epigenetic trajectories linked to tumor progression. Overall, we demonstrate that our long-read approach enables a uniquely comprehensive view of melanoma progression, highlighting that SVs and methylation played an important role in initiation, clonal diversification, and development of therapeutic resistance in this tumor, in consistence with recent clinical findings. We will release the sequencing data and curated variant calls to encourage developments of new computational methods. Chi-Ping Day, Yuelin Liu, Anton Goretsky, Ayse Keskus, Salem Malikic, Eva Perez-Guijarro, Glenn Merlino, Eytan Ruppin, Suleyman Cenk Sahinalp, Mikhail Kolmogorov. Full-range genomic analysis at single-cell resolution reveals genetic, epigenetic, and parallel evolution of melanoma subclones [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2026; Part 1 (Regular Abstracts); 2026 Apr 17-22; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2026;86(7 Suppl):Abstract nr 704.

Clonal evolution of cancer results in intratumor heterogeneity, making treatment and cure challenging. Single-cell sequencing has advanced our understanding of intratumor heterogeneity, but tracing subclonal evolution using mutational profiles of cells is limited by scale and noise. Moreover, available tumor progression tree inference methods usually offer a single tree to explain the progression of a tumor, and do not inform about alternative evolutionary scenarios. We introduce the bi-partition function for a tumor progression tree, to assess the reliability of any proposed subclonal structure in a single-cell sequenced tumor. By using the bi-partition function, we calculate the probability that any given subset R of mutation-profiled single cells from a tumor forms a clade rooted by a specified mutation ρ across all possible tumor progression trees. This provides the means to evaluate whether R forms a subclone with ρ as a possible subclonal driver, which is especially useful if the cells of R are biologically or clinically significant, e.g., have aggressive growth, therapy resistance, or metastatic potential. We also introduce an algorithm to estimate the bi-partition function, which treats the ground truth as a probability distribution derived from mutational profiles of single cells and samples a tumor progression tree from this distribution independently in each iteration. We prove that our algorithm’s estimate of the bi-partition function asymptotically approaches the ground truth and demonstrate its accuracy on simulated data. Applying our algorithm to the tumor progression tree inferred from single-cell-derived melanoma sublines revealed that, while major clades and their root mutations are robust, (i) the placement of one clade in the tree is unreliable, which we later observed to be a result of Loss of Heterozygosity, and (ii) some of the mutations identified as false positives in the tree are unreliable, which later turned out to be the result of a doublet - a subline which has contamination from another subline. Interestingly, bootstrapping, a technique commonly employed for species trees, failed to point out any of these issues. After correcting the input data for these issues, the reliability of the progression tree improved substantially, demonstrating how our bi-partition function algorithm can aid studies on tumor evolution and intratumor heterogeneity. Farid Rashidi Mehrabadi, Erfan Sadeqi Azer, John D. Bridgers, Teresa M. Przytycka, Salem Malikic, Funda Ergun, Cenk Sahinalp. A bi-partition function algorithm to evaluate inferred subclonal structures in single-cell sequencing data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2026; Part 1 (Regular Abstracts); 2026 Apr 17-22; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2026;86(7 Suppl):Abstract nr 6897.

Dynamic changes in lipid membrane composition are a common response to stress, often involving shifts in key lipid molecules. Phosphatidic acid (PA), a central precursor in lipid biosynthesis, accumulates when anionic phospholipid synthesis is blocked—lipids that are typically primary targets of membrane-active antimicrobial peptides (AMPs). This raises the question of how cationic AMPs adapt to such lipid remodeling, which is especially relevant given their promise as novel therapeutics against escalating antimicrobial resistance. Their killing mechanism is often unclear. To identify ongoing processes clearly linked to bacterial cell death, six assays targeting membrane integrity and cell viability were performed alongside bactericidal measurements. These assays were conducted on Escherichia coli and a mutant depleted of anionic phospholipids, treated with the cationic peptides melittin and LL-37. Correlation of assays generated characteristic antimicrobial profiles, providing insight into the peptides’ mechanisms. LL-37 acted independently of membrane composition, while melittin showed increased activity in the absence of anionic phospholipids. This study confirmed specific interactions with PA, but their action suggests targets beyond the membrane, as bacteria remained viable during membrane disruption but failed to form colonies. Overall, these findings indicate that both peptides can effectively handle lipid remodeling and uncover processes driving bacterial cell death.

This paper investigates the dynamics of a discrete-time Rayleigh-Duffing oscillator exhibiting chaos in the Li-Yorke sense. We use Marotto's theorem to prove the existence of chaos by finding snap-back repeller. It is shown that the system undergoes a Neimark-Sacker bifurcation and a period-doubling bifurcation. We compute the Lyapunov exponents numerically to show sensitive dependence on initial conditions and chaotic behavior. The illustration of the results is presented using numerical simulations.

The Wallace--Freeman estimator is a classical minimum message length estimator whose relationship with likelihood-based asymptotic theory has not been fully developed. We show that, in regular parametric models, the Wallace--Freeman criterion is equivalent, up to constants, to a penalised likelihood criterion with penalty weight \(n^{-1}\). This representation places the estimator within the standard theory of penalised M-estimation and yields existence, consistency, an asymptotic linear expansion, and asymptotic normality under regularity conditions. We further derive the first-order difference between the Wallace--Freeman estimator and the maximum likelihood estimator, showing that it is an explicit \(O(n^{-1})\) shift determined by the gradient of the Wallace--Freeman penalty. Combining this expansion with the Cox--Snell formula gives a first-order bias expansion for the Wallace--Freeman estimator. The result clarifies its relationship with maximum likelihood, Jeffreys-prior penalisation, and Firth-type bias reduction. We illustrate the theory for the Weibull model, where the penalty modifies the leading bias of the maximum likelihood estimator of the shape parameter.

Global birth rates have been in steady decline and are projected to continue this trajectory in the coming decades. While existing literature provides important insights into the demographic and socioeconomic dimensions of this trend, there remains a critical gap in theoretical frameworks that engage with the broader implications of declining fertility. Current family planning programs often concentrate on pregnancy and postnatal care but tend to overlook the preconception period, particularly the need to equip women with the resources and autonomy required to make informed decisions about reproduction. Such omissions may have unintended consequences for women’s reproductive choices and broader fertility patterns. Meanwhile, rather than centering policy efforts solely on increasing birth rates, it is imperative to shift the focus toward improving the quality of births which emphasizes the long-term comprehensive benefits to individuals, families and society. This approach necessitates the provision of comprehensive support covering the entire reproductive cycle for women, supported by robust engagement from the global health community. This study seeks to explore the multifaceted factors that shape women’s capacity and inclination to bear children under conditions conducive to positive maternal and infant outcomes. It introduces a holistic framework designed to inform the policies and practices of health and governmental institutions, with the aim of promoting women’s overall well-being and effective and sustainable fertility outcomes.

The Wallace--Freeman estimator is a classical invariant point estimator whose large-sample properties have not been fully developed in a modern asymptotic framework. We show that the estimator can be formulated as a penalised M-estimator with a specific penalty weight, yielding a unified route to its asymptotic analysis. This representation allows us to establish existence, consistency, an asymptotic linear expansion, and asymptotic normality under standard regularity conditions. We further derive the first-order difference between the Wallace--Freeman estimator and the maximum likelihood estimator, and show that this induces an explicit $O(n^{-1})$ bias correction determined by the gradient of the penalty. As a consequence, the Cox--Snell bias formula for the maximum likelihood estimator extends naturally to the Wallace--Freeman estimator by the addition of a penalty-driven correction term. As an illustration, we derive the first-order bias of the Wallace--Freeman estimator for the Weibull model and show how the penalty modifies the corresponding maximum likelihood bias. These results place the Wallace--Freeman estimator within the general theory of penalised likelihood and provide a rigorous asymptotic basis for its use in parametric inference.