Cancer screening is a programme for medical screening of asymptomatic people who are at risk of developing cancer. Typically, participants are regularly screened every few years using blood tests, urine tests, medical imaging, or other methods. Among cases who are screened regularly some are diagnosed with cancer based on screening tests (screen-detected cases) and some based on symptoms appearing in the interval between two consecutive screening tests (interval cases). The hypothesis is that the screening programmes improve chances of survival for screen-detected cases as these cases are diagnosed and treated at an earlier stage of the disease compared to counterfactual scenario where their cancer would have been detected based on symptoms. We would like to test this hypothesis empirically. So far, the problem has been tackled by comparing the survival functions of screen-detected cases and interval cases. Realizing that the direct comparison between these two groups would result in biased results, previous research focused on parametric solutions to remove the bias. We argue that the problem lies elsewhere – that this comparison, in fact, does not reflect the question of interest. Therefore, in this study, we precisely define the contrast corresponding to the hypothesis defined above. Since the contrast of interest refers to hypothetical quantities, we discuss which data and under what assumptions can be used for estimation. We also propose a non-parametric framework for evaluating the effectiveness of cancer screening programmes under certain assumptions. The proposed ideas are illustrated using simulated data. The problem is motivated by the need to evaluate breast cancer screening programme in Slovenia.

Survival analysis is a statistical method for evaluating time-to-event data, such as death or disease progression, in oncology trials. Usually, in such oncology trials, a new treatment regimen is compared to a control group, normally the standard of care. Traditional survival analysis methods like the Cox-proportional hazards model or the log-rank test assume the hazard ratio of two groups to be constant over time. However, this assumption is often violated in real-world applications. An example of that are immuno-oncology drugs, which often exhibit a delayed onset of their effects. To address this, more robust methods for survival analysis under non-proportional hazards have been developed. We propose a two-step procedure for comparing hazard functions of two groups in the presence of non-proportional hazards. The procedure starts with a pre-test to assess the proportional hazards assumption, followed by a method for comparing hazard functions that is conditioned on the pre-test result. In a simple framework, depending on the pre-test results either a standard log-rank test or a weighted log-rank test will be performed. We show for which scenarios such a two-step procedure might yield a type 1 error rate inflation and discuss how strict control can be achieved. The efficacy of the two-step approach will be evaluated through comparison with established methods such as weighted log-rank tests or max-combo test in broad simulation study.

The gold-standard design for non-inferiority studies is recommended by regulatory authorities in the United States as well as in Europe: it consists in a three-arm design including placebo in addition to the experimental and the active comparator groups (Koch A. & Röhmel J.,2013). Three-arm non-inferiority trials are challenging for the hypothesis formulation, and their design is often characterized by uncertainty in estimating the experimental treatment effect. Some methods have been proposed to optimize the recalculation of the sample size at interim analysis for Gaussian, Bernoulli, and Poisson outcomes but not for continuous skewed outcome.

Firstly, our research aims to evaluate, through simulations, how the algorithm for the recalculation of the sample size at interim in three-arm non-inferiority studies, with particular reference to Lei's design (Lei, 2020), is able to provide the acceptable level of power even in the presence of deviation from normality; secondly, to improve the applicability of the resampling algorithm in the study design with a gamma distributed outcome of interest.

After demonstrating that the power is still maintained at the predetermined level even in the presence of a deviation from normality, we questioned the hypothesis of homoskedasticity in the case of asymmetrical outcomes simulated as gamma variables. Thus, we provided a resampling algorithm that keeps the normal assumption but accounts for different standard deviations to be set across the three arms.

We found that if the discrepancy between the group variances is considered, we can estimate an adequate initial sample size to achieve the desired power, avoiding the risk of overestimation (saving patients) or underestimation (saving power), in case of gamma distributed outcomes. We provided a motivating example from COSTAMI trial (Desideri A. et al., 2003).

Lastly, we developed an intuitive Web application for the sample size/coverage probability estimation. The tool helps to keep track of the properties of the design, as it provides an estimate of the probability of success/failure of the study, giving us the possibility to choose the best reliable set of parameters to optimize the resources available for the trial.

Introduction
Immunity against infectious diseases is strongly driven by antibodies. Interventions, which can reduce the burden of infections, like vaccination, need to be evaluated through clinical studies. Being able to describe antibody kinetics, the change in antibody titer over time, is crucial in optimizing the design of immunization trials. This includes determining the appropriate sample size and sampling times to accurately describe the underlying kinetics.

Methods
We established a systematic review of models used to describe antibody kinetics and how they have been used in the process of study design. We implemented and extended found models to develop a framework for answering the key research question of how individuals should be monitored in immunization trials. We took a dual approach, first fixing number of individuals and samples per person, varying sampling schedules and secondly fixing the time points and varying the number of individuals to assess accuracy and variability of the estimated parameters. Where possible we provide analytical solutions. Further, we conducted simulations to evaluate the developed framework.

Results
We found 1439 abstracts, out of which 652 full texts were screened for eligibility. In total 270 publications are eligible for data extraction. Some publications contained unclear methods or insufficient information about the model. A few publications even provided wrong solutions for the system of differential equations. We saw frequent use of basic statistical models and hardly any study design considerations. Using an implemented plasma cell model, we found that frequency and timing of sampling influences the estimates and the variability of the underlying parameters.

Conclusion
The limited use of mathematical models describing antibody kinetics, especially regarding study design, highlights the need and importance of basic research. Through our work, we aim to provide a framework, which can be actively used in practice to improve infectious disease study design.

Mass spectrometry (MS) is a core technology for proteomics. It allows for the identification and quantification of proteins in biological samples. In a mass spectrometry experiment, peptides – smaller fragments of proteins - are ionized, separated based on their mass and charge, and quantified. Resulting data are complex and high-dimensional: they include up to thousands of proteins and tens of thousands of peptides. This type of data is important in drug discovery and other stages of drug development, and in various fields of proteomics research.

Typically, mass spectrometry data are used to estimate relative abundance of proteins in different biological conditions. One of the major challenges in the analysis of mass spectrometry is the protein inference problem: deriving a list of proteins that are present in the sample based on identified peptides. It is complicated due to three factors: false identifications of peptides based on mass spectra, presence of peptide sequences that can be attributed to multiple proteins (shared peptides) and one-hit wonders - proteins identified only by a single peptide. Similarly, protein quantification - estimating the relative abundance of proteins in different conditions - is difficult in the presence of shared peptides, as it is not clear how to distribute peptide abundance among their respective proteins. From statistical perspective, inclusion of shared peptides in models that are used to estimate protein abundances from peptide-level data introduces the multiple membership structure, in which observations (peptide intensities) may belong to multiple groups defined by proteins.

Typically, shared peptides are removed from analysis of MS data, which leads to loss of peptide-level information and lack of ability to estimate abundances of proteins that are identified only by shared peptides or by a single unique peptide. Our goal is to propose a statistical methodology capable of including shared peptides in downstream MS data analysis to increase the number of proteins that can be identified and quantified reliably, and improve the power of statistical analysis. In this talk, we will present two classes of non-linear models that can be used to describe labeled and label-free mass spectrometry experiments with shared peptides: models with peptide-specific weights and non-weighted models. In labeled experiments, multiple biological conditions or subjects may be measured jointly. In this case, peptides have natural quantitative profiles, which we use to estimate the degree of their protein membership (weights). We use these weights to estimate protein-level summaries of peptide data, which are then used for comparisons of biological conditions. For non-labeled experiments, we will present an approach that uses additional information from raw spectra to enable protein quantification with shared peptides. We will illustrate proposed models with biological data, and provide analytical and simulation study-based results on their statistical properties.

Research presented in this talk was done in collaboration with Genentech company, Northeastern University (USA) and Hasselt University (Belgium), and was financially supported by the National Science Center grant 2020/37/N/ST6/04070 (Poland).