Estimation and hypothesis testing in mixed linear models

Dissertação apresentada para obtenção do Grau de Doutor em Matemática, Estatística, pela Universidade Nova de Lisboa, faculdade de Ciências e Tecnologia

Assessment by doppler ultrasound of entheseal lesions in spondyloarthritis : a longitudial study to determine structural damage and disease activity lesions

RESUMO: Enthesitis is the hallmark of spondyloarthritis (SpA), and is observed in all subtypes. Wide information on SpA abnormalities, including synovitis, tendinitis and enthesitis, can be efficiently perceived by Doppler ultrasound. Furthermore, several studies on imaging of enthesis showed that imaging techniques are better than clinical examination to detect enthesis alterations; and vascularized enthesitis detected by Doppler ultrasound appears to be a valuable diagnostic tool to confirm SpA diagnosis. However, data published until now concerning entheseal elementary alterations that characterize SpA enthesitis (enthesis inflammatory activity) or enthesopathy (permanent structural changes) reflect rather the authors’ empiric opinion than a methodological validation process. In this sense it seems crucial to identify elementary entheseal lesions associated with activity or damage, in order to improve monitoring and treatment response in SpA patients. The development of better assessment tools is today a challenge and a need in SpA. The first study of this thesis focused on the analysis of the reliability of inter-lector and inter-ultrasonography equipment of Madrid sonography enthesitis index (MASEI). Fundamental data for the remaining unrolling project validity. In the second and third studies we concerned about two entheseal elemental lesions: erosions and bursa. In literature erosions represent a permanent structural damage, being useful for monitoring joint injury, disease activity and therapeutic response in many rheumatic diseases; and to date, this concept has been mostly applied in rheumatoid arthritis (RA). Unquestionably, erosion is a tissue-related damage and a structural change. However, the hypothesis that we decided to test was if erosions represent a permanent structural change that can only grow and worsen over time, as occurs in RA, or a transitory alteration. A longitudinal study of early SpA patients was undertaken, and the Achilles enthesis was used as a model. Our results strongly suggested that previously detected erosions could disappear during the course of the disease, being consistent with the dynamic behavior of erosion over time. Based on these striking results it seems reasonable to suggest that the new-bone formation process in SpA could be associated with the resolution of cortical entheseal erosion over time. These results could also be in agreement with the apparent failure of anti-tumor necrosis factor (TNF) therapies to control bone proliferation in SpA; and with the relation of TNF-α, Dickkopf-related protein 1 (Dkk-1) and the regulatory molecule of the Wnt signaling pathway in the bone proliferation in SpA. In the same model, we then proceeded to study the enthesis bursa. Interestingly, the Outcome Measures in Rheumatology Clinical Trials (OMERACT) enthesopathy definition does not include bursa as an elementary entheseal lesion. Nonetheless, bursa was included in 46% of the enthesis studies in a recently systematic literature review, being in agreement with the concept of “synovio-entheseal complex” that includes the link between enthesitis and osteitis in SpA. It has been clarified in recent data that there is not only a close functional integration of the enthesis with the neighboring bone, but also a connection between enthesitis and synovitis. Therefore, we tried to assess the prevalence and relevance of the bursa-synovial lesion in SpA. Our findings showed a significant increase of Achilles bursa presence and thickness in SpA patients compared to controls (healthy/mechanical controls and RA controls). These results raise awareness to the need to improve the enthesopathy ultrasonographic definition. In the final work of this thesis, we have explored new perspectives, not previously reported, about construct validity of enthesis ultrasound as a possible activity outcome in SpA. We performed a longitudinal Achilles enthesis ultrasound study in patients with early SpA. Achilles ultrasound examinations were performed at baseline, six- and twelve-month time periods and compared with clinical outcome measures collected at basal visit. Our results showed that basal erythrocyte sedimentation rate (ESR) and C-reactive protein (CRP) are higher in patients with Doppler signal in enthesis, and even that higher basal ESR, CRP and Ankylosing Spondylitis Disease Activity Score (ASDAS) predicted a higher Doppler signal (an ultrasound alteration accepted as representative of inflammation) six months later. Patients with very high disease activity assessed by ASDAS (>3.5) at baseline had significantly higher Achilles total ultrasound score verified at the same time; and ASDAS <1.3 predicted no Doppler signal at six and twelve months. This seems to represent a connection between classical biomarkers and clinical outcomes associated with SpA activity and Doppler signal, not only at the same time, but also for the following months. Remarkably, patients with inactive disease (ASDAS < 1.3) at baseline had no Doppler signal at six and twelve months. These findings reinforce the potential use of ultrasound related techniques for disease progression assessment and prognosis purposes. Intriguingly, Ankylosing Spondylitis Disease Activity Index (BASDAI) didn’t show significant differences between different cut-offs concerning ultrasound lesions or Doppler signal, while verified with ASDAS. These results seem to indicate that ASDAS reflects better than BASDAI what happens in the enthesis. The work herein discussed clearly shows the potential utility of ultrasound in enthesis assessment in SpA patients, and can be important for the development of ultrasound activity and structural damage scores for diagnosis and monitoring purposes. Therefore, local promotion of this technique constitutes a medical intervention that is worth being tested in SpA patients for diagnosis, monitoring and prognosis purposes.

A historical approach to the new secular stagnation hypothesis

In this paper, we analyze the behavior of real interest rates over the long-run using historical data for nine developed economies, to assess the extent to which the recent decline observed in most advanced countries is at odds with the past data, as suggested by the Secular Stagnation hypothesis. By using data from 1703 and performing stationarity and structural breaks tests, we find that the recent decline in interest rates is not explained by a structural break in the time series. Our results also show that considering long-run data leads to different conclusions than using short-run data.

Proving a market for a startup befor scaling using the hypothesis-driven entrepreneurship process

The year is 2015 and the startup and tech business ecosphere has never seen more activity. In New York City alone, the tech startup industry is on track to amass $8 billion dollars in total funding – the highest in 7 years (CB Insights, 2015). According to the Kauffman Index of Entrepreneurship (2015), this figure represents just 20% of the total funding in the United States. Thanks to platforms that link entrepreneurs with investors, there are simply more funding opportunities than ever, and funding can be initiated in a variety of ways (angel investors, venture capital firms, crowdfunding). And yet, in spite of all this, according to Forbes Magazine (2015), nine of ten startups will fail. Because of the unpredictable nature of the modern tech industry, it is difficult to pinpoint exactly why 90% of startups fail – but the general consensus amongst top tech executives is that “startups make products that no one wants” (Fortune, 2014). In 2011, author Eric Ries wrote a book called The Lean Startup in attempts to solve this all-too-familiar problem. It was in this book where he developed the framework for The Hypothesis-Driven Entrepreneurship Process, an iterative process that aims at proving a market before actually launching a product. Ries discusses concepts such as the Minimum Variable Product, the smallest set of activities necessary to disprove a hypothesis (or business model characteristic). Ries encourages acting briefly and often: if you are to fail, then fail fast. In today’s fast-moving economy, an entrepreneur cannot afford to waste his own time, nor his customer’s time. The purpose of this thesis is to conduct an in-depth of analysis of Hypothesis-Driven Entrepreneurship Process, in order to test market viability of a reallife startup idea, ShowMeAround. This analysis will follow the scientific Lean Startup approach; for the purpose of developing a functional business model and business plan. The objective is to conclude with an investment-ready startup idea, backed by rigorous entrepreneurial study.