Large Number of Rare Events: Diversity Analysis in Multiple Choice Questionnaires and Related Topics

The statistical analysis of a large number of rare events, (LNRE), which can also be called statistical theory of diversity, is the subject of acute interest both in statistical theory and in numerous applications. A careful eye will quickly see the presence of a large number of very rare objects almost everywhere: large numbers of rare species in ecosystems, large numbers of rare opinions in any opinion pool, large numbers of small admixtures in any solution and large numbers of rare words in any text are only few examples. In studying such objects, the interest for mathematical statisticians lies in the fact that most of the frequencies are small and, therefore, difficult to deal with. It is not immediately clear how one should be able to derive consistent and reliable inference from a large number of such frequencies. In this thesis we study the diversity of questionnaires with multiple answers. It has been demonstrated that this is a particular model of LNRE theory. In our analysis, the theories of large deviation, contiguity and Edgeworth expansion were employed, and limit theorems have been established

Large Number of Rare Events: Diversity Analysis in Multiple Choice Questionnaires and Related Topics

The statistical analysis of a large number of rare events, (LNRE), which can also be called statistical theory of diversity, is the subject of acute interest both in statistical theory and in numerous applications. A careful eye will quickly see the presence of a large number of very rare objects almost everywhere: large numbers of rare species in ecosystems, large numbers of rare opinions in any opinion pool, large numbers of small admixtures in any solution and large numbers of rare words in any text are only few examples. In studying such objects, the interest for mathematical statisticians lies in the fact that most of the frequencies are small and, therefore, difficult to deal with. It is not immediately clear how one should be able to derive consistent and reliable inference from a large number of such frequencies. In this thesis we study the diversity of questionnaires with multiple answers. It has been demonstrated that this is a particular model of LNRE theory. In our analysis, the theories of large deviation, contiguity and Edgeworth expansion were employed, and limit theorems have been established

Martingale limit theorems of divisible statistics in a multinomial scheme with mixed frequencies

The martingale approach to limit theorems of divisible statistics in non-classical multinomial schemes, established by Khmaladze in 1983, has shown great power for those models with all asymptotically Poissonian frequencies. We extended this approach to more general situations, which include both asymptotically Gaussian and Poissonian frequencies, and established functional limit theorems.Functional limit theorems Divisible statistics Multinomial scheme Mixed frequencies

Diversity analysis in multiple-choice questionnaires

We extend the analysis of the diversity of questionnaires with binary (yes-no) answers to the case of questionnaires with multiple answers. It has been demonstrated that the original techniques used by Khmaladze (2009) are universal and can be applied to prove limit theorems for more general cases. It was shown that this different framework again leads us to a model similar to that for a large number of rare events that Khmaladze obtained in Khmaladze (2009), namely, to the so called Karlin-Rouault law.Contiguity Edgeworth expansion Large deviation Large number of rare events Karlin-Rouault law

Impact of low-dose CT screening for lung cancer on ethnic health inequities in New Zealand: a cost-effectiveness analysis

Objective There are large inequities in the lung cancer burden for the Indigenous Māori population of New Zealand. We model the potential lifetime health gains, equity impacts and cost-effectiveness of a national low-dose CT (LDCT) screening programme for lung cancer in smokers aged 55–74 years with a 30 pack-year history, and for formers smokers who have quit within the last 15 years.Design A Markov macrosimulation model estimated: health benefits (health-adjusted life-years (HALYs)), costs and cost-effectiveness of biennial LDCT screening. Input parameters came from literature and NZ-linked health datasets.Setting New Zealand.Participants Population aged 55–74 years in 2011.Interventions Biennial LDCT screening for lung cancer compared with usual care.Outcome measures Incremental cost-effectiveness ratios were calculated using the average difference in costs and HALYs between the screened and the unscreened populations. Equity analyses included substituting non-Māori values for Māori values of background morbidity, mortality and stage-specific survival. Changes in inequities in lung cancer survival and ‘health-adjusted life expectancy’ (HALE) were measured.Results LDCT screening in NZ is likely to be cost-effective for the total population: NZ$34 400 per HALY gained (95$27 500 to NZ$42 900) and for Māori separately (using a threshold of gross domestic product per capita NZ$45 000). Health gains per capita for Māori females were twice that for non-Māori females and 25% greater for Māori males compared with non-Māori males. LDCT screening will narrow absolute inequities in HALE and lung cancer mortality for Māori, but will slightly increase relative inequities in mortality from lung cancer (compared with non-Māori) due to differential stage-specific survival.Conclusion A national biennial LDCT lung cancer screening programme in New Zealand is likely to be cost-effective, will improve total population health and reduce health inequities for Māori. Attention must be paid to addressing ethnic inequities in stage-specific lung cancer survival

Health system costs for individual and comorbid noncommunicable diseases: An analysis of publicly funded health events from New Zealand.

BackgroundThere is little systematic assessment of how total health expenditure is distributed across diseases and comorbidities. The objective of this study was to use statistical methods to disaggregate all publicly funded health expenditure by disease and comorbidities in order to answer three research questions: (1) What is health expenditure by disease phase for noncommunicable diseases (NCDs) in New Zealand? (2) Is the cost of having two NCDs more or less than that expected given the independent costs of each NCD? (3) How is total health spending disaggregated by NCDs across age and by sex?Methods and findingsWe used linked data for all adult New Zealanders for publicly funded events, including hospitalisation, outpatient, pharmaceutical, laboratory testing, and primary care from 1 July 2007 to 30 June 2014. These data include 18.9 million person-years and $26.4 billion in spending (US$ 2016). We used case definition algorithms to identify if a person had any of six NCDs (cancer, cardiovascular disease [CVD], diabetes, musculoskeletal, neurological, and a chronic lung/liver/kidney [LLK] disease). Indicator variables were used to identify the presence of any of the 15 possible comorbidity pairings of these six NCDs. Regression was used to estimate excess annual health expenditure per person. Cause deletion methods were used to estimate total population expenditure by disease. A majority (59%) of health expenditure was attributable to NCDs. Expenditure due to diseases was generally highest in the year of diagnosis and year of death. A person having two diseases simultaneously generally had greater health expenditure than the expected sum of having the diseases separately, for all 15 comorbidity pairs except the CVD-cancer pair. For example, a 60-64-year-old female with none of the six NCDs had $633 per annum expenditure. If she had both CVD and chronic LLK, additional expenditure for CVD separately was$6,443/$839/$9,225 for the first year of diagnosis/prevalent years/last year of life if dying of CVD; additional expenditure for chronic LLK separately was $6,443/$1,291/$9,051; and the additional comorbidity expenditure of having both CVD and LLK was$2,456 (95% confidence interval [CI] $2,238-$2,674). The pattern was similar for males (e.g., additional comorbidity expenditure for a 60-64-year-old male with CVD and chronic LLK was $2,498 [95$2,264-$2,632]). In addition to this, the excess comorbidity costs for a person with two diseases was greater at younger ages, e.g., excess expenditure for 45-49-year-old males with CVD and chronic LLK was 10 times higher than for 75-79-year-old males and six times higher for females. At the population level, 23.8% of total health expenditure was attributable to higher costs of having one of the 15 comorbidity pairs over and above the six NCDs separately; of the remaining expenditure, CVD accounted for 18.7%, followed by musculoskeletal (16.2%), neurological (14.4%), cancer (14.1%), chronic LLK disease (7.4%), and diabetes (5.5%). Major limitations included incomplete linkage to all costed events (although these were largely non-NCD events) and missing private expenditure.ConclusionsThe costs of having two NCDs simultaneously is typically superadditive, and more so for younger adults. Neurological and musculoskeletal diseases contributed the largest health system costs, in accord with burden of disease studies finding that they contribute large morbidity. Just as burden of disease methodology has advanced the understanding of disease burden, there is a need to create disease-based costing studies that facilitate the disaggregation of health budgets at a national level

One-way sensitivity analysis: tornado plot for pooled subtypes for the age group 50–54 y.

<p>One-way sensitivity analysis: tornado plot for pooled subtypes for the age group 50–54 y.</p

Scenario analyses: cost-effectiveness plane for the age group 50–54 y.

<p>GDP, gross domestic product.</p