When faced with death counts strati ed by age, analysts often calculate a crude mortality rate (CMR) as a single summary measure. This is done by simply dividing total death counts by total population counts. However, the crude mortality rate is not appropriate for comparing different populations due to the significant impact of age on mortality and the possibility of having different age structures for different populations. While a set of age-adjustment methods seeks to collapse age-specific mortality rates into a single measure that is free from the confounding effect of age structure, we focus on one of these methods called "direct age-standardization" method which summarizes and compares age-specific mortality rates by adopting a reference population. While qualitative insights in relation to age-standardization are often discussed, we seek to approximate age-standardized mortality rate of a population based on the corresponding CMR and the 90th quantile of its population distribution. This approximation is most useful when age-specific mortality data is unavailable. In addition, we provide quantitative insights related to age-standardization. We derive our model based on mathematical insights drawn from the explication of exact calculations and validate our model by using empirical data for a large number of countries under a large number of circumstances. We also extend the application of our approximation model to other age-standardized mortality indicators such as cause-specific mortality rate and potential years of life lost. In the second part of the thesis, we consider the formulation of a general risk management procedure, where risk needs to be measured and further mitigated. The formulation admits an optimization representation and requires as input the distributional information about the underlying risk factors. Unfortunately, for most risk factors it is known to be difficult to identify their distribution in full details, and more problematically the risk management procedure can be prone to errors in the input distribution. In particular, one of the most important distribution information is the covariance hat captures the spread and correlation among risk factors. We study the issue of covariance uncertainty in the problem of mitigating tail risk and by admitting an uncertainty set of covariance of risk factors, we propose a robust optimization model which minimizes risk for the worst scenario especially when data is insufficient and the number of risk factors is large. We will then transform our model into a computationally solvable one and test the model using real-world data.

BACKGROUND This thesis studies the relationship between area-level socioeconomic status and the incidence and 30-day survival of out of hospital cardiac arrest. The effect of socioeconomic status on health has been studied for over 150 years.  Although cardiac arrest is a major public health problem there has been very little focus on socioeconomic status and out of hospital cardiac arrest. DATA AND METHODS The cardiac arrest data are obtained from the Swedish cardiac arrest registry. Data on age structure and percentage of immigrants is from SCBs total population registry and socioeconomic data come from SCBs LISA database. The incidence analysis is made in two steps. The first step calculates the age standardized incidence and the second step is an OLS analysis. For the survival analysis a logistic regression analysis is made to measure the probability of survival in different income areas. RESULTS For the socioeconomic status – incidence analysis the results from the OLS analysis suggest that the incidence is almost twice as high in the lowest income area. Intercept (Highest group) = 26.8 and <140 000 (lowest group) = 24.5. In the survival analysis (using a binary logistic regression analysis) there was a significantly lower OR for the lowest income group for all patients (OR= 0.521, p= 0.049) and for the sub group (patients 18-75 years old) there was a significant negative relationship for the two lowest groups. <140 000 (OR= 0.444, p= 0.032) and 140 000-159 000 (OR= 0.620, p= 0.046). CONCLUSION There is a significant relationship between living in a poor neighborhood and out of hospital cardiac arrest. Those living in poorer areas have both an increased incidence and lower chance of survival of out of hospital cardiac arrest.