A new family of survival functions and a method for measuring risk inequalities

Sammanfattning: The present compilation thesis is divided into two sections, one for each of two separate methodological issues: reduction of random errors in mortality estimates and offsetting random variation related bias in data generated estimators of risk inequalities. Summary of section A In regard to the first issue a new family of survival functions is proposed. Its purpose is to provide valid and reliable age-specific estimates of death probabilities and life expectancies for all ages in the entire human life span. In Paper I, I introduced a five-parameter survival function intended to model mortality in modern female populations. It is shown that (i) the complement of the proposed survival function is a bona fide cumulative distribution function, and (ii) that the expected value of a random variable with such a distribution exists and is finite. In Paper II, I showed that the age pattern of mortality among Swedish males differed significantly from the age pattern among Swedish females and that some extra parameters were needed to accommodate an added risk of fatal injuries among males in the early adulthood. To address this shortcoming, I introduced an eight-parameter survival function intended to model mortality among males as a solution to the problem associated with the gender difference in mortality patterns. In Paper III, I addressed the use of collateral data as a means of improving the statistical precision of mortality estimates. A brief description of three main approaches that actuaries and demographers use to accomplish such improvements, namely, mortality laws, model life tables, and relational methods was given. I thereafter introduced a novel regression model that incorporates several beneficial principles from each of these approaches. The survival functions introduced in [Hannerz, 1999] resulted in an, on average, five-fold decrease in the standard error of estimated sex and age-specific one-year death probabilities, compared with frequency substitution estimates, when applied to mortality in the total population of Sweden 1982. In papers IV – VI, I applied the methods delineated in Papers I – III to estimate age, sex and diagnosisspecific life expectancies among individuals with a history of psychiatric and cerebrovascular disorders, respectively. Summary of section B The second methodological issue studied resulted in a Monte Carlo simulation procedure, which can be used to estimate excess fractions in the absence of a natural reference group. The procedure is based on the assumptions that the number of events in each group is Poisson distributed and that the true risk rates in the groups increases geometrically with their rank order. The methodological aspects of the procedure are described and discussed in Paper VII. In paper VIII the procedure is applied to industrial inequalities in rates of disability retirement and in paper IX to hospital contact due to mood disorders, in both studies among economically active people in Denmark. The Monte Carlo simulation procedure is designed to estimate excess fractions in situations where no natural reference group exists. Simpler methods are available when a reference group does exist. An overview of such measures is included in the thesis, and examples of excess fractions in relation to prespecified reference groups are given in Papers X and XI.