FOR DOCTORAL DEGREE ( Ph . D . )

Evaluating survival percentiles is a possible approach for the analysis of time-to-event outcomes that moves the focus from risk to time, as the proportion of events is fixed and the time by which that proportion is achieved is investigated. The development of statistical methods for conditional censored quantiles has opened up the possibility to use this approach in epidemiological studies. The aim of this doctoral thesis was to investigate the advantages of this method in epidemiology, by evaluating survival percentiles in observational studies on lifestyle and mortality, and by extending and further developing the statistical tools for the estimation of conditional survival percentiles. The percentile approach was used in a large prospective cohort of about 80.000 middle-aged and elderly Swedish men and women, with 15 years of follow-up during which 20% of the study population died. The impact of modifiable lifestyle factors such as fruit and vegetables consumption (Study I), sleep duration and physical activity (Study II), and processed and non-processed red meat consumption (Study III) on time to death were evaluated. Statistical modeling of conditional survival percentiles was conducted using Laplace regression. The epidemiological measure of exposure-outcome association was defined in terms of percentile difference (PD). Quantitative exposures were flexibly modeled using splines to investigate the dose-response shape. Low fruit and vegetables consumption (Study I) was found to be associated with progressively shorter survival up to 3 years (PD: -37 months; 95% CI: -58, -16) when comparing those who consumed 5 servings/day and those who never consumed fruit and vegetables. Long sleep duration, over 8 hours/day, (Study II) was associated with shorter survival (PD = -20 months; 95% CI: -30, -11) among those with low physical activity, comparing with those with 7 hours of sleeping per day. In Study III, compared with no consumption, higher intake of processed red meat (200 g/d) was associated with shorter survival (PD: -10 months; 95% CI: -18, -3). High and moderate intakes of non-processed red meat were associated with shorter survival only when accompanied by a high intake of processed red meat. Study IV and Study V introduced novel developments and extensions of the percentile approach. Study IV presented the meaning and evaluation of survival percentiles in those situations where the time variable of interest is attained age at the event rather than follow-up time. This change in the time-scale has important consequences on the definition and interpretation of the survival curve and related percentiles. The study described how to use multivariable Laplace regression models to estimate percentiles of age at death conditioning on age at entry into the study, exposures, and potential confounders. Study V focused on interaction analysis. Interaction can be evaluated on the additive or multiplicative scale, but its assessment in prospective studies is commonly limited to the multiplicative scenario. In this study the advantages of using a percentile approach in interaction analysis were presented. A measure of interaction in terms of time was introduced and how Laplace regression can be used to estimate a measure of interaction on the additive scale was described. Evaluating survival percentiles provides an intuitive and flexible approach for the analysis of timeto-event outcomes. With this method, results from prospective studies can be presented in terms of differences in survival time, facilitating both interpretation and communication of scientific findings. The introduction of a statistical technique to estimate conditional survival percentiles has substantially enriched its potentialities and eased its application in epidemiological research. The percentile approach should be considered as a possible complement to classical approaches and its use should be widespread. List of publications I. Bellavia A. , Larsson SC. , Bottai M. , Wolk A. , Orsini N. Fruit and vegetable consumption and all-cause mortality: a dose-response analysis. American Journal of Clinical Nutrition. 2013 Aug;98(2):454-9 II. Bellavia A. , Åkerstedt A. , Bottai M. , Wolk A. , Orsini N. Sleep duration and survival percentiles across categories of physical activity. American Journal of Epidemiology. 2014 Feb 15;179(4):484-91 III. Bellavia A. , Larsson SC. , Bottai M. , Wolk A. , Orsini N. Differences in survival associated with processed and with nonprocessed red meat consumption. American Journal of Clinical Nutrition. 2014 Sep;100(3):924-9 IV. Bellavia A. , Discacciati A. , Bottai M. , Wolk A. , Orsini N. Using Laplace regression to model and predict percentiles of age at death when age is the primary time scale. American Journal of Epidemiology. 2015 Jun;182(3):271-277 V. Bellavia A. , Bottai M. , Orsini N. Evaluating additive interaction using survival percentiles. Epidemiology. 2016. In press The articles will be referred to in the text by their Roman numerals, and are reproduced in full at the end of the text. Related publications  Bellavia A. , Bottai M. , Wolk A. , Orsini N. Physical activity and mortality in a prospective cohort of middle-aged and elderly men a time perspective. International Journal of Behavioral Nutrition and Physical Activity. 2013 Aug 8;10:94  Bellavia A. , Bottai M. , Wolk A. , Orsini N. Alcohol consumption and mortality: a dose-response analysis in terms of time. Annals of Epidemiology. 2014 Apr;24(4):291-6  Bellavia A. , Bottai M. , Discacciati A. , Orsini N. Adjusted survival curves with multivariable laplace regression. Epidemiology. 2015 Mar;26(2):e17-8.  Rahman I. , Bellavia A. , Wolk A. , Orsini N. Physical activity and heart failure risk in a prospective study of men. JACC: Heart Failure. 2015; 3(9), 681-687  Bellavia A. , Wolk A. , Orsini N. Differences in age at death according to smoking and age at menopause. Menopause. 2015 Jul 31. [Epub ahead of print]  Discacciati A. , Bellavia A. , Orsini N. , Greenland S. On the interpretation of risk and rate advancement periods. International Journal of Epidemiology. 2016. Conditionally accepted  Bellavia A. , Teknonidis TG. , Orsini N. , Wolk A. , Larsson SC. Quantifying the benefits of mediterranean diet in terms of survival. European Journal of Epidemiology. 2016. Conditionally accepted List of abbreviations AL AFT BMI CI COSM CVD FV HR MET PA PD PH RERI SD SMC Asymmetric Laplace Accelerated Failure Time Body Mass Index Confidence Interval Cohort of Swedish Men Cardiovascular Disease Fruit and Vegetables Hazard Ratio Metabolic Equivalent Physical Activity Percentile Difference Proportionality of the Hazard Relative Risk due to Interaction Standard Deviation Swedish Mammography Cohort