A percentile approach to time-to-event outcomes

Abstract

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 xed 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 pop- ulation died. The impact of modi able 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 de ned in terms of percentile di erence (PD). Quantitative exposures were exibly 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 con- sumed 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 de nition and interpretation of the survival curve and related percentiles. The study described how to use multivariable Laplace regression models to esti- mate 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 multiplica- tive 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 exible approach for the analysis of time- to-event outcomes. With this method, results from prospective studies can be presented in terms of di erences in survival time, facilitating both interpretation and communication of scienti c ndings. The introduction of a statistical technique to estimate conditional survival percentiles has substan- tially 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.