Forecasting age-specific breast cancer mortality using functional data models

Abstract

Accurate estimates of future age-specific incidence and mortality are critical for allocation of resources to breast cancer control programmes and evaluation of screening programmes. The purpose of this study is to apply functional data analysis techniques to model age-specific breast cancer mortality time trends, and forecast entire age-specific mortality functions using a state-space approach. We use annual unadjusted breast cancer mortality rates in Australia, from 1921 to 2001 in 5 year age groups (45 to 85+). We use functional data analysis techniques where mortality and incidence are modelled as curves with age as a functional covariate varying by time. Data are smoothed using non-parametric smoothing methods then decomposed (using principal components analysis) to estimate basis functions that represent the functional curve. Period effects from the fitted coefficients are forecast then multiplied by the basis functions, resulting in a forecast mortality curve with prediction intervals. To forecast, we adopt a state-space approach and an automatic modelling framework for selecting among exponential smoothing methods.Overall, breast cancer mortality rates in Australia remained relatively stable from 1960 to the late 1990s, but have declined over the last few years. A set of four basis functions minimized the mean integrated squared forecasting error and account for 99.3 per cent of variation around the mean mortality curve. Twenty year forecasts suggest a continuing decline, but at a slower rate, and stabilizing beyond 2010. Forecasts show a decline in all age groups with the greatest decline in older women. The proposed methods have the potential to incorporate important covariates such as hormone replacement therapy and interventions to represent mammographic screening. This would be particularly useful for evaluating the impact of screening on mortality and incidence from breast cancer.