Forecasting age-specific breast cancer mortality using functional data models
Accurate estimates of future age-specific incidence and mortality are critical for allocation of resources to breast cancer control programs and evaluation of screening programs. 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 function using a state-space approach. We use yearly 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 modeled as curves with age as a functional covariate varying by time. Data is smoothed using nonparametric smoothing methods then decomposed (using principal components analysis) to estimate basis functions that represent the functional curve. Period effects from the fitted functions 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 extension of the Pegels modeling framework for selecting among exponential smoothing methods. Overall, breast cancer mortality rates in Australia remained relatively stable from 1960 to the late 1990's but declined over the last few years. A set of K=4 basis functions minimized the mean integrated squared forecasting error (MISFE) and accounts for 99.3% of variation around the mean mortality curve. 20 year forecast suggest a continual decline at a slower rate and stabilize beyond 2010 and by age, forecasts show a decline in all age groups with the greatest decline in older women. We illustrate the utility of a new modelling and forecasting approach to model breast cancer mortality rates using a functional model of age. The methods have the potential to incorporate important covariates such as Hormone Replacement Therapy (HRT) and interventions to represent mammographic screening. This would be particularly useful for evaluating the impact of screening on mortality and incidence from breast cancer.
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