پیش بینی مرگ و میر سالانه ریه و سرطان برونش با استفاده از زمان بقای فردی  Forecasting annual lung and bronchus cancer deaths using individual survival times

1. Introduction Worldwide, approximately one death in eight is due to cancer. The estimated total number of cancer deaths worldwide in 2008 was 7.6 million, and the growth and aging of the population mean that this number is expected to reach 13.2 million in 2030 (American Cancer Society, 2011). It is predicted that around 585,720 people will die of cancer in the United States in 2014, a rate of about 1,600 per day (Siegel, Jiemin, Zou, & Jemal, 2014). Since billions of dollars are spent on research, treatment, prevention, and other cancer-related costs, accurate predictions ofthe numbers of cancer deaths are important for effective planning, resource allocation, and communication (Tiwari et al., 2004). Accurate predictions of the numbers of cancer deaths are beneficial for the public sector because they enable more precise allocations of health and welfare budgets. If the predicted number of deaths does not match the actual number of cancer deaths, then the planned budgets could be either too high or inefficient, leading to difficulties for governments. Accurate predictions are also critical in the private sector. For example, accurate forecasts of the numbers of cancer deaths allow insurance firms to predict the need for cancer insurance. For these reasons, there has been a considerable amount of research in recent years relating to the forecasting of the numbers of cancer deaths using aggregate-level data. Chen et al. (2012) compared the levels of accuracyof five time series models for four-year-ahead projections of the numbers of cancer deaths. The models were as follows: (1) the state space model, (2) the Bayesian state space model (Schmidt & Pereira, 2011), (3) two versions of the joinpoint regression model (Kim, Fay, Feuer, & Midthune, 2000), (4) the Nordpred model (Møller et al., 2003), and (5) a vector autoregressive model using the Hilbert–Huang transform (Huang et al., 1998). Chen et al. (2012) showed that the joinpoint model with the modified Bayesian information criterion had the smallest error among the various models tested. Tiwari et al. (2004) improved the existing state space model and revealed that the average squared deviations across cancer sites for the new model were substantially lower than those of other benchmark models. However, so far, such models have used only aggregatelevel mortality data. On the other hand, Verdecchia, De Angelis, and Capocaccia (2002) proposed the prevalence, incidence, and analysis model (PIAMOD) for predicting numbers of deaths using incidence data. The model first fitted the incidence based on age, period, and cohort, then derived the numbers of deaths. Some studies have used survival analysis to focus on the individual hazard or survival rate. The most prominent model in survival analysis is the proportional hazards regression model, proposed by Cox (1972). Since then, the Cox model has been used widely for specifying a linear relationship between hazard or survival rates and covariates in a variety of fields, such as engineering, economics, and sociology. In biometrics, there have been studies of methods for modeling an individual’s lifetime (Hakulinen & Tenkanen, 1987; Prentice & Kalbfleisch, 1979), which have generally involved the use of parametric models. One of the most popular of these is the Weibull model (Cox, 1972). Royston and Parmar (2002) developed flexible parametric models based initially on the assumption of a proportional hazards scaling of covariate effects. This class of models was based on a transformation of the survival function using a link function.