Functional Time Series Models to Estimate Future Age-Specific Breast Cancer Incidence Rates for Women in Karachi, Pakistan

Background： Breast cancer is the most common female cancer in Pakistan. The incidence of breast cancer in Pakistan is about 2.5 times higher than that in the neighboring countries India and Iran. In Karachi, the most populated city of Pakistan, the age-standardized rate of breast cancer was 69.1 per 100,000 women during 1998-2002, which is the highest recorded rate in Asia. The carcinoma of breast in Pakistan is an enormous public health concern. In this study, we examined the recent trends of breast cancer incidence rates among the women in Karachi. Methods： We obtained the secondary data of breast cancer incidence from various hospitals. They included Jinnah Hospital, KIRAN （Karachi Institute of Radiotherapy and Nuclear Medicine）, and Civil hospital, where the data were available for the years 2004-2011. A total of 5331 new cases of female breast cancer were registered during this period. We analyzed the data in 5-year age groups 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75＋. Nonparametric smoothing were used to obtained age-specific incidence curves, and then the curves are decomposed using principal components analysis to fit FTS （functional time series） model. We then used exponential smoothing statspace models to estimate the forecasts of incidence curve and construct prediction intervals. Results： The breast cancer incidence rates in Karachi increased with age for all available years. The rates increased monotonically and are relatively sharp with the age from 15 years to 50 years and then they show variability after the age of 50 years. 10-year forecasts for the female breast cancer incidence rates in Karachi show that the future rates are expected to remain stable for the age-groups 15-50 years, but they will increase for the females of 50-years and over. Hence in future, the newly diagnosed breast cancer cases in the older women in Karachi are expected to increase. Conclusion： Prediction of age related changes in breast cancer incidence rates will provide useful information for controlling the overall burden of cancer in Pakistan and also serve as a resource for health planning in future research. Moreover, these models will be the most useful for modeling and projecting future trends of other cancers and chronic diseases.

Measuring Global Warming: Global and Hemisphere Mean Temperature Anomalies Predictions Using Sliced Functional Time Series (SFTS) Model

In this study, the sliced functional time series (SFTS) model is applied to the Global, Northern and Southern temperature anomalies. We obtained the combined land-surface air and sea-surface water temperature from Goddard Institute for Space Studies (GISS), NASA. The data are available for Global mean, Northern Hemisphere mean and Southern Hemisphere means (monthly, quarterly and annual) since 1880 to present (updated through March 2019). We analyze the global surface temperature change, compare alternative analyses, and address the questions about the reality of global warming. We detected the outliers during the last century not only in global temperature series but also in northern and southern hemisphere series. The forecasts for the next twenty years are obtained using SFTS models. These forecasts are compared with ARIMA, Random Walk with drift and Exponential Smoothing State Space (ETS) models. The comparison is made on the basis of root mean square error (RMSE), mean absolute percentage error (MAPE) and the length of prediction intervals.

Modeling Breast Cancer Incidence Rates: A Comparison between the Components of Functional Time Series (FTS) Model Applied on Karachi (Pakistan) and US Data

Several studies showed that the breast cancer incidence rates are higher in high-income (developed) countries, due to the link of breast cancer with several risk factors and the presence of systematic screening policies. Some of the authors suggest that lower breast cancer incidence rates in low-income (developing) countries probably reflect international variation in hormonal factors and accessibility to early detection facilities. Recent studies showed that the breast cancer increased rapidly among women in Pakistan (a developing country) and it became the first malignancy among females of Pakistan. Although, the incidence rates may contain important evidence for understanding and control of the disease;however in Pakistan, the breast cancer incidence data have never been available in the last five decades since independence;rather, only hospital-based data are available. In this study, we intend to apply Functional Time Series (FTS) models to the breast cancer incidence rates of United State (developed country), and to see the difference between various components (age and time) of Functional Time Series (FTS) models applied independently on the breast cancer incidence rates of Karachi (Pakistan) and US. Past studies have already suggested that the incidence of US breast cancer cases was expected to increase in the coming decades. A progressive increase in the number of new cases is already predetermined by the high birth rate that occurred during the middle part of the century, and it will lead to nearly a doubling in the number of cases in about 4 decades. We also obtain 15 years predictions of breast cancer incidence rates in United States and compare them with the forecasts of incidence curves for Karachi. Development of methods for cancer incidence trend forecasting can provide a sound and accurate foundation for planning a comprehensive national strategy for optimal partitioning of research resources between the need for development of new treatments and the need for new research directed toward primary preventive measures.