This paper considers an improved confidence interval for the average annual percent change in trend analysis, which is based on a weighted average of the regression slopes in the segmented line regression model with unknown change-points. The performance of the improved confidence interval proposed by Muggeo is examined for various distribution settings, and two new methods are proposed for further improvement. The first method is practically equivalent to the one proposed by Muggeo, but its construction is simpler and it is modified to use the t-distribution instead of the standard normal distribution. The second method is based on the empirical distribution of the residuals and the resampling using a uniform random sample, and its satisfactory performance is indicated by a simulation study.

Since its release of Version 1.0 in 1998, Joinpoint software developed for cancer trend analysis by a team at the US National Cancer Institute has received a considerable attention in the trend analysis community and it became one of most widely used software for trend analysis. The paper published in Statistics in Medicine in 2000 (a previous study) describes the permutation test procedure to select the number of joinpoints, and Joinpoint Version 1.0 implemented the permutation procedure as the default model selection method and employed parametric methods for the asymptotic inference of the model parameters. Since then, various updates and extensions have been made in Joinpoint software. In this paper, we review basic features of Joinpoint, summarize important updates of Joinpoint software since its first release in 1998, and provide more information on two major enhancements. More specifically, these enhancements overcome prior limitations in both the accuracy and computational efficiency of previously used methods. The enhancements include: (i) data driven model selection methods which are generally more accurate under a broad range of data settings and more computationally efficient than the permutation test and (ii) the use of the empirical quantile method for construction of confidence intervals for the slope parameters and the location of the joinpoints, which generally provides more accurate coverage than the prior parametric methods used. We show the impact of these changes in cancer trend analysis published by the US National Cancer Institute.

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ImportanceTo make wise decisions about the health risks they face, people need information about the magnitude of the threats as well as the context, such as how risks compare. Such information is often presented by age, sex, and race but rarely accounts for smoking status, a major risk factor for many causes of death.ObjectiveTo update the National Cancer Institute’s Know Your Chances website to present mortality estimates for a broad set of causes of death and all causes combined by smoking status in addition to age, sex, and race.Design, Setting, and ParticipantsIn this cohort study, mortality estimates using life table methods were calculated with the National Cancer Institute’s DevCan software package, combining data from the US National Vital Statistics System, National Health Interview Survey–Linked Mortality Files, National Institutes of Health–AARP (American Association of Retired Persons), Cancer Prevention Study II, Nurses’ Health and Health Professions follow-up studies, and Women’s Health Initiative. Data were collected from January 1, 2009, to December 31, 2018, and analyzed from August 27, 2019, to February 28, 2023.Main Outcomes and MeasuresAge-conditional probabilities of dying due to various causes and all causes combined, accounting for competing causes of death, for people aged 20 to 75 years over the next 5, 10, or 20 years by sex, race, and smoking status.ResultsA total of 954 029 individuals aged 55 years or older (55.8% women) were included in the analysis. Regardless of sex or race, for never-smokers, coronary heart disease represented the highest 10-year chance of death after about 50 years of age, which is higher than for any malignant neoplasm. Among current smokers, the 10-year chance of death due to lung cancer was almost as high as for coronary heart disease in each group. For Black and White female current smokers aged from the mid-40s onward, the 10-year probability of death due to lung cancer was substantially higher than for breast cancer. After 40 years of age, the observed effect of never vs current smoking on the 10-year chance of death due to all causes approximated adding 10 years of age. After 40 years of age when conditioning on smoking status, mortality risk for Black individuals was approximately that of White individuals 5 years older.Conclusions and RelevanceUsing life table methods and accounting for competing risks, the revised Know Your Chances website presents age-conditional mortality estimates according to smoking status for a broad set of causes in the context of other conditions and all-cause mortality. The findings of this cohort study suggest that failing to account for smoking status results in inaccurate mortality estimates for many causes—namely, they are too low for smokers and too high for nonsmokers.