the attached paper uses simple linear regression models to estimate rates of decline of uncond prob dying.

Dear James,

Thank you so much for sharing the paper by Kwan et al. and suggest the application of log-linear regression model for assessing the progress of premature NCD mortality.

Best regards,

Ramon

Method 1: Log-linear regression model for assessing the progress of premature NCD mortality.

Kwan uses log-linear regression model ( logYi = α + βXi + εi ) to estimates the annual percent change (APC) derived from the slope coefficient β by the formula: APC = { Exp(β) -1} * 100

APC is interpret as the percent change of the response variable Y (probability of dying) per year.

In general terms, it could be interpret as percent of change of the response Y per unit of the independent variable X

In the case of assessing the progress of probability of dying from NCDs on year, the APC provides information about the rate of change per year and the type of trend in the period of time. For instance, for an APC equal to -2% says that the probability of dying is "decreasing" at a rate of 2% per year. Estimates of the APC uncertainty intervals provide information to test if the trend slope is different to zero.

The APC can be used to say that under the assumption that the trend continues, the target can be reach in certain year, or if the target is on track to be reached in a certain year.

Method 2: Joinpoint regression analysis

Method 1 has two disadvantages: 1) it assumes linearity of the trend (on a log scale) over the interval, which is not true in certain cases; and 2) it fails to characterize the trend when there is a high variability of the underlying data (e.g, sparse or small number data, data from the small geographic areas). The Joinpoint regression method overcomes those limitations.

More information about Joinpoint regression analysis is available here: https://surveillance.cancer.gov/joinpoint/

I also suggest to read this paper:

Clegg LX, Hankey BF, Tiwari R, Feuer EJ, Edwards BK. Estimating average annual per cent change in trend analysis. Statistics in Medicine. 2009;28(29):3670-3682. doi:10.1002/sim.3733. Available online: Article Comment on 'Estimating average annual per cent change in tre...

Any other method?

What about time series methods? Let's say exponential smoothing methods to project/forecast the response variable till the specific time when the target should be met.

Looking forward to your ideas. I will summarize all recommendations

If you want to be part of this effort, just let me know.

Best

Ramon

My first thought is to look at the rates of these deaths between the last-known rate of death and the rate of death at your current measuring point. Compare with a one-tailed test to determine if the current rate is significantly lower than the past rate.

This research paper [1] follows a different approach for measuring progress of indicators.

On the basis of past trends, indicator values were projected using a weighted average of the indicator and annualized rates of change from 1990 to 2016 with weights for each annual rate of change based on out-of-sample validity. There is more detailed information about this method on the paper.

[1] GBD 2016 SDG Collaborators. Measuring progress and projecting attainment on the basis of past trends of the health-related Sustainable Development Goals in 188 countries: an analysis from the Global Burden of Disease Study 2016. The Lancet. 12 Sept 2017: 390; 1423–59. 

Full-text available online: https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(17)32336-X/fulltext

Landrigan PJ, Fuller R, Acosta NJR, Adeyi O, Arnold R, et al. The Lancet Commission on pollution and health. The Lancet [Internet] 2017 Oct 19 [cited 2017 Dec 1];386:No. 10006 Available from: http://www.thelancet.com/commissions/pollution-and-health