A partial SMR approach to smoothing age-specific rates

Age-specific rates are the fundamental measures in epidemiology. For a small population, however, rate estimates can become unstable and the age curve may contain too much random variability to adequately assess the true underlying pattern. A further problem arises when one wishes to log-transform a rate with a zero count in its numerator. The author proposes a simple and non-iterative method to stabilize rates.

The method, referred to as the "partial SMR approach," relies on finding a standard population with a similar age curve with the study population. Real and simulated data were used to demonstrate its properties.

It is found that the choice of the standard is not critical. The method will offset automatically the role of a "dissimilar" standard; and according to the limited simulation studies, the result is still better than no smoothing. The method can also smooth the age curve adaptively, i.e., smoothing to varying degree according to internal stability of each age category. The method is asymptotically unbiased and does not have the zero-count problem. Among the various smoothing methods we have studied, the partial SMR smoothing produces the smallest mean square error and has the highest probability of successful capture of the specific pattern and trend in the age curve.

The partial SMR smoothing is a simple and effective method for smoothing age-specific rates.