Abstract
A method is presented for estimating the “underlying” infant mortality rates for areas with small populations, described and illustrated in a case study that estimates infant mortality rates for 66 of 89 local health areas in British Columbia where reported births were less than 649 in 2011, including 38 reporting zero infant deaths. The method generates non-zero infant mortality rates for all 66 districts. Although some judgment is needed with the method, it has sufficient transparency that estimates can be replicated. The results support the argument that the method can produce reasonable estimates of underlying infant mortality rates for small populations subject to high levels of stochastic variation.
Résumé
Une méthode est présentée pour estimer les taux de mortalité «sous-jacents» dans des zones à population réduite. Cette méthode est décrite et illustrée à l’aide d’une étude de la mortalité infantile au sein de 66 des 89 zones de santé de la Colombie-Britannique où les naissances déclarées étaient inférieures à 649 en 2011, et parmi lesquelles 38 zones ne signalaient aucun décès avant l’âge d’un an. La méthode génère des taux de mortalité infantile non nuls pour l'ensemble des 66 districts. Bien que la méthode nécessite un certain jugement, elle est suffisamment claire pour que les estimations puissent être répliquées. Les résultats corroborent l'argument selon lequel la méthode peut produire des estimations raisonnables des taux sous-jacents de mortalité infantile pour de petites populations soumises à de fortes variations stochastiques.
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Notes
Murray (1996) has argued that the infant mortality rate is flawed when it is used as an index of overall mortality (i.e., the mortality regime affecting a given population) and that Disability Adjusted life Expectancy (DALE) should be used in its place. However, it has been pointed out by Reidpath and Allotey (2003) that the infant mortality rate and the DALE are so highly correlated that it merely goes to reinforce the intuition that the causes of infant mortality are strongly related to those structural factors like economic development, general living conditions, social well-being, and environmental factors, and, and such, the infant mortality rate remains a useful and comparatively inexpensive indicator of population health. Guillot et al. (2013) also note that infant mortality is responsive to changes in annual mortality conditions because it involves a short lag between the timing of mortality exposures and the timing of corresponding births.
Although it uses a different context and terms, another example of the entire process can be found in Robinson (2015).
The third quartile was used as the point to distinguish between large populations and small populations because the distribution of populations across a given type of administrative area tends to be skewed. This effect is commonly known as the “rank-size rule” or “rank-size distribution” (Zipf 1949; Massey et al. 1980; Stephan and Stephan 1984; Swanson and Stephan 2004). When the births by Local Health Area were ranked in descending order and plotted, a distinct plateau is seen that starts approximately at the 74th percentile (approximately the third quartile) and continues approximately to the 11th percentile, whereupon the number again increases. The plateau suggested that those at or above this level were different in terms of size than those below this level. Other ways could be used to distinguish between large and small populations that may be useful. However, given that this paper represents an initial exploration of this method, it seems appropriate to examine other ways to distinguish large from small populations in subsequent research.
Note that as stated in the text, the validity test mimics the fact that for its 58 counties California reports IMRs only for 43 of them for the 2009–2011 period, leaving the remaining 15 counties without reported IMRs. As such, the validity test was set up as if there were 43 units for which IMRs were reported and 15 for which they were not. However, all of the data used in the validity test were generated from the synthetic population that is based on Model Life Table, level 23, as described in the text. The reporting structure as well as the actual data for California can be found through the Open Portal service provided by the California Health and Human Services Agency via a download of a CVS data set assembled by the California Department of Public Health. This data set can be accessed by going to https://data.chhs.ca.gov/dataset/infant-mortality-deaths-per-1000-live-births-lghc-indicator-01/resource/ae78da8f-1661-45f6-b2d0-1014857d16e3 and then clicking on the “download” tab, which downloads the file, “Infant Mortality, Deaths Per 1000 Live Births (LGHC Indicator 01) (CSV)” in CVS form. Once downloaded, it can be saved as an excel file. The data in this file include the infant mortality rates (identified as “rate” in the file) and the infant deaths (identified as “numerator” in the file) and live births (identified as “denominator” in the file) used to calculate the IMRs for all counties and other administrative areas, including the state as a whole. The data represent the period 2009–2011. A description of the methods, caveats, and so forth associated with this data set can be found on the ULR shown above.
In the validity test, different populations are simulated from a common beta-distribution, and the result is that the two sets of populations, large and small, are normally distributed around the intrinsic mean IMR of the “population.” The simulation shows that the adjusted IMRs of the small populations move closer the underlying IMR, which indicates that the method works when both the small and large populations represent samples taken from the same underlying population. If the small populations represent a sample from a different population than the sample of large population, then the adjustment may yield a “biased” estimate of the former’s underlying IMR. This shows the importance of having a reference set that conceptually represents a sample from the same underlying population as the small population sample. One way to visualize the unbiased and biased outcomes is to picture the case where the method yields: (1) an “unbiased” estimate, which is when the mean IMR of the large populations is between the underlying IMR and the mean IMR of the small populations, and (2) a “biased” estimate when the method does not move the mean IMR for the small population closer to its underlying IMR, which occurs where the mean IMR of the small population is between the underlying IMR and the mean IMR of the large populations.
Although Green and Armstrong (2015) discuss simple vs. complex methods in terms of forecasting, their discussion applies here in that the beta-binomial approach falls into the simple methodological category rather than the complex category. Adapting their discussion to methods in general, the work of Green and Armstrong (2015) suggests that while there is no evidence that shows complexity improves accuracy, complexity remains popular among (1) researchers, because they are rewarded for publishing in highly ranked journals, which favor complexity; (2) methodologists, because complex methods can be used to provide information that support decision makers’ plans; and (3) clients, who may be reassured by incomprehensibility. We believe that the argument by Green and Armstrong (2015) can be applied to Bayesian methods, which represents the “complex” alternative to the “simple” beta-binomial approach. We prefer the beta-binomial approach, however, not only because of the argument presented by Green and Armstrong, but also because the application of a Bayesian approach can be difficult, effortful, opaque, and even counter-intuitive (Goodwin 2015).
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Acknowledgments
The author thanks the following for suggestions and advice: Dr. Augustine Kposowa (Professor, University of California Riverside), Dr. Richard Verdugo (retired, National Education), Dr. Jack Baker (Chief Analyst, HealthFitness Corporation), and Dr. Tom Burch (Affiliated Professor, University of Victoria). In addition, comments by two anonymous reviewers were very useful.
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Swanson, D.A. Estimating the Underlying Infant Mortality Rates for Small Populations, Even Those Reporting Zero Infant Deaths: a Case Study of 66 Local Health Areas in British Columbia. Can. Stud. Popul. 46, 173–187 (2019). https://doi.org/10.1007/s42650-019-00014-7
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DOI: https://doi.org/10.1007/s42650-019-00014-7