On Measures of Association for Multiple-Cause Mortality : Do We Need More Measures ?

More than 70 measures exist for analyzing the binary association of a 2x2 contingency table. Of these, only five are used in multiple-cause mortality. The aim of the paper is to answer the question of whether these measures are adequate. Building on comparative reviews of measures of association, the paper identifies three additional measures as suitable candidates. These additional measures, together with the five existing ones, are assessed for their theoretical utility based on seven criteria laid out in the paper. Subsequently, the same measures are applied to South African multiple-cause data that comprises over four million records. The multiple-cause software Cause_limp v1.1 was used to extract the data for the cell entries of the 2x2 contingency table, with diabetes as a multiple-cause and cardiac arrest as a co-morbid condition. The paper concludes that existing measures of multiple-cause mortality need to be supplemented with other measures, in particular the Positive Matching Index (PMI). This measure is found to satisfy all the criteria laid out, and produces the most consistent results among all the measures compared.


Résumé
Il existe plus de 70 mesures pour analyser les associations binaires de la méthode croisée 2x2.De ces mesures, seulement cinq sont utilisées dans les cas de cause complexe de mortalité.Le but de l'article est de répondre à la question de savoir si ces mesures sont adéquates.En renforçant les critiques comparatives des mesures d'association, l'article identifie trois mesures additionnelles pouvant convenir.Ajoutées aux cinq mesures qui existent déjà, ces mesures additionnelles sont évaluées à la lumière de leur utilité théorique basée sur sept critères énoncés dans l'article.Par la suite, les mêmes mesures sont appliquées aux données relatives aux causes complexes de mortalité In multiple causes of death, two co-morbid causes can be found together in a record (a) or can both be absent from it (d).Further, a record can contain either of the two co-morbid causes (b or c).Ideally, the recorded causes of death should depend on the actual causes present at the time of death.In such a situation, the values of the cells a, b, c, and d would be accurate and objective.In reality, recorded causes of death depend on several factors.One important factor is the place of death.More information is available for deaths taking place in hospitals than those taking place out of hospitals or after discharge.Part of the reason for this is that deaths taking place in hospitals have been attended by physicians and hence are more likely to have more complete medical charts and hence more information on causes of death than deaths taking place out of hospitals (Wall et al. 2005).Another factor pertains to the certification practices of physicians.This is partly related to the training of physicians and the "acceptability" among physicians of recording certain causes of death (Speizer et al. 1977).Yet another factor has to do with coding practice in the statistical office.Variation in coding practices, for policy reasons or otherwise, could lead to some discrepancies between actual and recorded causes of death (Jougla et al. 2008).For these and other reasons, the 2x2 matrix in multiple-cause analysis reflects both the actual number of deaths due to the different co-morbid combinations as well as other factors related to the certification and coding processes.This makes analysis of association in multiplecause data slightly different from that in other disciplines, such as ecology, for example.Taking these factors into account, we propose below criteria for a useful measure of association for multiple-cause mortality.In proposing the criteria, we draw upon existing work in the area by Janson and Vegelius (1981), Tulloss (1997), and Warrens (2008a, 2008b).We review their criteria in the light of their relevance to multiple-cause analysis.Relevant ones are accepted and/or modified, and irrelevant ones are dropped from the selected criteria.
The proposed criteria for an ideal index of multiple-cause association are as follows: • The ideal measure of association M should have a minimum of zero (0) when there is no occurrence of the two disease conditions together (Janson and Vegelius 1981; Tulloss 1997);

•
The ideal measure of association M should have a maximum value of unity (1) when the two disease conditions are always together (Janson and Vegelius 1981; Tulloss 1997); • Since theoretically each value of the 2x2 matrix could be zero, the multiplecause index of association M should either be free of indeterminacies or should be defined in such as way that indeterminacies are avoided (Warrens 2008a);

Introduction
An extant problem in the analysis of multiple-cause mortality is to study the joint occurrence of two different causes of death.From the joint occurrence, different patterns of association can be studied, and these have implications for understanding causation, as well as assessing the quality of coding.The starting point in this kind of analysis is summarization of the data in a 2x2 binary table.The two columns show the presence or absence of a disease of interest, and the rows would show the presence or absence of a co-morbid condition of interest.Once this has been done, analysis of the contingency table could then draw upon the rich body of knowledge on indices of association (similarity) to summarize the tables.Surprisingly, this approach has been lacking in the literature.The different measures used in multiple-cause mortality have been summarized in Bah and Mahibur Rahman (2009).The paper identifies ten measures of association used in multiple-cause mortality research.Of these measures, only five can be derived from a 2x2 contingency table.But based on 2x2 contingency table, there are over 70 indices of similarity coming from an active area of multidisciplinary research spanning a period of over a century (Choi et al. 2010).The paper draws upon this rich literature to select some indices with potential relevance to multiple causemortality analysis.Some of the measures are then applied to real data.The methods and materials used for the application are described, followed by a description of the results.The results are discussed in light of the question posed in the paper, and finally a conclusion is reached.

Methods and materials
This section is divided into two parts; one part deals with the theoretical assessment of measures of association, with the aim of arriving at ideal measure(s) of association for multiple-cause mortality.The second part deals with the application of the reviewed measures to real data, with the aim of empirically reconfirming the appropriateness of the chosen measure(s) of association.

Theoretical assessment
The general framework used for the measures of association is the 2x2 contingency table shown in Table 1.
en Afrique du Sud, comprenant plus de quatre millions de dossiers.On a utilisé le logiciel de cause complexe Cause_limp v1.

Application to real data
The data used in the study is the national data on causes of death in South Africa and covers the period 1997 to 2005.The data for this study period consist of a little over 4.2 million records.The variables used in the analysis are the following: age, sex, all the multiple causes listed on the certificate (five causes in all), the underlying cause of death, the province of residence, and the province of death.The first stage of the analysis of the cause of death data was done using Cause_Limp v1.1, a public-domain software application for analysing South African multiple-cause data (Bah 2009).The software routinely eliminates all stillbirths and deceased cases with unknown sex before doing a sex-specific analysis.The geographic filter also allows one to specify region of residence and region of death.In this case, the analysis is restricted to those whose region of residence and of death are the same.The perspective used is that of the resident population.The software produces the contingency tables used for computing different indices of similarity.
For illustrative purposes, the disease of interest chosen is diabetes (ICD 10 codes: E10-E14) and the co-morbid condition selected is cardiac arrest (ICD 10 code: I46).Part of the reason for choosing these causes of death is that they are not diseases that physicians would shy away from reporting if they were found to be present.In the South African context, these are not considered as disease, having any stigma attached to them, unlike a disease such as HIV.

Results
As with the section on methods and materials, this section is divided into two parts.The first part deals with the results of the theoretical assessment of the different selected measures in the light of the criteria laid out above, and the second sections deals with their practical application.

Results of the theoretical assessment
The results in Table 4 show that only the PMI has a range from 0 to 1, and only the PMI satisfies all the seven criteria laid out above.We apply these seven criteria to the five existing association measures of multiple-cause mortality as described in Bah and Mahibur Rahman (2009).These are given in Table 2.We add to these the "best" recommended measures according to the reviews summarised in Appendix 1.The TSI has not been included, as it has been superseded by the PMI.These measures are shown in Table 3.

Results of the application to real data
The cell entries for the 2x2 table involving diabetes and cardiac arrest are shown in Table 5.The results were obtained from Cause_Limp v1.1.From these cell entries, all the selected indices of association were computed.These results are shown in Tables 6 and 7, for males and females, respectively.The same results are graphically shown in Figures 1a and 1b for males, and in Figures 2a and 2b for females.
The results from Table 5 show that for both males and females the number of cases with cardiac arrest as a co-morbid condition with diabetes present (a) or without diabetes (b) declined rapidly between 1997 and 2000 but remained largely stable afterwards.Not surprisingly, the increase in deaths experienced in South Africa during the 2000s is reflected in the deaths not related to cardiac arrest (c and d).
With the exception of the PMI, none of the measures reviewed in the paper was able to capture this reality.Only the PMI reflected this reality, showing a decline between 1997 and 2000 and constancy afterwards.find the existing measures to be wanting.It is known that during the 2000s South African mortality increased rapidly.This has mostly been attributed to the increase in deaths due to HIV/AIDS (Bah 2005).What is also known (from this study) is that the multiple causes of death due to diabetes and cardiac arrest exhibited two different trends during the study period.Between 1997 and 2000, there was a fairly rapid decrease in the number of cases of deaths due to cardiac arrest, with or without diabetes.Afterwards, the trend remained largely stationary.Of all the different measures used in the study, the-above described pattern was best captured by the PMI, for both males and females.One of the main reasons for this is that the PMI excludes the "non-matches" of no cardiac arrest and no diabetes, and hence is protected from the influence of the rapid increase in those deaths.All the other measures had included "non-matches" and hence exhibited an unrealistic fluctuating trend during the study period.

Conclusion
This study has shown that the existing measures of multiple-cause association have been found to be inadequate.They do not satisfy all the seven criteria set forth for the qualities of an ideal measure of multiple-cause association.The measures also performed poorly upon application to real multiple-cause data.One of the main reasons for the shortcoming in these existing measures is their inclusion of non-matches.The PMI, on the other hand, fulfilled all the criteria set forth and performed very well on real multiple-cause data.It is recommended that the PMI be used for studies on multiple-cause association based on a 2x2 matrix of the presence/absence of two co-morbid conditions.

Discussion
The question posed in this paper is whether we need more measures of association for multiple-cause mortality.The corollary to this question is whether the existing measures of association used in multiple-cause mortality are adequate.Our analysis leads us to the answer that existing measures of association for multiple-cause mortality are not adequate enough.The measures fail to satisfy all the theoretical criteria set forth in the paper.These criteria are well established and build upon existing works on measures of association in other fields.When we compare the performance of the measures against actual developments we still