Can Multivariate Analysis Rule Out Causality?
Marshall J. Graney · Journal of the American Geriatrics Society · 1996
In this issue of the Journal of the American Geriatrics Society, Thomas, Goode, Tarquine, and Allman examine the question of a spurious relationship between hospital-acquired pressure ulcers and subsequent death within 1 year of hospital discharge.1 They conclude: “New pressure ulcers appear to be markers for coexisting illnesses, impaired nutrition, and functional status rather than independent risk factors for mortality.” Indeed, with the introduction of other variables, the initially significant effect of pressure ulcers fades into obscurity. However, is multivariate analysis sufficient to rule out a causal relationship? There are various reasons why multivariate analysis cannot definitively rule out causality. Arguments could be based on the likelihood of sampling errors or on the validity of nonexperimental methodology in general, but we will leave these debates for another time. Instead, let us focus on a limitation of the statistical procedure itself. Thomas et al. document that pressure ulcers are a significant univariate predictor of mortality. Other variables were also found to have significant univariate associations with mortality in their data, and some of these variables — including measures of nutrition, activity level at discharge, and comorbidity — were also found to have significant multivariate associations with mortality. But an important issue that is not explicitly addressed by the multivariate analysis is the intercorrelation among the predictor variables. See also p 1435. Intercorrelation between predictor variables is a common problem faced by researchers seeking to make causal inferences. First, significant predictors of death in the final multiple regression model — nutritional status, discharge activity level, and comorbidity — are all related to both pressure ulcer incidence and death. Second, there can be no doubt that both the variables that were statistically significant in multivariate analysis and pressure ulcer incidence are markers for other variables in the etiological chain preceding death, but these variables were not specified in the model. Thus, there are reasons why the shared variance between variables cannot be automatically and uniquely attributed to either pressure ulcers, nutritional status, discharge activity level, or comorbidity. Without explicit causal models expressly designed to examine these relationships between variables, we cannot, even hypothetically, attribute all mortality effects of shared variance between pressure ulcers and other univariate predictors to factors other than pressure ulcers. An alternative statistical method to the data analysis strategy used in this study is available. Path analysis was developed and introduced in the 1930s by Sewell Wright2 and was later elaborated by C.C. Li.3 A more recent explication is also available.4 Causal inference in nonexperimental research, using path analysis, breaks down univariate associations into constituent parts, estimating direct, indirect, and total effects of variables in explicit causal models. It is usually possible to create many different causal models with the same data, and comparisons of alternative models for treatment of indirect effects are practical, interesting, and informative. Alternative causal models must be considered in reaching conclusions about causality. In this study the direct effect, per se, of pressure ulcers was found to be not statistically significant in the final model. However, these same data documented that the total effect of pressure ulcers, which includes both direct effect and indirect effects via variance shared with other predictors in the model, was statistically significant. This total effect of pressure ulcer incidence on death within 1 year of hospital discharge yields a risk odds ratio of 2.38 (χ2 = 6.05, P = .014) according to data published by Thomas et al. Association and causation are confused easily in logical reasoning, and we often hear it said that association is not causation. Perhaps the common confusion of association with causation arises because association is an essential component in making a causal inference, that is to say, association is a necessary but not sufficient argument in support of a conclusion that a causal relationship exists. However, it does not follow that because association is a necessary precondition to a causal inference, the absence of a significant direct effect estimated in multivariate analysis rules out causality. Indirect effects of incident pressure ulcers must be considered in accounting for their total effect. Although Thomas et al. present convincing results, it is possible to test many different models using their data. The ambiguity of how to attribute effects of variance shared between predictor variables reminds us that their results are based on a statistical model, not directly based on reality itself. It is likely that the relationship between pressure ulcers and mortality is a spurious result of both pressure sores and mortality being results of factors identified in the final model and factors outside the model, and this hypothesis merits documentation via path analysis. Findings from path analysis may provide further support for this study's recommendations about targeting at-risk hospital patients for nutritional, mobility as well as hospital complication interventions that will address factors that are precursors to both pressure ulcers and mortality.