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A second issue is the validity of the conclusions drawn from these methods. Rosenbaum stressed that statistical significance is an unreliable proxy for the degree of association between an exposure and an outcome. He proposed that higher correlation can be achieved by a better specification of the model, and a more appropriate definition of the outcome. Greenland made a similar point: He recommended that we “not focus on the magnitude of the parameter estimates, but rather look at the extent to which the parameter estimates agree with the direction of the predicted effects” and to “be careful about interpreting statistical significance” (15).
Greenland’s approach is a promising and valuable direction, although his use of the “significance” of the coefficient for the sake of the conclusion seems overly specific. The sense of his approach is to develop a numerical method for calculating the effect of an unmeasured variable on the causal effect, as compared to Rosenbaum’s analytic approach to test for the statistical significance of the coefficient in the regression model. In other words, Greenland’s approach is to make a numeric judgment of the effect size, whereas Rosenbaum’s is an analytic estimation of the probability that the coefficient is significant. Nevertheless, Greenland’s approach to sensitivity analysis may be promising for the future direction of causal inference.
This technique differs from the traditional Cox model, as it relies on the unmeasured assumption that the disability is a cause of the mortality. However, as there may be an unmeasured confounder, it is unclear if this is a valid assumption. In addition, this method may yield biased estimates of the mortality hazard ratio. The accuracy of the estimated effect depends on how much the disabled population has diverged from the disabled-free population in the pre-disability status and how informative the disability is as a cause of mortality.
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