Increased efficiency of analyses: cumulative logistic regression vs ordinary logistic regression.

The common practice of collapsing inherently continuous or ordinal variables into two categories causes information loss that may potentially weaken power to detect effects of explanatory variables and result in Type II errors in statistical inference. The purpose of this investigation was to illustrate, using a substantive example, the potential increase in power gained from an ordinal instead of a dichotomous specification for an inherently continuous response. Ordinary (OLR) and cumulative logistic regression (CLR) modeling were used to test the hypothesis that the risk of alveolar bone loss over 2 years is greater for subjects with poorer control of non-insulin-dependent diabetes mellitus (NIDDM) than for those who do not have diabetes or have better controlled NIDDM. There were 359 subjects; 21 of whom had NIDDM. Analysis of main effects using OLR for the dichotomous outcome (no change in radiographic bone loss vs any change) produced parameter estimates for better control and poorer control that were not statistically significant. CLR analysis of main effects using a 4-category ordinal specification for radiographic bone loss also produced a parameter estimate for better control that was not statistically significant, but which estimated poorer control to have a significant effect. The fit of this CLR model was significantly better at P < 0.05 than that for the OLR. While an OLR model testing the interaction between age and control status did not converge after 100 iterations, the CLR interaction model converged without difficulty and estimated a significant effect for interaction between age and poorer control. Results from the CLR analysis, in contrast to the OLR model, would lead one to conclude that the risk for more severe bone loss progression after 2 years is greater in subjects with poorer controlled NIDDM and that subjects with better controlled NIDDM may not have greater risk of bone loss progression than those without diabetes. The use of an ordinal instead of a dichotomous specification for an inherently continuous response provided increased power, more precise parameter estimates, and a significantly better fitting model. In estimating parameter estimates for odds ratios or risks, it is important to consider using ordinal logistic regression where the response is inherently continuous or ordinal.