Table 3. Multivariate analysis of the predictors of MCI or dementia versus NC among all subjects by fitting multiple logistic regression model with the stepwise variable selection method.

Covariate	Estimated Regression Coefficient	Estimated Standard Error	z Value	p Value	Estimated Odds Ratio	95% C.I. of Odds Ratio
Intercept	30.069	9.211	3.26	0.0011	–	–
MoCA score (0, 1, …, 30)	-0.817	0.240	-3.40	0.0007	0.4416	0.276–0.707
Food preparation score of the Lawton IADL scale in the past (0, 1)	-4.798	1.608	-2.98	0.0028	0.0082	< 0.001–0.193
Calculation score of the MMSE (0, 1, …, 5)	-1.986	0.953	-2.08	0.0371	0.1372	0.021–0.888

Abbreviations: NC, Normal control; MCI, Mild cognitive impairment; MoCA, Montreal Cognitive Assessment; MMSE, Mini-Mental State Examination; Lawton IADL scale, Lawton Instrument Activities of Daily Living scale; and 95% C.I., 95% Confidence Interval.

Goodness-of-fit assessment: n = 102, the estimated area under the Receiver Operating Characteristic (ROC) curve = 0.99 > 0.7, and the modified Hosmer and Lemeshow goodness-of-fit F test p = 0.7479 > 0.05 (df = 9, 92), which indicated an excellent fit.

Prediction: To calculate the estimated probability of being MCI or dementia (i.e., the predicted value, ${\widehat{P}}_i$) given the observed covariate values, we can use the following formula. According to the above fitted multiple logistic regression model

$$\begin{array}{l}\mathrm{logit}\left({\widehat{P}}_i\right)=\log \left(\frac{{\widehat{P}}_i}{1‑{\widehat{P}}_i}\right)\\ =30.069‑0.817\times \left(\mathrm{MoCA}\mathrm{score}\right)‑4.798\times \left(\mathrm{food}\mathrm{preparation}\mathrm{score}\mathrm{of}\mathrm{the}\mathrm{Lawton}\mathrm{IADL}\mathrm{scale}\mathrm{in}\mathrm{the}\mathrm{past}\right)‑1.986\times \left(\mathrm{calculation}\mathrm{score}\mathrm{of}\mathrm{the}\mathrm{MMSE}\right)\end{array}$$

the predicted value of observation i is

$${\widehat{P}}_i=\frac{1}{1+\exp \left\{‑\left[30.069‑0.817\times \left(\mathrm{MoCA}\mathrm{score}\right)‑4.798\times \left(\mathrm{food}\mathrm{preparation}\mathrm{score}\mathrm{of}\mathrm{the}\mathrm{Lawton}\mathrm{IADL}\mathrm{scale}\mathrm{in}\mathrm{the}\mathrm{past}\right)‑1.986\times \left(\mathrm{calculation}\mathrm{score}\mathrm{of}\mathrm{the}\mathrm{MMSE}\right)\right]\right\}}$$

where the MoCA score = 0, 1, …, or 30, food preparation score of the Lawton IADL scale in the past = 0, or 1, and calculation score of the MMSE = 0, 1, …, or 5.