Misuses of correlation and regression analyses in orthodontic research: The problem of mathematical coupling

Personalized redox biology: Designs and concepts

Personalized interventions are regarded as a next-generation approach in almost all fields of biomedicine, such as clinical medicine, exercise, nutrition and pharmacology. At the same time, an increasing body of evidence indicates that redox processes regulate, at least in part, multiple aspects of human physiology and pathology. As a result, the idea of applying personalized redox treatments to improve their efficacy has gained popularity among researchers in recent years. The aim of the present primer-style review was to highlight some crucial yet underappreciated methodological, statistical, and interpretative concepts within the redox biology literature, while also providing a physiology-oriented perspective on personalized redox biology. The topics addressed are: (i) the critical issue of investigating the potential existence of inter-individual variability; (ii) the importance of distinguishing a genuine and consistent response of a subject from a chance finding; (iii) the challenge of accurately quantifying the effect of a redox treatment when dealing with 'extreme' groups due to mathematical coupling and regression to the mean; and (iv) research designs and analyses that have been implemented in other fields, and can be reframed and exploited in a redox biology context.

Profile changes following extraction orthodontic treatment: A comparison of first versus second premolar extraction

OBJECTIVE

To determine the change in the soft tissue profile following extraction orthodontic treatment with either first or second premolar extractions.

METHODS

This was a retrospective clinical study of 81 consecutive orthodontic patients treated with extraction of four premolars. Patients were divided into two treatment groups according to whether four first premolar teeth (PM1 treatment group, n=48) or four second premolar teeth were removed (PM2 treatment group, n=33) during treatment. Changes in the nasolabial angle and the distance of the upper and lower lips to E-plane were compared pre- and post-treatment. Age, sex, upper lip thickness, facial convexity, facial axis, upper and lower arch crowding at pre-treatment, use of molar anchorage and the amount of retrusion of the maxillary and mandibular incisor teeth during treatment were used as explanatory variables.

RESULTS

When facial convexity and facial axis at pre-treatment, the use of maxillary anchorage and the amount of retrusion of the maxillary and mandibular incisor teeth achieved as a consequence of treatment were taken into account, there was less than one degree (0.67°) difference between the change in the nasolabial angle in the PM1 treatment group compared to the PM2 treatment group (P>0.05). The mean change in the upper lip position relative to E-plane and the mean change in lower lip position relative to E-plane were also similar for the two groups.

CONCLUSION

The change in soft tissue profile following orthodontic treatment was similar regardless of whether first premolar or second premolar teeth were removed.

Assessing the Relationship between the Baseline Value of a Continuous Variable and Subsequent Change Over Time

Analyzing the relationship between the baseline value and subsequent change of a continuous variable is a frequent matter of inquiry in cohort studies. These analyses are surprisingly complex, particularly if only two waves of data are available. It is unclear for non-biostatisticians where the complexity of this analysis lies and which statistical method is adequate. With the help of simulated longitudinal data of body mass index in children, we review statistical methods for the analysis of the association between the baseline value and subsequent change, assuming linear growth with time. Key issues in such analyses are mathematical coupling, measurement error, variability of change between individuals, and regression to the mean. Ideally, it is better to rely on multiple repeated measurements at different times and a linear random effects model is a standard approach if more than two waves of data are available. If only two waves of data are available, our simulations show that Blomqvist’s method – which consists in adjusting for measurement error variance the estimated regression coefficient of observed change on baseline value – provides accurate estimates. The adequacy of the methods to assess the relationship between the baseline value and subsequent change depends on the number of data waves, the availability of information on measurement error, and the variability of change between individuals.

Are energy-dense foods really cheaper? Reexamining the relation between food price and energy density

BACKGROUND

The inverse relation between energy density (kcal/g) and energy cost (price/kcal) has been interpreted to suggest that produce (fruit, vegetables) is more expensive than snacks (cookies, chips).

OBJECTIVE

The objective of this study was to show the methodologic weakness of comparing energy density with energy cost.

DESIGN

The relation between energy density and energy cost was replicated in a random-number data set. Additionally, observational data were collected for produce and snacks from an online supermarket. Variables included total energy (kcal), total weight (g), total number of servings, serving size (g/serving), and energy density (kcal/g). Price measures included energy cost ($/kcal), total price ($), unit price ($/g), and serving price ($/serving). Two-tailed t tests were used to compare price measures by food category. Relations between energy density and price measures within food categories were examined with the use of Spearman rank correlation analysis.

RESULTS

The relation between energy density and energy cost was shown to be driven by the algebraic properties of these variables. Food category was strongly correlated with both energy density and food price measures. Energy cost was higher for produce than for snacks. However, total price and unit price were lower for produce. Serving price and serving size were greater for produce than for snacks. Within food categories, energy density was uncorrelated with most measures of food price, except for a weak positive correlation with serving price within the produce category.

CONCLUSION

The findings suggest the relation between energy density and food price is confounded by food category and depends on which measure of price is used.

Improving the concordance between various anteroposterior cephalometric measurements using Procrustes analysis

The aim of this study was to investigate a method which minimizes the effects of geometric distortion on various cephalometric measurements used to determine sagittal discrepancy, such as ANB angle, Wits appraisal, AB plane angle, projections on the palatal plane, Frankfort horizontal (FH) plane, the mandibulomaxillary bisector, and the SN line, in an attempt to optimize the correlation between them. This was accomplished by superimposing the Bolton 12-year male-female averaged template on a patient's tracing using Procrustes analysis and performing measurements while exchanging the patient's reference landmarks/planes (point N, the mandibulomaxillary bisector, FH plane, occlusal plane, palatal plane, and SN line) with those of the template. The normalized measurements were then compared with their classic counterparts using correlation coefficients. The above cephalometric analyses, classic and normalized, were applied to 71 patients [26 males: mean age 13.1 years, standard deviation (SD) 1.1 years and 45 females: mean age of 14.6 years, SD 8.2 years]. Spearman's rank correlation coefficient was calculated between the classic measurements and their normalized counterparts, resulting in a consistent increase in the correlation between the normalized measurements in comparison with the classic ones. This increase varied in absolute value from 0.052 to 0.405. All normalized measurements were highly correlated (P > 0.742, absolute value). Although correlation calculations do not represent a true measure of diagnostic performance, it is hoped that improving their correspondence heightens the possibility of the different tests agreeing on the patient's sagittal discrepancy, decreasing the possibility of differing, or even totally opposing diagnostic outcomes resulting from their application to (clear-cut) Class I, II, and III patients.