Mathematical coupling can undermine the statistical assessment of clinical research: illustration from the treatment of guided tissue regeneration

Identifying predictors of resilience to stressors in single-arm studies of pre-post change

Many older adults experience a major stressor at some point in their lives. The ability to recover well after a major stressor is known as resilience. An important goal of geriatric research is to identify factors that influence resilience to stressors. Studies of resilience in older adults are typically conducted with a single-arm where everyone experiences the stressor. The simplistic approach of regressing change versus baseline yields biased estimates due to mathematical coupling and regression to the mean (RTM). We develop a method to correct the bias. We extend the method to include covariates. Our approach considers a counterfactual control group and involves sensitivity analyses to evaluate different settings of control group parameters. Only minimal distributional assumptions are required. Simulation studies demonstrate the validity of the method. We illustrate the method using a large, registry of older adults (N  =7239) who underwent total knee replacement (TKR). We demonstrate how external data can be utilized to constrain the sensitivity analysis. Naive analyses implicated several treatment effect modifiers including baseline function, age, body-mass index (BMI), gender, number of comorbidities, income, and race. Corrected analysis revealed that baseline (pre-stressor) function was not strongly linked to recovery after TKR and among the covariates, only age and number of comorbidities were consistently and negatively associated with post-stressor recovery in all functional domains. Correction of mathematical coupling and RTM is necessary for drawing valid inferences regarding the effect of covariates and baseline status on pre-post change. Our method provides a simple estimator to this end.

Risk Factors for Non-Resilient Outcomes in Older Adults after Total Knee Replacement in the FORCE-TJR Cohort

BACKGROUND

Total knee replacement (TKR) is a common procedure in older adults. Physical resilience may be a useful construct to explain variable outcomes. We sought to define a simple measure of physical resilience and identify risk factors for non-resilient patient outcomes.

METHODS

Secondary analysis of FORCE-TJR cohort study, a prospective registry of total joint replacement. Analysis included 7,239 adults ages 60 or older who underwent TKR between 2011- 2015. Measures included sociodemographic and health factors. Outcomes were categorized as physically resilient versus non-resilient based on the change from baseline to 1-year follow up for three patient-reported outcomes: the physical component summary (PCS), bodily pain (BP), and vitality (VT) from the Short Form-36 (SF-36) subcomponent scores, at pre-op and 1-year post-procedure. Associations were expressed as relative risk of physically non-resilient outcomes using generalized linear regression models, with Poisson distribution and log link.

RESULTS

Age, BMI, and Charlson Comorbidity Index (CCI) were associated with increased risk of physically non-resilient outcomes across PCS, BP, and VT: age, per 5-years for PCS (RR=1.18[1.12-1.23]), BP (RR=1.06[1.01-1.11), and VT (RR=1.09[1.06-1.12]); BMI, per 5 Kg/m 2, for PCS (RR=1.13[1.07-1.19]), BP (RR=1.06[1.00-1.11]), and VT (RR=1.08[1.04-1.11]); and CCI for PCS CCI=1 (RR=1.38[1.20-1.59]), CCI=2-5 (RR=1.59[1.35-1.88]), CCI>=6 (RR=1.55[1.31-1.83]. Household-income >$45,000 associated with lower risk for PCS (RR=0.81[0.70-0.93]), BP (RR=0.80[0.69-0.91],), and VT (RR=0.86[0.78-0.93]).

CONCLUSIONS

We operationalized physical resilience and identified factors predicting resilience after TKR. This approach may aid clinical risk stratification, guide further investigation of causes, and ultimately aid patients through the design of interventions to enhance physical resilience.

Antidepressant treatment effects and country income: meta-regression analysis of individual participant data from duloxetine trials

OBJECTIVE

In recent decades, significant numbers of pharmaceutical trials have gradually been relocated to low- and middle-income countries. However, there is little evidence regarding the transferability of trial outcomes across countries. Analysing duloxetine randomised controlled trials (RCTs) conducted in different countries, we investigated whether per capita gross national income (GNI) and healthcare expenditure (HE) are associated with pre-post mean changes of depression severity and differences in duloxetine-placebo effect sizes.

METHOD

Meta-analyses included RCTs investigating duloxetine efficacy in patients with depression. Individual participant data (IPD) from multi-centre duloxetine trials were provided by the manufacturer. Data extracted from published reports also entered analyses in case of trials conducted in only one country. A meta-regression approach was applied to analyse associations of GNI and HE with standardised pre-post mean change using raw score standardisation (SMCR) and comparative effect size, that is, the mean differences (MD) in pre-post effect size between duloxetine and placebo treatment.

RESULTS

23 trials with 8417 randomised participants entered analyses. Regression coefficients indicated a negative linear relationship of SMCR with GNI (z-standardised β = -3.61, R²  = 14.8%, p < 0.001) and HE (β = -4.72, R²  = 24.8%, p < 0.001) for participants treated with duloxetine. Similar associations were found for placebo treatment (GNI: β = -3.52, R²  = 23.8%, p < 0.001; β = -3.34, R²  = 21.0% p < 0.001). Neither GNI nor HE was associated with the MD between duloxetine and placebo pre-post differences.

CONCLUSIONS

Findings challenge the idea of the universal transferability of antidepressant trial outcomes across countries. Understanding the results of antidepressant RCTs demands more sophisticated clarification of context factors involved in determining effectiveness of antidepressant medication and should be discussed with a view to socio-economic context in their countries of origin.

Statistical Considerations for Drawing Conclusions About Recovery

BACKGROUND

Numerous studies have found associations when change scores are regressed onto initial impairments in people with stroke (slopes ≈ 0.7). However, there are important statistical considerations that limit the conclusions we can draw about recovery from these studies.

OBJECTIVE

To provide an accessible checklist of conceptual and analytical issues on longitudinal measures of stroke recovery. Proportional recovery is an illustrative example, but these considerations apply broadly to studies of change over time.

METHODS

Using a pooled data set of n = 373 Fugl-Meyer Assessment upper extremity scores, we ran simulations to illustrate 3 considerations: (1) how change scores can be problematic in this context; (2) how "nil" and nonzero null-hypothesis significance tests can be used; and (3) how scale boundaries can create the illusion of proportionality, whereas other analytical procedures (eg, post hoc classifications) can augment this problem.

RESULTS

Our simulations highlight several limitations of common methods for analyzing recovery. We find that uniform recovery leads to similar group-level statistics (regression slopes) and individual-level classifications (into fitters and nonfitters) that have been claimed as evidence for the proportional recovery rule. New analyses, however, also speak to the complexities in variance about the regression slope.

CONCLUSIONS

Our results highlight that one cannot identify whether proportional recovery is true or not based on commonly used methods. We illustrate how these techniques, measurement tools, and post hoc classifications (eg, nonfitters) can create spurious results. Going forward, the field needs to carefully consider the influence of these factors on how we measure, analyze, and conceptualize recovery.

The effect of test modality on dynamic exercise biomarkers in children, adolescents, and young adults

Cardiopulmonary exercise testing (CPET) modalities, treadmill (TM), and cycle ergometer (CE), influence maximal gas exchange and heart rate (HR) responses. Little is known regarding CPET modality effect on submaximal biomarkers during childhood and adolescence. Ninety‐four healthy participants (7–34 y.o., 53% female) performed TM and CE CPET to address two major gaps: (1) the effect of modality on submaximal CPET biomarkers, and (2) estimation of work rate in TM CPET. Breath‐by‐breath gas exchange enabled calculation of linear regression slopes such as V˙O₂/ΔHR and ΔV˙E/ΔV˙CO₂. Lean body mass (LBM) was measured with dual X‐ray absorptiometry. We tested a novel TM CPET estimate of work rate based on TM velocity², incline, and body mass (VIM). Like the linear relationship between V˙O₂ and work rate in CE CPET, V˙O₂ increased linearly with TM VIM. TM ΔV˙O₂/ΔHR was highly correlated with CE (r = 0.92), and each increased substantially with LBM (P < 0.0001 for TM and CE). ΔV˙O₂/ΔHR was to a small (~8.7%) but significant extent larger in TM (1.6 mL/min/beat, P = 0.04). In contrast, TM and CE ΔV˙E/ΔV˙CO₂ decreased significantly with LBM, supporting earlier observations from CE CPET. For both CE and TM, males had significantly higher ΔV˙O₂/ΔHR but lower ΔV˙E/ΔV˙CO₂ than females. Novel TM CPET biomarkers such as ΔVIM/ΔHR and ∆V˙O₂/ΔVIM paralleled effects of LBM observed in CE CPET. TM and CE CPET submaximal biomarkers are not interchangeable, but similarly reflect maturation during critical periods. CPET analysis that utilizes data actually measured (rather than estimated) may improve the clinical value of TM and CE CPET.

A new approach to estimate aerobic fitness using the NHANES dataset

INTRODUCTION

Physical activity and fitness are essential for healthy growth in children. The National Health and Nutrition Examination Survey (NHANES) evaluated fitness by estimating V̇O2 max from submaximal measurements of heart rate (HR) during graded treadmill exercise. Our aims were (a) to examine how well NHANES methodology used to estimate V̇O2 max correlated with actual VO2 max and (b) to evaluate a novel fitness metric using actual data collected during exercise and its relationship to physical activity and sedentary time, lipid profiles, and body composition.

METHODS

Fifty-three adolescents completed NHANES submaximal exercise protocol and maximal graded cardiopulmonary exercise testing. We used a novel approach to quantifying fitness (Δvelocity × incline × body mass (VIM)/ΔHR slopes) and evaluated its relationship to physical activity and sedentary time using NHANES data (n = 4498). In a subset (n = 740), we compared ΔVIM/ΔHR slopes to NHANES estimated V̇O2 max and examined their relationship to cardiovascular risk factors (BMI percentiles and lipid levels).

RESULTS

Measured V̇O2 peak was moderately correlated with NHANES estimated V̇O2 max (r = 0.53, P < 0.01). Significantly higher ΔVIM/ΔHR slopes were associated with increased physical activity and decreased sedentary time. ΔVIM/ΔHR slopes were negatively associated with LDL, triglycerides, and BMI percentiles (P < 0.01). In general, the two fitness models were similar; however, ΔVIM/ΔHR was more discriminating than NHANES in quantifying the relationship between fitness and LDL levels.

CONCLUSION

We found that the NHANES estimated V̇O2 max accounted for approximately 28% of the variability in the measured V̇O2 peak. Our approach to estimating fitness (ΔVIM/ΔHR slopes) using actual data provided similar relationships to lipid levels. We suggest that fitness measurements based on actually measured data may produce more accurate assessments of fitness and, ultimately, better approaches linking exercise to health in children.

Severe acute malnutrition and mortality in children in the community: Comparison of indicators in a multi-country pooled analysis

OBJECTIVES

This study aims to describe the mortality risk of children in the community who had severe acute malnutrition (SAM) defined by either a mid-upper arm circumference (MUAC) <115mm, a low weight-for-height Z-score (WHZ) <-3 or both criteria.

METHODS

We pooled individual-level data from children aged 6-59 months enrolled in 3 community-based studies in the Democratic Republic of the Congo (DRC), Senegal and Nepal. We estimate the mortality hazard using Cox proportional hazard models in groups defined by either anthropometric indicator.

RESULTS

In total, we had 49,001 time points provided by 15,060 children available for analysis, summing to a total of 143,512 person-months. We found an increasing death rate with a deteriorating nutritional status for all anthropometrical indicators. Children identified as SAM only by a low MUAC (<115mm) and those identified only by a low WHZ (Z-score <-3) had a similar mortality hazard which was about 4 times higher than those without an anthropometric deficit. Having both a low MUAC and a low WHZ was associated with an 8 times higher hazard of dying compared to children within the normal range. The 2 indicators identified a different set of children; the proportion of children identified by both indicators independently ranged from 7% in the DRC cohort, to 35% and 37% in the Senegal and the Nepal cohort respectively.

CONCLUSION

In the light of an increasing popularity of using MUAC as the sole indicator to identify SAM children, we show that children who have a low WHZ, but a MUAC above the cut-off would be omitted from diagnosis and treatment despite having a similar risk of death.

Severely malnourished children with a low weight-for-height have similar mortality to those with a low mid-upper-arm-circumference: II. Systematic literature review and meta-analysis

BACKGROUND

The WHO recommended criteria for diagnosis of sever acute malnutrition (SAM) are weight-for-height/length Z-score (WHZ) of <- 3Z of the WHO₂₀₀₆ standards, a mid-upper-arm circumference (MUAC) of < 115 mm, nutritional oedema or any combination of these parameters. A move to eliminate WHZ as a diagnostic criterion has been made on the assertion that children with a low WHZ are healthy, that MUAC is a "superior" prognostic indicator of mortality and that adding WHZ to the assessment does not improve the prediction of death. Our objective was to examine the literature comparing the risk of death of SAM children admitted by WHZ or MUAC criteria.

METHODS

We conducted a systematic search for reports which examined the relationship of WHZ and MUAC to mortality for children less than 60 months. The WHZ, MUAC, outcome and programmatic variables were abstracted from the reports and examined. Individual study's case fatality rates were compared by chi-squared analysis and random effects meta-analyses for combined data.

RESULTS

Twenty-one datasets were reviewed. All the patient studies had an ascertainment bias. Most were inadequate because they had insufficient deaths, used obsolete standards, combined oedematous and non-oedematous subjects, did not report the proportion of children with both deficits or the deaths occurred remotely after anthropometry. The meta-analyses showed that the mortality risks for children who have SAM by MUAC < 115 mm only and those with SAM by WHZ < -3Z only are not different.

CONCLUSIONS

As the diagnostic criteria identify different children, this analysis does not support the abandonment of WHZ as an important independent diagnostic criterion for the diagnosis of SAM. Failure to identify such children will result in their being denied treatment and unnecessary deaths from SAM.

Severely malnourished children with a low weight-for-height have a higher mortality than those with a low mid-upper-arm-circumference: III. Effect of case-load on malnutrition related mortality- policy implications

BACKGROUND

Severe acute malnutrition (SAM) is diagnosed when the weight-for-height Z-score (WHZ) is <-3Z of the WHO2006 standards, or a mid-upper-arm circumference (MUAC) of < 115 mm or there is nutritional oedema. Although there has been a move to eliminate WHZ as a diagnostic criterion we have shown that children with a low WHZ have at least as high a mortality risk as those with a low MUAC. Here we take the estimated case fatality rates and published case-loads to estimate the proportion of total SAM related deaths occurring in children that would be excluded from treatment with a MUAC-only policy.

METHODS

The effect of varying case-load and mortality rates on the proportion of all deaths that would occur in admitted children was examined. We used the same calculations to estimate the proportion of all SAM-related deaths that would be excluded with a MUAC-only policy in 48 countries with very different relative case loads for SAM by only MUAC, only WHZ and children with both deficits. The case fatality rates (CFR) are taken from simulations, empirical data and the literature.

RESULTS

The relative number of cases of SAM by MUAC alone, WHZ alone and those with both criteria have a dominant effect on the proportion of all SAM-related deaths that would occur in children excluded from treatment by a MUAC-only program. Many countries, particularly in the Sahel, West Africa and South East Asia would fail to identify the majority of SAM-related deaths if a MUAC only program were to be implemented. Globally, the estimated minimum number of deaths that would occur among children excluded from treatment in our analyses is 300,000 annually.

CONCLUSIONS

The number, proportion or attributable fraction of children excluded from treatment with any change of current policy are the correct indicators to guide policy change. CRFs alone should not be used to guide policy in choosing whether or not to drop WHZ as a diagnostic for SAM. All the criteria for diagnosis of malnutrition need to be retained. It is critical that methods are found to identify those children with a low WHZ, but not a low MUAC, in the community so that they will not remain undetected.

Severely malnourished children with a low weight-for-height have a higher mortality than those with a low mid-upper-arm-circumference: I. Empirical data demonstrates Simpson's paradox

BACKGROUND

According to WHO childhood severe acute malnutrition (SAM) is diagnosed when the weight-for-height Z-score (WHZ) is <-3Z of the WHO2006 standards, the mid-upper-arm circumference (MUAC) is < 115 mm, there is nutritional oedema or any combination of these parameters. Recently there has been a move to eliminate WHZ as a diagnostic criterion on the assertion that children meeting the WHZ criterion are healthy, that MUAC is universally a superior prognostic indicator of mortality and that adding WHZ to the assessment does not improve the prediction; these assertions have lead to a controversy concerning the role of WHZ in the diagnosis of SAM.

METHODS

We examined the mortality experience of 76,887 6-60 month old severely malnourished children admitted for treatment to in-patient, out-patient or supplementary feeding facilities in 18 African countries, of whom 3588 died. They were divided into 7 different diagnostic categories for analysis of mortality rates by comparison of case fatality rates, relative risk of death and meta-analysis of the difference between children admitted using MUAC and WHZ criteria.

RESULTS

The mortality rate was higher in those children fulfilling the WHO2006 WHZ criterion than the MUAC criterion. This was the case for younger as well as older children and in all regions except for marasmic children in East Africa. Those fulfilling both criteria had a higher mortality. Nutritional oedema increased the risk of death. Having oedema and a low WHZ dramatically increased the mortality rate whereas addition of the MUAC criterion to either oedema-alone or oedema plus a low WHZ did not further increase the mortality rate. The data were subject to extreme confounding giving Simpson's paradox, which reversed the apparent mortality rates when children fulfilling both WHZ and MUAC criteria were included in the estimation of the risk of death of those fulfilling either the WHZ or MUAC criteria alone.

CONCLUSIONS

Children with a low WHZ, but a MUAC above the SAM cut-off point are at high risk of death. Simpson's paradox due to confounding from oedema and mathematical coupling may make previous statistical analyses which failed to distinguish the diagnostic groups an unreliable guide to policy. WHZ needs to be retained as an independent criterion for diagnosis of SAM and methods found to identify those children with a low WHZ, but not a low MUAC, in the community.

Toothbrushing behaviour and periodontal pocketing: An 11-year longitudinal study

AIM

To explore the association between toothbrushing behaviour and change in periodontal pocketing among adults.

METHODS

We pooled data from 1,025 adults, aged 30-89 years, who participated in two national surveys in Finland (Health 2000 and Health 2011, BRIF8901) and reported their toothbrushing frequency. A cumulative measure of regular toothbrushing was created by counting the number of times participants reported brushing twice or more daily across the two surveys (ranging from 0 to 2). The association between toothbrushing behaviour and the number of teeth with periodontal pocket depth (PPD) ≥4 mm over 11 years was assessed in linear regression models adjusting for confounders.

RESULTS

There was a clear dose-response relationship between toothbrushing frequency (either at baseline or follow-up) and change in number of teeth with PPD ≥ 4 mm. There was also evidence of a cumulative effect of regular toothbrushing on change in number of teeth with PPD ≥ 4 mm. Participants who reported brushing twice or more a day in both surveys developed 1.99 (95% CI: 1.02-2.95) fewer teeth with PPD ≥ 4 mm than those who did not report this behaviour in any survey.

CONCLUSION

This 11-year prospective study showed that toothbrushing behaviour was associated with smaller increments in the number of teeth with periodontal pocketing.

The misleading concept of initial severity in depression clinical trials: development and results from a mathematical model

OBJECTIVE

Recently, meta-analytic studies have suggested a positive relationship between initial severity and magnitude of treatment efficacy. The aim of the current study was to develop a mathematical model to test the assumption concerning the role of initial severity in treatment response.

METHODS

A number of experimental artificial datasets were developed on the basis of three different scenarios which reflect a pre-determined effect of initial severity. They were used to test for correlations at the patient level as well as at the meta-analysis level (trial level).

RESULTS

The results suggested that in all scenarios and analyses the correlations were so high that a ceiling effect was obvious. The testing concerned changes from baseline, but not differences between arms.

CONCLUSIONS

Overall the data suggest that the question concerning the role of initial severity cannot be answered. Any allegations on such a role are based on flawed methodology and do not take into consideration the true nature of data.

Caries increment in young children in Skaraborg, Sweden: associations with parental sociodemography, health habits, and attitudes

AIM

To explore parental sociodemography, oral health habits, and attitudes in relation to dental caries increment in their children.

DESIGN

A longitudinal questionnaire and clinical study. The children were followed annually from age 3 years (n = 271) to 6 years (n = 243). Carious lesions of different depth were registered (initial and manifest) by four calibrated dentists. The parents filled out a questionnaire. Statistics included factor analyses, Cronbach's alpha together with bivariate and multivariate logistic regression analyses.

RESULTS

Most of the parents exhibited positive health behaviour and attitudes. 'Late start of toothbrushing of child' was, however, common (≥1 year; 29%) and 'external locus of control' showed a high mean value (10,1; possible range 3-15). In a multivariate model, 'parent born abroad' (OR 3.26, 95% CI 1.85-5.76) and 'parental indulgence' (OR 3.20, 95% CI 1.37-7.51) were the most important for the development of carious lesions in the children.

CONCLUSIONS

This study identified 'parent born abroad' and 'parental indulgence' as significant risk factors for caries in the age period 3 to 6 years. Identifying parents with the greatest need should be emphasized, in order to target promotion and prevention activities.

Statistical Power for Analyses of Changes in Randomized Controlled Trials

Randomized controlled trials (RCTs) are widely recommended as the most useful study design to generate reliable evidence and guidance to daily practices in medicine and dentistry. However, it is not well-known in dental research that different statistical methods of data analysis can yield substantial differences in study power. In this study, computer simulations are used to explore how using different univariate and multivariate statistical methods of analyzing change in continuous outcome variables affects study power, and the sample size required for RCTs. Results show that, in general, analysis of covariance (ANCOVA) yields greater power than other statistical methods in testing the superiority of one treatment over another, or in testing the equivalence between two treatments. Therefore, ANCOVA should be used in preference to change score or percentage change score to reduce type II error rates.

Accelerated HF-rTMS Protocol has a Rate-Dependent Effect on dACC Activation in Alcohol-Dependent Patients: An Open-Label Feasibility Study

BACKGROUND

The application of accelerated high-frequency (HF) repetitive transcranial magnetic stimulation (rTMS) could be a potential treatment option for alcohol-dependent patients and may result in a faster clinical response. In this open-label HF-rTMS feasibility study, we wanted to replicate previous findings of baseline brain activation as a predictor of relapse, and to evaluate how this intervention influences the relapse neurocircuit of "treatment-seeking" alcohol-dependent patients, by means of functional magnetic resonance imaging (fMRI) cue-exposure paradigms. Because relapsing patients have a diminished resilience of the emotion regulation/cognitive control system, before HF-rTMS treatment, we expected lower neuronal activation of especially the ventromedial prefrontal cortex and anterior cingulate cortex (ACC) during the presentation of alcohol-related cues in these patients. The relapse neurocircuit should be modified after accelerated HF-rTMS treatment, only in those patients who did not relapse.

METHODS

After being administered a single sham-controlled HF-rTMS session (20 Hz to 110% motor threshold), 19 alcohol-dependent patients received an accelerated HF-rTMS protocol, consisting of 14 right dorsolateral prefrontal cortical sessions spread over 3 days. Before and after stimulation, during fMRI patients were confronted with a block and an event-related alcoholic cue-exposure paradigm. Relapse was defined as the consumption of any amount of alcohol within 4 weeks after the stimulation. A region of interest analysis was performed to evaluate how HF-rTMS exerts its effect.

RESULTS

After 4 weeks, 13 of 19 patients had already consumed alcohol. When abstainers were compared to patients who had relapsed, we found higher dorsal ACC (dACC) activation at baseline, but only during the blocked cue-exposure paradigm. The effects of HF-rTMS on dACC blood oxygen level-dependent response were negatively correlated with the baseline dACC activation. Due to susceptibility artifacts located at the ventral cortical aspects in 6 of our participants, reliable data were only obtained for the ACC.

CONCLUSIONS

Our data indicate that higher baseline dACC activation may serve as a protective mechanism regarding relapse. For the first time, it is demonstrated that accelerated HF-rTMS treatment influences dACC activation in a rate-dependent manner: the lower the baseline dACC activation, the more dACC activity was increased after HF-rTMS treatment.

A multilevel modelling solution to mathematical coupling

Owing to mathematical coupling, statistical analyses relating change to baseline values using correlation or regression are erroneous, where the statistical procedure of testing the null hypothesis becomes invalid. Alternatives, such as Oldham’s method and the variance ratio test, have been advocated, although these are limited in the presence of measurement errors with non-constant variance. Furthermore, such methods prohibit the consideration of additional covariates (e.g., treatment group within trials) or confounders (e.g., age and gender). This study illustrates the more sophisticated approach of multilevel modelling (MLM) which overcomes these limitations and provides a comprehensive solution to the analysis of change with respect to baseline values. Although mathematical coupling is widespread throughout applied research, one particular area where several studies have suggested a strong relationship between baseline disease severity and treatment effect is guided tissue regeneration (GTR) within dental research. For illustration, we use GTR studies where the original data were found to be available in the literature for reanalysis. We contrast the results from an MLM approach and Oldham’s method with the standard (incorrect) approach that suffers from mathematical coupling. MLM provides a robust solution when relating change to baseline and is capable of simultaneously dealing with complex error structures and additional covariates and/or potential confounders.

The role of sleep duration in diabetes and glucose control

Sleep curtailment is common in the Westernised world and coincides with an increase in the prevalence of type 2 diabetes mellitus (T2DM). This review considers the recently published evidence for whether sleep duration is involved in the development of T2DM in human subjects and whether sleep has a role to play in glucose control in people who have diabetes. Data from large, prospective studies indicate a U-shaped relationship between sleep duration and the development of T2DM. Smaller, cross-sectional studies also support a relationship between short sleep duration and the development of both insulin resistance and T2DM. Intervention studies show that sleep restriction leads to insulin resistance, with recent sleep extension studies offering tantalising data showing a potential benefit of sleep extension on glucose control and insulin sensitivity. In people with established diabetes the published literature shows an association between poor glucose control and both short and long sleep durations. However, there are currently no studies that determine the causal direction of this relationship, nor whether sleep interventions are likely to offer benefit for people with diabetes to help them achieve tighter glucose control.

Order in the absence of an effect: Identifying rate-dependent relationships

The heterogeneity of group data can obscure a significant effect of an intervention due to differential baseline scores. Instead of discarding the seemingly heterogeneous response set, an orderly lawful relationship could be present. Rate dependence describes a pattern between a baseline and the change in that baseline following some intervention. To highlight the importance of analyzing data from a rate-dependent perspective, we (1) briefly review research illustrating that rate-dependent effects can be observed in response to both drug and non-drug interventions in varied schedules of reinforcement in clinical and preclinical populations; (2) observe that the process of rate-dependence likely requires multiple parts of a system operating simultaneously to evoke differential responding as a function of baseline; and (3) describe several statistical methods for consideration and posit that Oldham's correlation is the most appropriate for rate-dependent analyses. Finally, we propose future applications for these analyses in which the level of baseline behavior exhibited prior to an intervention may determine the magnitude and direction of behavior change and can lead to the identification of subpopulations that would be benefitted. In sum, rate dependence is an invaluable perspective to examine data following any intervention in order to identify previously overlooked results.

Testing the relation between percentage change and baseline value

Testing the relation between percentage change and baseline value has been controversial, but it is not clear why this practice may yield spurious results. In this paper, we first explained why the usual testing of the relation between percentage change and baseline value is inappropriate and then demonstrated how the appropriate null hypothesis could be formulated. We also proposed a simple procedure for testing the appropriate null hypothesis based on the assumption that when there is no relation between percentage change and baseline value, the coefficients of variation for repeated measurements of a random variable should remain unchanged. Two examples were used to demonstrate how the usual testing gave rise to misleading results, whilst results from our simple test were in general consistent with those from simulations. We also undertook simulations to investigate the impact of measurement errors on the performance of the proposed test. Results suggested the type-I error rates increased with the magnitude of measurement errors, whilst the statistical power to detect a genuine relation decreased. The usual approach to testing the relation between percentage change and baseline value tended to yield misleading results and should be avoided.

Moderation of antidepressant and placebo outcomes by baseline severity in late-life depression: A systematic review and meta-analysis

BACKGROUND

Baseline severity is a crucial moderator of trial outcomes in adult depression, with the advantage of antidepressants over placebo increasing as severity increases. However, this relationship has not been examined in late-life depression.

METHODS

PubMed, Embase, Web of Science, PsycINFO, and Cochrane were searched for studies published through September 2014. Randomized, acute phase, and double-blind studies comparing an antidepressant group with a placebo group in depressed elderly patients were included.

RESULTS

Nineteen studies met all inclusion criteria. Within-group effect sizes revealed significant improvement in antidepressant groups (g=1.35, p<.000), as well as in placebo groups (g=.96, p<.000). Change in depressive symptoms assessed by Hamilton Depression Rating Scale (HDRS) was moderated by baseline severity in antidepressant groups (Z=2.67, p=.008) and placebo groups (Z=4.46, p<.000). However, this would be expected as a result of regression toward the mean, and mean differences between groups did not increase (r=.19, p=.469) as a function of baseline severity.

LIMITATIONS

Limited to published data and information was only analyzed at the level of treatment groups.

CONCLUSION

Baseline severity was not associated with an antidepressant-placebo difference and placebo responses are large in the treatment of depressed elderly people. We propose a stepwise approach, i.e., to initially offer elderly depressed patients psychosocial interventions and only consider antidepressants if patients do not respond.

From Randomized Controlled Trials of Antidepressant Drugs to the Meta-Analytic Synthesis of Evidence: Methodological Aspects Lead to Discrepant Findings

During the last decade, several meta-analytic studies employing different methodological approaches have had inconsistent conclusions regarding antidepressant efficacy. Herein, we aim to comment on methodological aspects that may have contributed to disparate findings. We initially discuss methodological inconsistencies and limitations related to the conduct of individual antidepressant randomized controlled trials (RCTs), including differences in allocated samples, limitations of psychometric scales, possible explanations for the heightened placebo response rates in antidepressant RCTs across the past two decades as well as the reporting of conflicts of interest. In the second part of this article, we briefly describe the various meta-analyses techniques (e.g., simple random effects meta-analysis and network meta-analysis) and the application of these methods to synthesize evidence related to antidepressant efficacy. Recently published antidepressant metaanalyses often provide discrepant results and similar results often lead to different interpretations. Finally, we propose strategies to improve methodology considering real-world clinical scenarios.

Burning issues in the meta-analysis of pharmaceutical trials for depression

During the last decade a number of meta-analytic studies have been published and they triggered a debate on the true clinical usefulness of antidepressants. The current article comments on problems within the randomized controlled trials design, the study samples, the psychometric scales, the methods of meta-analysis, the interpretation of the results, and the reporting of conflicts of interest. Although the meta-analyses published so far agree that medication works in severe depression, they question its efficacy in mild cases. However, several methodological issues should be clarified before conclusions are definite. Different methods give different results and similar results seem to entertain a variety of interpretations. In the future it is important to address all of these problems, and to improve methodology on the basis of clinically informed choices. Otherwise, meta-analysis risks alienation from clinical reality and thus risks becoming the 21(st) century psychoanalysis.

No role for initial severity on the efficacy of antidepressants: results of a multi-meta-analysis

INTRODUCTION

During the last decade, a number of meta-analyses questioned the clinically relevant efficacy of antidepressants. Part of the debate concerned the method used in each of these meta-analyses as well as the quality of the data set.

MATERIALS AND METHODS

The Kirsch data set was analysed with a number of different methods, and eight key questions were tackled. We fit random effects models in both Bayesian and frequentist statistical frameworks using raw mean difference and standardised mean difference scales. We also compare between-study heterogeneity estimates and produce treatment rank probabilities for all antidepressants. The role of the initial severity is further examined using meta-regression methods.

RESULTS

The results suggest that antidepressants have a standardised effect size equal to 0.34 which is lower but comparable to the effect of antipsychotics in schizophrenia and acute mania. The raw HDRS difference from placebo is 2.82 with the value of 3 included in the confidence interval (2.21-3.44). No role of initial severity was found after partially controlling for the effect of structural (mathematical) coupling. Although data are not definite, even after controlling for baseline severity, there is a strong possibility that venlafaxine is superior to fluoxetine, with the other two agents positioned in the middle. The decrease in the difference between the agent and placebo in more recent studies in comparison to older ones is attributed to baseline severity alone.

DISCUSSION

The results reported here conclude the debate on the efficacy of antidepressants and suggest that antidepressants are clearly superior to placebo. They also suggest that baseline severity cannot be utilized to dictate whether the treatment should include medication or not. Suggestions like this, proposed by guidelines or institutions (e.g. the NICE), should be considered mistaken.

Key statistical and analytical issues for evaluating treatment effects in periodontal research

Statistics is an indispensible tool for evaluating treatment effects in clinical research. Due to the complexities of periodontal disease progression and data collection, statistical analyses for periodontal research have been a great challenge for both clinicians and statisticians. The aim of this article is to provide an overview of several basic, but important, statistical issues related to the evaluation of treatment effects and to clarify some common statistical misconceptions. Some of these issues are general, concerning many disciplines, and some are unique to periodontal research. We first discuss several statistical concepts that have sometimes been overlooked or misunderstood by periodontal researchers. For instance, decisions about whether to use the t-test or analysis of covariance, or whether to use parametric tests such as the t-test or its non-parametric counterpart, the Mann-Whitney U-test, have perplexed many periodontal researchers. We also describe more advanced methodological issues that have sometimes been overlooked by researchers. For instance, the phenomenon of regression to the mean is a fundamental issue to be considered when evaluating treatment effects, and collinearity amongst covariates is a conundrum that must be resolved when explaining and predicting treatment effects. Quick and easy solutions to these methodological and analytical issues are not always available in the literature, and careful statistical thinking is paramount when conducting useful and meaningful research.

Inverted BMI rather than BMI is a better proxy for percentage of body fat

BACKGROUND

Percentage of body fat (BF%) is a known risk factor for a range of healthcare problems but is difficult to measure. An easy to measure proxy is the weight/height(2) ratio known as the Body Mass Index (BMI kg/m(2)). However, BMI does have some inherent weaknesses which are readily overcome by its inverse iBMI (1000/BMI, cm(2)/kg).

METHODS

The association between BF% and both BMI and iBMI together with their distributional properties was explored using previously published data from healthy (n = 2993) and diseased populations (n = 298).

RESULTS

BMI is skewed whereas iBMI is symmetrical and so is better approximated by the normal distribution. The relationship between BF% and BMI is curved, but that of iBMI and BF% is linear and thus iBMI explains more of the variation in BF% than BMI. For example a unit increase in BMI for a group of thin women represents an increase of 2.3% in BF, but for obese women this represents only a 0.3% increase in BF-a 7-fold difference. The curvature stems from body mass being the numerator in BMI but the denominator in BF% resulting in a form of hyperbolic curve which is not the case with iBMI. Furthermore, BMI and iBMI have different relationships (interaction) with BF% for men and women, but these differences are less marked with iBMI.

CONCLUSIONS

Overall, these characteristics of iBMI favour its use over BMI, especially in statistical models.

Mathematical coupling may account for the association between baseline severity and minimally important difference values

OBJECTIVE

To generate anchor-based values for the "minimally important difference" (MID) for a number of commonly used patient-reported outcome (PRO) measures and to examine whether these values could be applied across the continuum of preoperative patient severity.

STUDY DESIGN AND SETTING

Six prospective cohort studies of patients undergoing elective surgery at hospitals in England and Wales. Patients completed questionnaires about their health and health-related quality of life before and after surgery. MID values were calculated using the mean change score for a reference group of patients who reported they were "a little better" after surgery minus the mean change score for those who said they were "about the same." Pearson's correlation was used to examine the association between baseline severity and change scores in the reference group. Baseline severity was expressed in two ways: first in terms of preoperative scores and second in terms of the average of pre- and postoperative scores (Oldham's method).

RESULTS

Of the 10 PRO measures examined, eight demonstrated a moderate or high positive association between preoperative scores and MID values. Only two measures demonstrated such an association when Oldham's measure of baseline severity was used.

CONCLUSION

In general, there is little association between baseline severity and MID values. However, a moderate association persists for some measures, and it is recommended that researchers continue to test for this relationship when generating anchor-based MID values from change scores.

[Not Available]

The objective was to assess the effect of examination rates on national caries indices of 5, 12 and 17-year-old children/adolescents in Finland. The data were gathered from patient records of the Public Dental Service (PDS) units (n=205, 73%) and from a national register. The data included PDS-specific total numbers of examined children/adolescents and means of decayed (d/D) teeth, dmft/DMFT-values and proportions of caries-free. For analytical purposes, the PDS-specific mean values weighted by the PDS population were calculated to imply the traditionally calculated figures. New PDS-specific examination-rate-adjusted mean values were calculated by using the predicted outcome values at 100% examination rates. The results showed that low examination rates were associated with slightly poorer oral health. The examination-rate-adjusted mean d/D- values indicated better oral health than the traditional indices. The adjustment slightly worsened oral health in proportions of caries-free, and had almost no effect on dmft/DMFT-value. Overall, the influence was modest. The high proportions of healthy children that are examined (against recommendation) and the relatively small number of those having extensive disease (frequently examined as recommended) probably mask the influence of examination rates on the indices in Finland. We conclude that in international comparisons, traditionally calculated indices seem to be sufficiently valid.

Caries increment in children aged 3-5 years in relation to parents' dental attitudes: Oslo, Norway 2002 to 2004

OBJECTIVES

To assess the relationship between parents' dental attitudes and the caries increment in their children from the age of 3 to 5 years.

METHODS

Data based on parental questionnaires and dental examinations were collected from children participating in a follow-up study from age 3 years (n = 354) in 2002 to 5 years (n = 304) in 2004. The children were categorized as western-native (WN) and immigrants (IM). The items used were significantly related to caries experience in a multicentre study [Pine et al. (2004)Community Dent Health, vol. 21, pp. 121-30]. The responses to attitudinal items were weighted as positive if they would promote good dental health, and negative if not. Composite attitudinal variables relating to hygiene, diet and indulgence were calculated as a summation of the weighted responses to selected items. Regression analyses (bivariate and multiple) were performed to assess associations during the period between the attitudinal predictors/other control variables and caries increment (Deltad(3-5)mfs).

RESULTS

Bivariate logistic regression analyses revealed that 'Attitude to Diet' and 'Parental Indulgence' were clearly related to caries increment. The more exposed children were to negative parental attitudes, the higher the OR. 'Attitude to Diet' also persisted in a multiple logistic regression model, showing a higher OR value than caries experience. 'Immigrant Status' was the most potent predictor of caries increment. Parents were found to be more indulgent among IM than among WN groups.

CONCLUSION

Parental dental attitudes are clearly shown to be associated with caries increment in early childhood. The relationship is of such strength that it deserves to be taken into account in future preventive dental strategies.

Revisiting the relation between change and initial value: a review and evaluation

The relation between initial disease status and subsequent change following treatment has attracted great interest in clinical research. However, statisticians have repeatedly warned against correlating/regressing change with baseline due to two methodological concerns known as mathematical coupling and regression to the mean. Oldham's method and Blomqvist's formula are the two most often adopted methods to rectify these problems. The aims of this article are to review briefly the proposed solutions in the statistical and psychological literature, and to clarify the popular misconception that Blomqvist's formula is superior to Oldham's method. We argue that this misconception is due to a failure to recognize that the heterogeneity of individual responses to treatment is a source of regression to the mean in the analysis of the relation between change and initial value. Furthermore, we demonstrate how each method actually answers different research questions, and how confusion arises when this is not always understood.

Ecological time-trend analysis of caries experience at 12 years of age and caries incidence from age 12 to 18 years: Norway 1985-2004

OBJECTIVES

The purpose of the present investigation was to report on caries experience among Norwegian 12-year-olds from 1985 to 2004 and to assess caries incidence from 12 to 18 years of age for birth cohorts 1973 to 1986.

MATERIAL AND METHODS

Aggregated data from the Norwegian Public Dental Services and from official statistics were employed. Information was available about the number of subjects, the proportion receiving treatment, sales of fluoride tablets, socio-demographics, caries prevalence, and the number of decayed, missing, and filled teeth (DMFT).

RESULTS

An almost linear decline in caries prevalence and mean D3MFT (dentine level) occurred among 12-year-old children from 1985 until the year 2000, but from 2000 to 2004 an increasing trend was observed. The highest mean 6-year D3MFT increment (age 12-18 years) was 4.1 (cohort 1976), while the lowest was 3.2 (cohorts 1982 and 1983). In multiple linear regression analyses of trend, baseline D3MFT accounted for more than 91% of total explained variance in D3MFT increment (Models I and III). Without baseline D3MFT as predictor (Models II and IV), there was a significant association between education, social assistance, mobility, infant mortality, percentage examined, and the additive interaction terms year + income and year + education and D3MFT increment after controlling for confounding and multicollinearity.

CONCLUSIONS

Four consecutive years of increase in caries experience among 12-year-old children after 15 years of decline and evidence of stability or increase of the caries increment from 12 to 18 years of age among Norwegian teenagers give cause for concern.

Statistics in orthopaedic papers

Although the importance of sound statistical principles in the design and analysis of data has gained prominence in recent years, biostatistics, the application of statistics to the analysis of biological and medical data, is still a subject which is poorly understood and often mishandled. This review introduces, in the context of orthopaedic research, the terminology and the principles involved in simple data analysis, and outlines areas of medical statistics that have gained prominence in recent years. It also lists and provides an insight into some of the more common errors that occur in published orthopaedic journals and which are frequently encountered at the review stage in papers submitted to the Journal of Bone and Joint Surgery.

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

INTRODUCTION

The aim of this article was to encourage good practice in the statistical analyses of orthodontic research data. Our objective was to highlight the statistical problems caused by mathematical coupling (MC) in correlation and regression analyses. These statistical problems are among the most common pitfalls in orthodontic research when exploring associations among clinical variables. This article will show why these problems arise and how they can be avoided and overcome.

METHODS

Four orthodontic journals were electronically and manually searched for articles that used correlation and regression analyses. Studies that seemed to suffer from MC in their statistical analyses were identified and carefully examined.

RESULTS

Several examples from our search illustrate that MC in correlation and regression analyses can potentially cause misleading results. More appropriate statistical methods are available and should be used to eliminate confusing results and improve any subsequent interpretations. Because many clinical and radiographic variables used in orthodontic research are correlated due to direct or indirect MC, interpretation of studies in the literature needs to be cautious.

CONCLUSIONS

Correlation and regression analyses are useful tools in orthodontic research when their assumptions and limitations are recognized. However, greater care is required in formulating research questions and experimental designs. It is prudent to seek statistical advice when orthodontic research involves complex data analyses.

Evaluating the quality of active-control trials in periodontal research

AIM

The increasing popularity of randomized-controlled trials (RCTs) has raised the issue of their quality. Frequently overlooked are the differences between superiority and equivalence trials. The purpose of this study was to apply specific methodological criteria to evaluate the quality of active-control trials using studies that compared guided tissue regeneration (GTR) with enamel matrix derivatives (EMD).

MATERIALS AND METHODS

Seven RCTs were identified in the literature. Standard methodological criteria and seven additional criteria for trials using active-control groups were used to evaluate the quality of the seven RCTs.

RESULTS

Two trials were considered as superiority trials. The remaining five provided no clear statement of their research aim. However, two claimed that EMD and GTR were equally effective, because their results failed to show a significant difference between EMD and GTR. Most trials did not meet the majority of the design criteria.

CONCLUSIONS

The general lack of compliance with quality criteria might place doubt on the value of these trials and may render any conclusions questionable. It is therefore important to distinguish clearly between superiority trials and equivalence trials, and to incorporate appropriate additional criteria in the design of future RCTs with active-control groups.

The problem of analysing the relationship between change and initial value in oral health research

The relationship between initial disease status and subsequent change following treatment has attracted great interest in dental research. However, medical statisticians have repeatedly warned against correlating/regressing change with baseline because of two methodological concerns known as mathematical coupling and regression to the mean. In general, mathematical coupling occurs when one variable directly or indirectly contains the whole or part of another, and the two variables are then analyzed by using correlation or regression. Consequently, the statistical procedure of testing the null hypothesis - that the coefficient of correlation or the slope of regression is zero - may become inappropriate. Regression to the mean occurs with any variable that fluctuates within an individual or a population, either owing to measurement error and/or to physiological variation. The aim of this article was to clarify the conceptual confusion around mathematical coupling and regression to the mean within the statistical literature, and to correct a popular misconception about the correct analysis of the relationship between change and initial value. As examples that use inappropriate methods to analyze the relationship between change and baseline are still found in leading dental journals, this article seeks to help oral health researchers understand these problems and explain how to overcome them.

Problems of correlations between explanatory variables in multiple regression analyses in the dental literature

Multivariable analysis is a widely used statistical methodology for investigating associations amongst clinical variables. However, the problems of collinearity and multicollinearity, which can give rise to spurious results, have in the past frequently been disregarded in dental research. This article illustrates and explains the problems which may be encountered, in the hope of increasing awareness and understanding of these issues, thereby improving the quality of the statistical analyses undertaken in dental research. Three examples from different clinical dental specialties are used to demonstrate how to diagnose the problem of collinearity/multicollinearity in multiple regression analyses and to illustrate how collinearity/multicollinearity can seriously distort the model development process. Lack of awareness of these problems can give rise to misleading results and erroneous interpretations. Multivariable analysis is a useful tool for dental research, though only if its users thoroughly understand the assumptions and limitations of these methods. It would benefit evidence-based dentistry enormously if researchers were more aware of both the complexities involved in multiple regression when using these methods and of the need for expert statistical consultation in developing study design and selecting appropriate statistical methodologies.

Adjunctive benefits of systemic amoxicillin and metronidazole in non-surgical treatment of generalized aggressive periodontitis: a randomized placebo-controlled clinical trial

BACKGROUND

The objective of this study was to assess the adjunctive clinical effect of the administration of systemic amoxicillin and metronidazole in the non-surgical treatment of generalized aggressive periodontitis (GAP).

METHODS

Forty-one systemically healthy subjects with GAP were included in this 6-month double-blind, placebo-controlled, randomized clinical trial. Patients received a course of full-mouth non-surgical periodontal treatment delivered over a 24 h period using machine-driven and hand instruments. Test subjects received an adjunctive course of systemic antibiotic consisting of 500 mg amoxicillin and 500 mg metronidazole three times a day for 7 days. Clinical parameters were collected at baseline, and at 2 and 6 months post-treatment.

RESULTS

In both the test and the placebo groups, all clinical parameters improved at 2 and 6 months. In deep pockets (> or =7 mm), the test treatment resulted in an additional 1.4 mm (95% confidence interval 0.8, 2.0 mm) in full-mouth probing pocket depth (PPD) reduction and 1 mm (0.7, 1.3 mm) of life cumulative attachment loss (LCAL) gain at 6 months. In moderate pockets (4-6 mm), the adjunctive benefit was smaller in magnitude: PPD reduction was 0.4 mm (0.1, 0.7 mm) and LCAL gain was 0.5 mm (0.2, 0.8 mm). In addition, the 6-month data showed LCAL gains > or =2 mm at 25% of sites in test patients compared with 16% in placebo (p=0.028). Similarly, PPD reductions of 2 mm or more were observed in 30% of sites in test and 21% of sites in placebo patients. Seventy-four percent of pockets with PPD > or =5 mm at baseline were 4 mm or shallower at 6 months in the test group. This compared with 54% in the placebo group (p=0.008). Disease progression at 6 months was observed at 1.5% of test and 3.3% of sites in test and placebo, respectively (p=0.072).

CONCLUSIONS

These data indicate that a 7-day adjunctive course of systemic metronidazole and amoxicillin significantly improved the short-term clinical outcomes of full-mouth non-surgical periodontal debridement in subjects with GAP.

The relationship between baseline value and its change: problems in categorization and the proposal of a new method

Oral health researchers have shown great interest in the relationship between the initial status of diseases and subsequent changes following treatment. Two main approaches have been adopted to provide evidence of a positive association between baseline values and their changes following treatment. One approach is to use correlation or regression to test the relationship between baseline measurements and subsequent change (correlation/regression approach). The second approach is to categorize the lesions into subgroups, according to threshold values, and subsequently compare the treatment effects across the two (or more) subgroups (categorization approach). However, the correlation/regression approach suffers a methodological weakness known as mathematical coupling. Consequently, the statistical procedure of testing the null hypothesis becomes inappropriate. Categorization seems to avoid the problem of mathematical coupling, although it still suffers regression to the mean. We show, first, how the appropriate null hypothesis may be established to analyze the relationship between baseline values and change in the correlation approach and, second, we use computer simulations to investigate the impact of regression to the mean on the significance testing of the differences in the average treatment effects (or average baseline values) in the categorization approach. Data available from previous literature are reanalyzed by testing the appropriate null hypotheses and the results are compared to those from testing the usual (incorrect) null hypothesis. The results indicate that both the correlation and categorization approaches can give rise to misleading conclusions and that more appropriate methods, such as Oldham's method and our new approach of deriving the correct null hypothesis, should be adopted.

Collinearity in linear regression is a serious problem in oral health research

The aim of this article is to encourage good practice in the statistical analysis of dental research data. Our objective is to highlight the statistical problems of collinearity and multicollinearity. These are among the most common statistical pitfalls in oral health research when exploring the relationship between clinical variables using multiple regression analysis. We hope that this article will show why these problems arise and how they can be avoided and overcome. Examples from the periodontal literature will be used to illustrate how collinearity and multicollinearity can seriously distort the model development process as a result of the phenomenon of mathematical coupling. Knowledge of these problems can help to eliminate misleading results and improve any subsequent interpretations. Regression analyses are useful tools in oral health research when their limitations are recognized. However, care is required in planning and it is worthwhile seeking statistical advice when formulating the study's research questions.