Confidence intervals for the mean of a variable taking the values 0,1 and 2

A randomised controlled trial evaluating the impact of oral health advice on gingival health using intra oral images combined with a gingivitis specific toothpaste

OBJECTIVES

Does a complex intervention of oral hygiene advice (OHA) delivered with intra-oral scanner images, anti-gingivitis toothpaste and motivational reminders, improve oral health more than a standard of care control arm of fluoride toothpaste, with OHA without scanner images?

METHODS

Adult participants with pre-existing gingivitis were randomised to intervention or control. Following enrolment, baseline and each subsequent visit (V) (3-weeks, V2; 3-months, V3; 6-months, V4) followed the same schedule. Bleeding on Probing (BOP) was assessed and Intra Oral Scan IOS(1) recorded. Plaque was disclosed, scored and re-scanned (IOS(2)). The intervention group received OHA with IOS images, control group receiving OHA without IOS images. Participants brushed with their allocated toothpaste (fluoride, control; anti-gingivitis, intervention), IOS(3) was recorded. Between visits participants brushed with their allocated toothpaste, intervention group received motivational reminders.

RESULTS

BOP scores from baseline were significantly improved in the intervention group compared to control at all visits for all surfaces (p<0.001); differences at V4 were 0.292 (all), 0.211 (buccal/labial) and 0.375 (lingual/palatal). Plaque scores from baseline pre-brushing to each visit pre- and post-brushing also favoured the intervention group, the difference always significant on lingual/palatal surfaces (p<0.05), significant for all but pre-brushing-V4 (p<0.05) on all surfaces, but only significant for pre-brushing-V3 (p<0.05) buccally/labially. Differences from baseline to post-brushing at V4 were: 0.200 (all), 0.098 (buccal/labial) and 0.291 (lingual/palatal).

CONCLUSION

A complex intervention comprising OHA delivered with IOS-images, anti-gingivitis toothpaste and motivational reminders improved gingival health more than existing standard of care-OHA together with a standard fluoride toothpaste over a 6-month period.

CLINICAL SIGNIFICANCE STATEMENT

Intra-oral scans (IOS) are now frequently used in general dental practice for a variety of purposes. IOS use, in combination with motivational texts and an anti-gingivitis toothpaste, could be further deployed to promote oral hygiene behaviour change in patients and improve gingival health, in a cost-effective manner.

Clinical trials evaluating desensitising agents. Some design and analysis issues

INTRODUCTION

The purpose of this short communication is to draw attention to an efficient design for trials to evaluate desensitising agents, and an appropriate statistical analysis.

METHODS

Two recent sensitivity trials conducted by the Bristol Dental School Clinical Trials Group are reviewed.

RESULTS

The methodology used was effective to establish efficacy of the products evaluated.

CONCLUSIONS

This methodology is recommended for wider use.

CLINICAL SIGNIFICANCE

Effective clinical trial methodology enables establishment of efficacy of desensitising products leading to patient benefit.

A randomised controlled trial to compare the efficacy of an aluminium lactate/potassium nitrate/hydroxylapatite toothpaste with a control toothpaste for the prevention of dentine hypersensitivity

OBJECTIVES

To determine the efficacy of a cosmetic aluminium lactate/potassium nitrate/hydroxylapatite toothpaste for the reduction of dentine hypersensitivity (DH) pain as compared to a control toothpaste containing potassium nitrate.

METHODS

The study was a randomised, examiner-blind, two treatment arm, parallel controlled trial in healthy adults with at least 2 sensitive teeth (Schiff >2). At baseline, immediately after treatment and at 7 and 14 days of twice-daily brushing of the test or control toothpaste the sensitivity of 2 test teeth was measured following iced-water (Schiff and VAS) and tactile (Yeaple probe) stimuli, and a whole mouth plaque score was obtained. Participants also completed a whole-mouth VAS and DHEQ15 quality of life questionnaire at baseline, 7 and 14 days.

RESULTS

Both toothpastes reduced DH in test teeth, but pain reduction in the test group was significantly better at all timepoints and by all measures (p = 0.005, tooth-level VAS immediately after brushing; p < 0.001 all other comparisons). There was a relative risk reduction of Schiff sensitivity of 55 % immediately after brushing which rose to 81 % after 7 and 88.6 % after 14 days (all p < 0.001). There were no differences in plaque, whole mouth VAS or DHEQ15 scores at any time point.

CONCLUSION

This study demonstrated the efficacy of an aluminium lactate/potassium nitrate/hydroxylapatite toothpaste compared to a potassium nitrate control toothpaste for the prevention of dentine hypersensitivity both immediately and over a 2 week period. This agent appears to have potential for pain alleviation from the common oral pain condition of DH and further research is warranted.

CLINICAL SIGNIFICANCE

DH pain, whilst transient in nature, is arresting in magnitude, affecting quality of life. Daily application of efficacious toothpastes can relieve DH pain however, as yet, there is no gold standard treatment. The results of this study support further investigation of an aluminium lactate/potassium nitrate/hydroxylapatite toothpaste for DH management.

Postoperative intravenous parecoxib sodium followed by oral celecoxib post total knee arthroplasty in osteoarthritis patients (PIPFORCE): a multicentre, double-blind, randomised, placebo-controlled trial

OBJECTIVES

To evaluate the morphine-sparing effects of the sequential treatment versus placebo in subjects undergoing total knee arthroplasty (TKA), the effects on pain relief, inflammation control and functional rehabilitation after TKA and safety.

DESIGN

Double-blind, pragmatic, randomised, placebo-controlled trial.

SETTING

Four tertiary hospitals in China.

PARTICIPANTS

246 consecutive patients who underwent elective unilateral TKA because of osteoarthritis (OA).

INTERVENTIONS

Patients were randomised 1:1 to the parecoxib/celecoxib group or the control group. The patients in the parecoxib/celecoxib group were supplied sequential treatment with intravenous parecoxib 40 mg (every 12 hours) for the first 3 days after surgery, followed by oral celecoxib 200 mg (every 12 hours) for up to 6 weeks. The patients in the control group were supplied with the corresponding placebo under the same instructions.

PRIMARY AND SECONDARY OUTCOME MEASURES

The primary endpoint was the cumulative opioid consumption at 2 weeks post operation (intention-to-treat analysis). Secondary endpoints included the Knee Society Score, patient-reported outcomes and the cumulative opioid consumption.

RESULTS

The cumulative opioid consumption at 2 weeks was significantly smaller in the parecoxib/celecoxib group than in the control group (median difference, 57.31 (95% CI 34.66 to 110.33)). The parecoxib/celecoxib group achieving superior Knee Society Scores and EQ-5D scores and greater Visual Analogue Scale score reduction during 6 weeks. Interleukin 6, erythrocyte sedation rate and C-reactive protein levels were reduced at 72 hours, 2 weeks and 4 weeks and prostaglandin E2 levels were reduced at 48 hours and 72 hours in the parecoxib/celecoxib group compared with the placebo group. The occurrence of adverse events (AEs) was significantly lower in the parecoxib/celecoxib group.

CONCLUSIONS

The sequential intravenous parecoxib followed by oral celecoxib regimen reduces morphine consumption, achieves better pain control and functional recovery and leads to less AEs than placebo after TKA for OA.

TRIAL REGISTRATION NUMBER

ClinicalTrials.gov (ID: NCT02198924).

Interval estimation of proportion ratios for stratified bilateral correlated binary data

Confidence interval (CI) methods for the ratio of two proportions in the presence of correlated bilateral binary data are constructed for comparative clinical trials with stratified design. Simulations are conducted to evaluate the performance of the presented CIs with respect to mean coverage probability (MCP), mean interval width (MIW), and the ratio of mesial non-coverage probability to the distal non-coverage probability (RMNCP). Based on the empirical results, we suggest the use of the proposed CI method based on the complete score statistics (CS) for general applications. An example from a rheumatology study is used to demonstrate the proposed methodologies.

Cross-cultural adaptation, reliability and validity of the Turkish version of the Upper Limb Functional Index (ULFI)

STUDY DESIGN

Clinical measurement.

BACKGROUND

The Upper Limb Functional Index (ULFI) is a patient reported outcome (PRO) measure with sound clinimetric properties and clinical viability for determination of upper limb function.

PURPOSE-METHODS

The aims of this study were to cross-culturally adapt the ULFI for Turkish-speaking patients (ULFI-Tk) and investigate the reliability and validity in patients with upper limb problems. Patients (n=l02, age 49.1±16.6) with upper limb disorders were consecutively recruited. All participants completed the ULFI-Tk and the Disability of Arm, Shoulder and Hand Turkish-version (DASH-Tk) criterion at baseline and day-three.

RESULTS

The ULFI-Tk demonstrated good internal consistency (α=0.87), moderate criterion validity (DASH-Tk:r=0.68;p<0.05), moderate reliability (ICC2:1=0.72,CI=0.58-0.80) and strong error measurement (SEM=2.94;MDC90=5.35). Exploratory factor analysis demonstrated a dual factor structure that explained 31.2% of total variance.

CONCLUSIONS

The ULFI-Tk is a reliable and valid PRO that could be used to assess upper limb musculoskeletal disorders in Turkish speaking patients

LEVEL OF EVIDENCE

Class 2.

Corrected profile likelihood confidence interval for binomial paired incomplete data

Clinical trials often use paired binomial data as their clinical endpoint. The confidence interval is frequently used to estimate the treatment performance. Tang et al. (2009) have proposed exact and approximate unconditional methods for constructing a confidence interval in the presence of incomplete paired binary data. The approach proposed by Tang et al. can be overly conservative with large expected confidence interval width (ECIW) in some situations. We propose a profile likelihood-based method with a Jeffreys' prior correction to construct the confidence interval. This approach generates confidence interval with a much better coverage probability and shorter ECIWs. The performances of the method along with the corrections are demonstrated through extensive simulation. Finally, three real world data sets are analyzed by all the methods. Statistical Analysis System (SAS) codes to execute the profile likelihood-based methods are also presented.

A non-iterative implementation of Tango's score confidence interval for a paired difference of proportions

For matched-pair binary data, a variety of approaches have been proposed for the construction of a confidence interval (CI) for the difference of marginal probabilities between two procedures. The score-based approximate CI has been shown to outperform other asymptotic CIs. Tango's method provides a score CI by inverting a score test statistic using an iterative procedure. In this paper, we propose an efficient non-iterative method with closed-form expression to calculate Tango's CIs. Examples illustrate the practical application of the new approach.

Lower limb functional index: development and clinimetric properties

BACKGROUND

Existing lower-limb, region-specific, patient-reported outcome measures have clinimetric limitations, including limitations in psychometric characteristics (eg, lack of internal consistency, lack of responsiveness, measurement error) and the lack of reported practical and general characteristics. A new patient-reported outcome measure, the Lower Limb Functional Index (LLFI), was developed to address these limitations.

OBJECTIVE

The purpose of this study was to overcome recognized deficiencies in existing lower-limb, region-specific, patient-reported outcome measures through: (1) development of a new lower-extremity outcome scale (ie, the LLFI) and (2) evaluation of the clinimetric properties of the LLFI using the Lower Extremity Functional Scale (LEFS) as a criterion measure.

DESIGN

This was a prospective observational study.

METHODS

The LLFI was developed in a 3-stage process of: (1) item generation, (2) item reduction with an expert panel, and (3) pilot field testing (n=18) for reliability, responsiveness, and sample size requirements for a larger study. The main study used a convenience sample (n=127) from 10 physical therapy clinics. Participants completed the LLFI and LEFS every 2 weeks for 6 weeks and then every 4 weeks until discharge. Data were used to assess the psychometric, practical, and general characteristics of the LLFI and the LEFS. The characteristics also were evaluated for overall performance using the Measurement of Outcome Measures and Bot clinimetric assessment scales.

RESULTS

The LLFI and LEFS demonstrated a single-factor structure, comparable reliability (intraclass correlation coefficient [2,1]=.97), scale width, and high criterion validity (Pearson r=.88, with 95% confidence interval [CI]). Clinimetric performance was higher for the LLFI compared with the LEFS on the Measurement of Outcome Measures scale (96% and 95%, respectively) and the Bot scale (100% and 83%, respectively). The LLFI, compared with the LEFS, had improved responsiveness (standardized response mean=1.75 and 1.64, respectively), minimal detectable change with 90% CI (6.6% and 8.1%, respectively), and internal consistency (α=.91 and .95, respectively), as well as readability with reduced user error and completion and scoring times.

LIMITATIONS

Limitations of the study were that only participants recruited from outpatient physical therapy clinics were included and that no specific conditions or diagnostic subgroups were investigated.

CONCLUSION

The LLFI demonstrated sound clinimetric properties. There was lower response error, efficient completion and scoring, and improved responsiveness and overall performance compared with the LEFS. The LLFI is suitable for assessment of lower-limb function.

Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables

Background

The number of events per individual is a widely reported variable in medical research papers. Such variables are the most common representation of the general variable type called discrete numerical. There is currently no consensus on how to compare and present such variables, and recommendations are lacking. The objective of this paper is to present recommendations for analysis and presentation of results for discrete numerical variables.

Methods

Two simulation studies were used to investigate the performance of hypothesis tests and confidence interval methods for variables with outcomes {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, and {0, 1, 2, 3, 4, 5}, using the difference between the means as an effect measure.

Results

The Welch U test (the T test with adjustment for unequal variances) and its associated confidence interval performed well for almost all situations considered. The Brunner-Munzel test also performed well, except for small sample sizes (10 in each group). The ordinary T test, the Wilcoxon-Mann-Whitney test, the percentile bootstrap interval, and the bootstrap-t interval did not perform satisfactorily.

Conclusions

The difference between the means is an appropriate effect measure for comparing two independent discrete numerical variables that has both lower and upper bounds. To analyze this problem, we encourage more frequent use of parametric hypothesis tests and confidence intervals.

Confidence interval construction for proportion ratio in paired studies based on hybrid method

In this article, we consider confidence interval construction for proportion ratio in paired samples. Previous studies usually reported that score-based confidence intervals consistently outperformed other asymptotic confidence intervals for correlated proportion difference and ratio. However, score-based confidence intervals may not possess closed-form solutions and iterative procedures are therefore required. This article investigates the problem of confidence interval construction for ratio of two correlated proportions based on a hybrid method. Briefly, the hybrid method simply combines two separate confidence intervals for two individual proportions to produce a hybrid confidence interval for the ratio of the two individual proportions in paired studies. Most importantly, confidence intervals based on this hybrid method possess explicit solutions. Our simulation studies indicate that hybrid Wilson score confidence intervals based on Fieller's theorem performs well. The proposed confidence intervals will be illustrated with three real examples.

Modification of the upper limb functional index to a three-point response improves clinimetric properties

STUDY DESIGN

Observational two-stage.

INTRODUCTION

To achieve optimal clinimetric properties for outcome measures, both practical and psychometric, ongoing improvements are required.

PURPOSE OF THE STUDY

To evaluate if the Upper Limb Functional Index (ULFI) clinimetric properties are improved by modification to a three-point response option and to verify the factor structure.

METHODS

Stage 1, calibration (n=139) used ULFI dichotomous responses, and stage 2, validation (n=117) used a three-point response option. The clinimetric properties were compared in physical therapy outpatients with the QuickDASH as the reference standard. Repeated measurements were made at two to four weekly intervals.

RESULTS

The ULFI three-point response option improved reliability [intraclass correlation coefficient (2,1)=0.98], internal consistency (alpha=0.92), QuickDASH concurrent validity (r=0.86), and responsiveness. Minimal detectable change (90% confidence interval) was 7.9%, and factor structure was unidimensional. Missing responses were <0.5%, and practical characteristics were unchanged.

CONCLUSIONS

The enhanced reliability and reduced errors with unchanged practicality demonstrate the ULFI improvements through modification to a three-point response option.

LEVEL OF EVIDENCE

2c.

Confidence intervals for a difference between proportions based on paired data

We construct several explicit asymptotic two-sided confidence intervals (CIs) for the difference between two correlated proportions using the method of variance of estimates recovery (MOVER). The basic idea is to recover variance estimates required for the proportion difference from the confidence limits for single proportions. The CI estimators for a single proportion, which are incorporated with the MOVER, include the Agresti-Coull, the Wilson, and the Jeffreys CIs. Our simulation results show that the MOVER-type CIs based on the continuity corrected Phi coefficient and the Tango score CI perform satisfactory in small sample designs and spare data structures. We illustrate the proposed CIs with several real examples.

A comparison of methods for the construction of confidence interval for relative risk in stratified matched-pair designs

A stratified matched-pair study is often designed for adjusting a confounding effect or effect of different trails/centers/ groups in modern medical studies. The relative risk is one of the most frequently used indices in comparing efficiency of two treatments in clinical trials. In this paper, we propose seven confidence interval estimators for the common relative risk and three simultaneous confidence interval estimators for the relative risks in stratified matched-pair designs. The performance of the proposed methods is evaluated with respect to their type I error rates, powers, coverage probabilities, and expected widths. Our empirical results show that the percentile bootstrap confidence interval and bootstrap-resampling-based Bonferroni simultaneous confidence interval behave satisfactorily for small to large sample sizes in the sense that (i) their empirical coverage probabilities can be well controlled around the pre-specified nominal confidence level with reasonably shorter confidence widths; and (ii) the empirical type I error rates of their associated test statistics are generally closer to the pre-specified nominal level with larger powers. They are hence recommended. Two real examples from clinical laboratory studies are used to illustrate the proposed methodologies.

A generalisation of the tail-based P-value to characterise the conformity of trinomial proportions to prescribed norms

The traditional concept of a P-value comparing an observed binomial probability to a prescribed value is extended to the ordered trinomial case in which target proportions have been specified for `excellent', `acceptable' and `unacceptable' quality. The resulting trinomial probabilities are summarised by calculating two aggregate probabilities, relating to outcomes unequivocally better than, and unequivocally worse than, that actually observed, based on these assumed target proportions. Accumulations of exactly calculated tail probabilities on a mid-P basis are recommended.

Phototoxic reaction and porphyrin fluorescence in skin after topical application of methyl aminolaevulinate

BACKGROUND

Photodynamic therapy using topical methyl aminolaevulinate (MAL) is a new treatment modality for skin disorders. MAL is metabolized into endogenous porphyrins, which act as photosensitizers when illuminated.

OBJECTIVES

To evaluate the severity and duration of skin photosensitivity after MAL application, and to investigate its relation to the presence of endogenous porphyrins.

METHODS

Placebo and 160 mg g(-1) MAL creams were randomly assigned to contralateral sites located at the forearms and fingertips of 16 healthy volunteers and were applied for 3 h. The porphyrin content in the skin was monitored by in situ fluorescence measurements following cream removal. Phototoxic reaction was evaluated after exposure to a high dose of red light.

RESULTS

The porphyrin fluorescence in forearm skin peaked about 1 h after the cream removal, was halved after 8 h, and was reduced by > 90% within 24 h. Most forearm sites were photosensitive at 1 and 8 h following cream removal. Six subjects were still sensitive at 24 h, and at this time point the phototoxicity was coincidental with residual porphyrin fluorescence. In general, all reactions were mild or moderate, and included pain, erythema, oedema and transient hyperpigmentation. No photosensitivity or porphyrin fluorescence was detected at 48 h. At the fingertips photosensitivity was absent except for sporadic cases of mild pain.

CONCLUSIONS

Topical MAL application and exposure to red light induced mild and moderate phototoxicity. The photosensitivity ceased within 24-48 h after cream removal, and its duration was associated with the degradation of porphyrins.

Confidence interval construction for proportion difference in small-sample paired studies

Paired dichotomous data may arise in clinical trials such as pre-/post-test comparison studies and equivalence trials. Reporting parameter estimates (e.g. odds ratio, rate difference and rate ratio) along with their associated confidence interval estimates becomes a necessity in many medical journals. Various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions. Nevertheless, the performance of these asymptotic methods may have poor coverage properties in small samples. In this article, we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small-sample paired data. Specifically, we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test. The exact unconditional confidence interval guarantees the coverage probability, and it is recommended if strict control of coverage probability is required. However, the exact method tends to be overly conservative and computationally demanding. Our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small-sample designs, and yet they are relatively easy to implement computationally. We illustrate the methods using real examples from a pain management study and a cancer study.

Simple improved confidence intervals for comparing matched proportions

For binary matched-pairs data, this article discusses interval estimation of the difference of probabilities and an odds ratio for comparing 'success' probabilities. We present simple improvements of the commonly used Wald confidence intervals for these parameters. The improvement of the interval for the difference of probabilities is to add two observations to each sample before applying it. The improvement for estimating an odds ratio transforms a confidence interval for a single proportion.