A non-iterative accurate asymptotic confidence interval for the difference between two proportions

Use of Amitriptyline in the Treatment of Headache After Traumatic Brain Injury: Lessons Learned From a Clinical Trial

OBJECTIVES

The primary outcome of this study was to assess the efficacy and safety of preventive treatment with amitriptyline on headache frequency and severity after mild traumatic brain injury (mTBI).

BACKGROUND

Despite the fact that headache is the most common and persistent physical symptom after TBI, there has been little research on the longitudinal course or pharmacologic treatment of this disorder. Of those who have headache after injury, about 60% continue to complain of headache at 3 months post injury, with higher levels of disability than those without headache. There have been no prospective, randomized, controlled trials of a pharmacologic agent for headache after TBI. Additionally, a brain-injured population may be more susceptible to side effects of medication.

DESIGN

This is a single-center phase II trial of amitriptyline to prevent persistent headache after an mTBI. Medication dose was gradually increased from 10 to 50 mg daily.

RESULTS

Fifty participants were enrolled and 33 who completed the 90-day assessment were included in the final analysis. In order to detect a possible cognitive impact of the study drug, 24 participants were randomly assigned to start amitriptyline immediately after study enrollment and 26 were assigned to start 30 days after enrollment. Forty-nine percent (18/37) of those assigned to take medication took none throughout the study period, with less compliance in younger participants with mean ages of 32.7 in those who did not take any medication, 33.4 who were less than 80% compliant, and 42.3 who were compliant (P = .013). Compliance in keeping a daily headache diary was low, with 29/50 participants (58%) meeting daily entry completion, and only 10 participants maintaining 100% diary completion. No differences were found between those who started medication immediately vs at day 30 in headache frequency or severity.

CONCLUSIONS

While headache is the most common symptom following mTBI, current evidence does not support a specific treatment. No differences were noted in headache frequency compared to our prior study. However, the current sample had significantly lower headache severity (15% vs 36% with pain rating of 6 or above, P = .015) compared to our prior study. Our current study was not able to determine whether there is any benefit for the use of amitriptyline as a headache preventive because of difficulty with study recruitment and compliance. The challenges with recruitment and retention in the mTBI population were instructive, and future research in this area will need to identify strategies to improve recruitment, diary compliance, and medication adherence in this population.

One-tailed asymptotic inferences for the difference of proportions: Analysis of 97 methods of inference

Two-tailed asymptotic inferences for the difference d = p₂ - p₁ with independent proportions have been widely studied in the literature. Nevertheless, the case of one tail has received less attention, despite its great practical importance (superiority studies and noninferiority studies). This paper assesses 97 methods to make these inferences (test and confidence intervals [CIs]), although it also alludes to many others. The conclusions obtained are (1) the optimal method in general (and particularly for errors α = 1% and 5%) is based on arcsine transformation, with the maximum likelihood estimator restricted to the null hypothesis and increasing the successes and failures by 3/8; (2) the optimal method for α = 10% is a modification of the classic model of Peskun; (3) a more simple and acceptable option for large sample sizes and values of d not near to ±1 is the classic method of Peskun; and (4) in the particular case of the superiority and inferiority tests, the optimal method is the classic Wald method (with continuity correction) when the successes and failures are increased by one. We additionally select the optimal methods to make compatible the conclusions of the homogeneity test and the CI for d, both for one tail and for two (methods which are related to arcsine transformation and the Wald method).

The Clavicle Trial: A Multicenter Randomized Controlled Trial Comparing Operative with Nonoperative Treatment of Displaced Midshaft Clavicle Fractures

BACKGROUND

The treatment of displaced midshaft clavicle fractures remains controversial.

METHODS

We undertook a multicenter randomized controlled trial to compare effectiveness and safety between nonoperative management and ORIF (open reduction and internal fixation) for displaced midshaft clavicle fractures in adults. Three hundred and one eligible adult patients were randomized to 1 of the 2 treatment groups and followed at 6 weeks, 3 months, and 9 months after recruitment. The primary outcome was the rate of radiographically evident nonunion at 3 months following treatment. Secondary outcomes were the rate of radiographically evident nonunion at 9 months, limb function measured using the Constant-Murley Score and DASH (Disabilities of the Arm, Shoulder and Hand) score, and patient satisfaction.

RESULTS

There was no difference in the proportion of patients with radiographic evidence of nonunion at 3 months between the operative (28%) and nonoperative (27%) groups, whereas at 9 months the proportion with nonunion was significantly lower (p < 0.001) in the operative group (0.8%) than in the nonoperative group (11%). The DASH and Constant-Murley scores and patient satisfaction were all significantly better in the operative group than in the nonoperative group at 6 weeks and 3 months.

CONCLUSIONS

Although at 3 months there was no evidence that surgery had reduced the rate of nonunion of displaced midshaft clavicle fractures, at 9 months nonoperative treatment had led to a significantly higher nonunion rate (11% compared with <1%). The rate of secondary surgical intervention during the trial period was 12 (11%) of the 147 patients in the nonoperative group. ORIF is a safe and reliable intervention with superior early functional outcomes and should be considered for patients who sustain this common injury.

LEVEL OF EVIDENCE

Therapeutic Level I. See Instructions for Authors for a complete description of levels of evidence.

Prediction of spontaneous preterm birth using quantitative fetal fibronectin after recent sexual intercourse

OBJECTIVE

The purpose of this study was to determine the effect of sexual intercourse on the accuracy of quantitative fetal fibronectin (qfFN) in the prediction of spontaneous preterm birth (sPTB) in asymptomatic high-risk women.

STUDY DESIGN

This was a prospective masked predefined subanalysis of a larger study of cervicovaginal fluid qfFN concentration in high-risk women asymptomatic of preterm labor. Women who had sexual intercourse within 48 hours of qfFN testing (n = 61; 18(+0)-34(+6) weeks' gestation) were compared with controls from the same database without a history of pretest sexual intercourse, matched according to gestational age at testing and delivery, risk factor for sPTB, and ultrasonographic cervical length measurement.

RESULTS

The median concentration of qfFN in women who had sexual intercourse within 48 hours of testing was 53 ng/mL (quartiles 6, 189), compared with 5 ng/mL (quartiles 2, 12) in the control group. The average qfFN concentration was 6.36 (95% confidence interval [CI], 3.43-11.8) times higher in the sexual intercourse group compared with controls (P < .0001). The false-positive rate was 56% (27 of 50) compared with 6% (3 of 52) in the control group (risk difference, 48%; 95% CI, 33-63; P < .001). The false-negative rate was 45% (5 of 11) vs 89% (8 of 9) in the control group (risk difference, -43%; 95% CI, -79 to -8; P = .043).

CONCLUSION

Sexual intercourse within 48 hours of testing is associated with increased levels of fetal fibronectin in vaginal secretions and an increased rate of false-positive results in the prediction of sPTB in asymptomatic women.

Confidence intervals for the difference between independent binomial proportions: comparison using a graphical approach and moving averages

This paper uses graphical methods to illustrate and compare the coverage properties of a number of methods for calculating confidence intervals for the difference between two independent binomial proportions. We investigate both small-sample and large-sample properties of both two-sided and one-sided coverage, with an emphasis on asymptotic methods. In terms of aligning the smoothed coverage probability surface with the nominal confidence level, we find that the score-based methods on the whole have the best two-sided coverage, although they have slight deficiencies for confidence levels of 90% or lower. For an easily taught, hand-calculated method, the Brown-Li 'Jeffreys' method appears to perform reasonably well, and in most situations, it has better one-sided coverage than the widely recommended alternatives. In general, we find that the one-sided properties of many of the available methods are surprisingly poor. In fact, almost none of the existing asymptotic methods achieve equal coverage on both sides of the interval, even with large sample sizes, and consequently if used as a non-inferiority test, the type I error rate (which is equal to the one-sided non-coverage probability) can be inflated. The only exception is the Gart-Nam 'skewness-corrected' method, which we express using modified notation in order to include a bias correction for improved small-sample performance, and an optional continuity correction for those seeking more conservative coverage. Using a weighted average of two complementary methods, we also define a new hybrid method that almost matches the performance of the Gart-Nam interval.

Improved Detection of Silent Atrial Fibrillation Using 72-Hour Holter ECG in Patients With Ischemic Stroke

Background and Purpose—

Adequate diagnosis of atrial fibrillation (AF), including paroxysmal AF, is an important part of stroke workup. Prolonged ECG monitoring may improve the detection of paroxysmal, previously undiagnosed AF (unknown AF). Therefore, we evaluated systematic 72-hour Holter ECG monitoring to detect unknown AF for the workup of patients with stroke.

Methods—

Unselected survivors of a stroke or transient ischemic attack (TIA) without known AF were enrolled in a prospective, multicenter cohort study of 72-hour Holter ECG monitoring in 9 German secondary and tertiary stroke centers between May 2010 and January 2011. In addition to standardized workup of stroke pathogenesis according to the German Stroke Unit protocol, all patients underwent 72-hour Holter ECG monitoring directly after admission. All ECGs were centrally analyzed by 2 independent observers. We determined the proportion of unknown AF and compared the detection rates of 72- and 24-hour monitoring.

Results—

A total of 1135 patients were enrolled (mean age, 67 years [SD, 13.1 years], 45% women, 29% TIA). Unknown AF was detected in 49 out of 1135 patients (4.3%, [95% confidence interval, 3.4–5.2%]) by 72-hour ECG monitoring. Unknown AF was diagnosed in 29 patients (2.6%) within the first 24 hours of ECG monitoring, and in 20 more patients only by 72 hours of ECG monitoring. The number needed to screen by 72-hour ECG was 55 patients (95% confidence interval [35–123]) for each additional AF diagnosis. Patients with unknown AF were significantly older and had more often a history of previous stroke. Patients with unknown AF were equally distributed within categories of pathogenesis according to Trial of Org 10172 in Acute Stroke Treatment (TOAST) classification.

Conclusions—

In unselected survivors of stroke or TIA, 72-hour ECG monitoring is feasible and improves the detection rate of silent paroxysmal AF.

Investigation of the human serotonin receptor gene HTR3B in bipolar affective and schizophrenic patients

The neurotransmitter serotonin (5-hydroxytryptamine, 5-HT) mediates a multitude of central nervous functions by activating 5-HT receptor subtypes. A dysfunction of serotonergic neurotransmission is considered to play a major role in the pathophysiology of complex neuropsychiatric disorders. In our study, a mutation screen of the serotonin receptor gene HTR3B was carried out to explore a putative contribution to the etiology of bipolar affective disorder (BPAD) and schizophrenia (SZ). Screening of 49 patients suffering from BPAD, 78 patients with SZ and 62 control individuals revealed eleven sequence variations including a 3 bp deletion within the 5'UTR (5' untranslated region), four exonic and five intronic SNPs as well as a point mutation in the 3'UTR of HTR3B. Four of these sequence variations have not been described previously. Statistical computation rated most variants as probably non-disease related polymorphisms. However, IVS6 + 31C > T, IVS6 + 40C > A, and 1386T > C were solely detected in bipolar affective patients and in none of the controls. Interestingly, we observed a significant underrepresentation of the 3 bp deletion -100_-102delAAG in an extended sample of 162 bipolar affected patients compared to controls (allele-wise: 8% vs. 15%, P = 0.006, OR = 0.49, 95% CI: 0.3-0.82; genotype-wise: 15,5% vs. 29,0%, P = 0.005, OR = 0.45, 95% CI: 0.26-0.77). We suggest that this deletion may influence translational efficiency, thereby possibly affecting the development of bipolar affective disease.

Sample size determination for equivalence test using rate ratio of sensitivity and specificity in paired sample data

Before implementing a new diagnostic test, we may wish to study whether this test is noninferior to a reference test with respect to the sensitivity and/or the specificity. This paper discusses sample size determination for one-sided equivalence (or noninferiority) testing of the rate ratio using paired-sample data. Using large sample theory, this paper derives asymptotic sample size formulae for the required number of subjects giving a desired power 100(1 - beta)% at a specified alpha-level. To evaluate the accuracy of these formulae, this paper considers several test statistics and uses Monte Carlo simulation to estimate the corresponding type I error and power with the given resulting sample sizes in a variety of situations. Finally, this paper notes those situations for which the asymptotic sample size formulae developed here are of limited use and suggests a simple empirical adjustment to alleviate this limitation.

Calculating confidence intervals for the number needed to treat

The number needed to treat (NNT) has gained much attention in the past years as a useful way of reporting the results of randomized controlled trials with a binary outcome. Defined as the reciprocal of the absolute risk reduction (ARR), NNT is the estimated average number of patients needed to be treated to prevent an adverse outcome in one additional patient. As with other estimated effect measures, it is important to document the uncertainty of the estimation by means of an appropriate confidence interval. Confidence intervals for NNT can be obtained by inverting and exchanging the confidence limits for the ARR provided that the NNT scale ranging from 1 through infinity to -1 is taken into account. Unfortunately, the only method used in practice to calculate confidence intervals for ARR seems to be the simple Wald method, which yields too short confidence intervals in many cases. In this paper it is shown that the application of the Wilson score method improves the calculation and presentation of confidence intervals for the number needed to treat. Control Clin Trials 2001;22:102-110

Nasal carriage as a source of Staphylococcus aureus bacteremia. Study Group

BACKGROUND

The consequences of infection with Staphylococcus aureus can be severe, so strategies for prevention are important. We examined S. aureus isolates from blood and from nasal specimens to determine whether the organisms in the bloodstream originated from the patient's own flora.

METHODS

In a multicenter study, swabs for culture were obtained from the anterior nares of 219 patients with S. aureus bacteremia. A total of 723 isolates were collected and genotyped. In a second study, 1640 S. aureus isolates from nasal swabs were collected over a period of five years and then compared with isolates from the blood of patients who subsequently had S. aureus bacteremia.

RESULTS

In the multicenter study of S. aureus bacteremia, the blood isolates were identical to those from the anterior nares in 180 of 219 patients (82.2 percent). In the second study, 14 of 1278 patients who had nasal colonization with S. aureus subsequently had S. aureus bacteremia. In 12 of these 14 patients (86 percent), the isolates obtained from the nares were clonally identical to the isolates obtained from blood 1 day to 14 months later.

CONCLUSIONS

A substantial proportion of cases of S. aureus bacteremia appear to be of endogenous origin since they originate from colonies in the nasal mucosa. These results provide support for strategies to prevent systemic S. aureus infections by eliminating nasal carriage of S. aureus.

Comparing diagnostic tests: a simple graphic using likelihood ratios

The diagnostic abilities of two or more diagnostic tests are traditionally compared by their respective sensitivities and specificities, either separately or using a summary of them such as Youden's index. Several authors have argued that the likelihood ratios provide a more appropriate, if in practice a less intuitive, comparison. We present a simple graphic which incorporates all these measures and admits easily interpreted comparison of two or more diagnostic tests. We show, using likelihood ratios and this graphic, that a test can be superior to a competitor in terms of predictive values while having either sensitivity or specificity smaller. A decision theoretic basis for the interpretation of the graph is given by relating it to the tent graph of Hilden and Glasziou (Statistics in Medicine, 1996). Finally, a brief example comparing two serodiagnostic tests for Lyme disease is presented. Published in 2000 by John Wiley & Sons, Ltd.

Delay in diagnosis of breast cancer

OBJECTIVES

To assess the consequences of physician delay in the diagnosis of breast cancer by comparing stage, treatment, and outcome of patients with and without delay, and to identify patient characteristics that may make diagnosis more difficult. SUMMARY BACKGROUND INFORMATION: Delay in diagnosis of breast cancer is the most common clinical scenario resulting in malpractice litigation.

METHODS

The records of 1014 patients were reviewed and the events preceding the diagnosis were reconstructed. Accurate assessment of the physician delay in diagnosis could be made for 606 patients, 51 (8%) with physician delay >3 months. Patients with delay were comparable to patients without delay in terms of age, height, weight, age at menarche, pregnancies, children, proportion in menopause, age at menopause, and family history of breast cancer.

RESULTS

Thirty-six percent of patients who had a delay in diagnosis had normal mammograms versus 7% of patients without delay. Cancers in patients with delay were significantly larger on average than in those without delay, but there were no significant differences in pathology, differentiation, nodal status, TNM stage, treatment, or outcome.

CONCLUSIONS

Physician delay in the diagnosis of breast cancer is common, and patients with delay are similar to patients without delay, although they are more likely to have normal mammograms. The consequences of physician delay in terms of stage at diagnosis, treatment, and outcome were not statistically significant.

Exact 95% confidence intervals for differences in binomial proportions

A method is described that allows exact 95% confidence intervals to be computed for differences in binomial proportions. The method itself is not iterative, but it uses the iteratively computed 95% confidence intervals for the individual binomial proportions. The method converges with the usual normal approximation method, as denominators become large. It correlates very closely with the Yates-corrected chi-square test. The method works regardless of the definition of success or failure in the proportions and regardless of the order of the proportions.