Notes on interval estimation of the generalized odds ratio under stratified random sampling

It is not rare to encounter the patient response on the ordinal scale in a randomized clinical trial (RCT). Under the assumption that the generalized odds ratio (GOR) is homogeneous across strata, we consider four asymptotic interval estimators for the GOR under stratified random sampling. These include the interval estimator using the weighted-least-squares (WLS) approach with the logarithmic transformation (WLSL), the interval estimator using the Mantel-Haenszel (MH) type of estimator with the logarithmic transformation (MHL), the interval estimator using Fieller's theorem with the MH weights (FTMH) and the interval estimator using Fieller's theorem with the WLS weights (FTWLS). We employ Monte Carlo simulation to evaluate the performance of these interval estimators by calculating the coverage probability and the average length. To study the bias of these interval estimators, we also calculate and compare the noncoverage probabilities in the two tails of the resulting confidence intervals. We find that WLSL and MHL can generally perform well, while FTMH and FTWLS can lose either precision or accuracy. We further find that MHL is likely the least biased. Finally, we use the data taken from a study of smoking status and breathing test among workers in certain industrial plants in Houston, Texas, during 1974 to 1975 to illustrate the use of these interval estimators.

Hypothesis testing and estimation in ordinal data under a simple crossover design

Since each patient serves as his/her own control, the crossover design can be of use to improve power as compared with the parallel-groups design in studying noncurative treatments to certain chronic diseases. Although the research studies on the crossover design have been quite intensive, the discussions on analyzing ordinal data under such a design are truly limited. We propose using the generalized odds ratio (GOR) for paired sample data to measure the relative effect on patient responses for both treatment and period in ordinal data under a simple crossover trial. Assuming the treatment and period effects are multiplicative, we note that one can easily derive the maximum likelihood estimator (LE) in closed forms for the GOR of treatment and period effects. We develop asymptotic and exact procedures for testing treatment and period effects. We further derive asymptotic and exact interval estimators for the GOR of treatment and period effects. We use the data taken from a crossover trial to assess the clarity of leaflet instructions between two devices among asthma patients to illustrate the use of these test procedures and estimators developed here.

Notes on testing noninferiority in multivariate binary data under the matched-pair design

Since therapeutic efficacy is often measured by multiple endpoints, it will be of use if one can incorporate the information on various variables of response into procedures for testing noninferiority to improve power of a univariate test procedure for each individual variable. On the basis of the proposed mixed effects logistic regression model for multivariate binary data under the matched-pairs design, we develop procedures for testing noninferiority with respect to the odds ratio in multivariate binary data under the matched-pair design. We discuss use of Bonferroni's and Scheffe's methods to control the inflation in Type I error due to multiple tests. We further employ Monte Carlo simulation to evaluate and compare the performance of these test procedures. Finally, we use the data taken from a crossover clinical trial that monitored several adverse events of an antidepressive drug to illustrate the use of test procedures derived here.

Obstructive lung disease does not increase lung cancer mortality among female never-smokers in Hong Kong

SETTING

High lung cancer mortality is observed among female never-smokers in Hong Kong.

OBJECTIVE

To examine the relationship between obstructive lung disease (chronic obstructive pulmonary disease and/or asthma) and lung cancer mortality by sex and smoking status.

DESIGN

A cohort of elderly clients (aged ≥65 years) in a health maintenance programme were followed prospectively through linkage with the territory-wide death registry for causes of death, using identity card number as the unique identifier.

RESULTS

After 516,055 person-years of follow-up, respectively 1297, 872 and 1908 deaths were caused by lung cancer, other tobacco-related malignancies and non-tobacco-related malignancies. In the overall analysis, obstructive lung disease was independently associated with mortality due to lung cancer (aHR 1.86, P < 0.001) after adjustment for potential confounders. However, no association was detected among female never-smokers (HR 0.97, P = 0.909), in sharp contrast with female ever-smokers, male never-smokers and male ever-smokers (HR 1.98, 2.34 and 2.09, respectively, P from 0.047 to <0.001). Consistent results were observed after exclusion of all deaths in the initial 3 years.

CONCLUSION

Obstructive lung disease exerted differential effects on lung cancer mortality across different sex and smoking subgroups in this Asian population, with a conspicuous absence of effect among female never-smokers.

Analysis of Poisson frequency data under a simple crossover trial

When the frequency of occurrence for an event of interest follows a Poisson distribution, we develop asymptotic and exact procedures for testing non-equality, non-inferiority and equivalence, as well as asymptotic and exact interval estimators for the ratio of mean frequencies between two treatments under a simple crossover design. Using Monte Carlo simulations, we evaluate the performance of these test procedures and interval estimators in a variety of situations. We note that all asymptotic test procedures developed here can generally perform well with respect to Type I error and can be preferable to the exact test procedure with respect to power if the number of patients per group is moderate or large. We further find that in these cases the asymptotic interval estimator with the logarithmic transformation can be more precise than the exact interval estimator without sacrificing the accuracy with respect to the coverage probability. However, the exact test procedure and exact interval estimator can be of use when the number of patients per group is small. We use a double-blind randomized crossover trial comparing salmeterol with a placebo in exacerbations of asthma to illustrate the practical use of these estimators.

Notes on interval estimation of the gamma correlation under stratified random sampling

We have developed four asymptotic interval estimators in closed forms for the gamma correlation under stratified random sampling, including the confidence interval based on the most commonly used weighted-least-squares (WLS) approach (CIWLS), the confidence interval calculated from the Mantel-Haenszel (MH) type estimator with the Fisher-type transformation (CIMHT), the confidence interval using the fundamental idea of Fieller's Theorem (CIFT) and the confidence interval derived from a monotonic function of the WLS estimator of Agresti's α with the logarithmic transformation (MWLSLR). To evaluate the finite-sample performance of these four interval estimators and note the possible loss of accuracy in application of both Wald's confidence interval and MWLSLR using pooled data without accounting for stratification, we employ Monte Carlo simulation. We use the data taken from a general social survey studying the association between the income level and job satisfaction with strata formed by genders in black Americans published elsewhere to illustrate the practical use of these interval estimators.

A semi-parametric approach to the frequency of occurrence under a simple crossover trial

To analyze the frequency of occurrence for an event of interest in a crossover design, we propose a semi-parametric approach. We develop two point estimators and four interval estimators in closed forms for the treatment effect under a random effects multiplicative risk model. Using Monte Carlo simulations, we evaluate these estimators and compare the four interval estimators with the classical interval estimator suggested elsewhere in a variety of situations. We note that the point estimator using the ratio of two arithmetic averages of mean frequencies under a multiplicative risk model can be comparable to the point estimator using the ratio of two geometric averages of mean frequencies. We note that as long as the number of patients per group is large, all the four interval estimators developed here can perform well. We also note that the classical interval estimator derived under the commonly assumed Poisson distribution for the frequency data can be conservative and lose precision if the Poisson distribution assumption is violated. We use a double-blind randomized crossover trial comparing salmeterol with a placebo in exacerbations of asthma to illustrate the practical use of these estimators.

Exact sample-size determination in testing non-inferiority under a simple crossover trial

For testing the non-inferiority (or equivalence) of an experimental treatment to a standard treatment, the odds ratio (OR) of patient response rates has been recommended to measure the relative treatment efficacy. On the basis of an exact test procedure proposed elsewhere for a simple crossover design, we develop an exact sample-size calculation procedure with respect to the OR of patient response rates for a desired power of detecting non-inferiority at a given nominal type I error. We note that the sample size calculated for a desired power based on an asymptotic test procedure can be much smaller than that based on the exact test procedure under a given situation. We further discuss the advantage and disadvantage of sample-size calculation using the exact test and the asymptotic test procedures. We employ an example by studying two inhalation devices for asthmatics to illustrate the use of sample-size calculation procedure developed here.

Interval estimation of the proportion ratio in repeated binary measurements under a stratified randomized clinical trial with noncompliance

The proportion ratio (PR) of a positive response between an experimental treatment and a standard treatment (or placebo) is often used to measure the relative treatment efficacy in a randomized clinical trial (RCT). For ethical reasons, it is almost inevitable to encounter some patients not complying with their assigned treatment. Furthermore, when there are confounders in a RCT or meta-analysis, we commonly employ stratified analysis to control the confounding effects on interval estimation of the PR. On the basis of a general risk multiplicative model, we focus our discussion on interval estimation of the PR in repeated binary data under a stratified RCT with noncompliance. We develop seven asymptotic closed-form interval estimators for the PR. We apply Monte Carlo simulation to study the finite-sample performance of these interval estimators in a variety of situations. We note that the two interval estimators with the logarithmic transformation based on the commonly used weighted least squares (WLS) approach can be liberal, while the three interval estimators with the Mantel-Haenszel (MH) weight derived from various methods can consistently perform well. We also note that the two estimators with the estimated optimal weight defined in the context using Fieller's Theorem and a randomization-based approach may not necessarily produce a confidence interval preferable to the MH-type interval estimators for the PR with respect to accuracy and precision.

The relaxation effect and mechanism of action of higenamine in the rat corpus cavernosum

Higenamine mediates cardiotonic, vascular relaxation and bronchodilator effects. The relaxation effects and the mechanism of action of higenamine on the rat corpus cavernosum (CC) were assessed to investigate the effect of higenamine on penile erection. Strips of CC and aorta were used in organ baths for isometric tension studies. Tension was measured with isometric force transducers, and muscle relaxation was expressed as the percent decrease in precontraction induced by phenylephrine (PE). The relaxation reactions were investigated in an endothelial-denuded group and groups pretreated with N(G)-nitro-L-arginine methyl ester (NO synthesis inhibitor), propranolol (β-receptor blocker), indomethacin (COX inhibitor), glibenclamide (K(+)(ATP) channel inhibitor), 4-aminopyridine (membrane potential-dependent potassium channel inhibitor) and methylene blue (guanylyl cyclase inhibitor) for 30 min. Intracavernous pressure (ICP) was assessed in rats after the intravenous administration of higenamine, and changes in guanosine 3',5'-cyclic monophosphate and adenosine 3',5'-cyclic monophosphate (cAMP) concentrations were measured on the basis of the higenamine concentration. Also, the combined reaction of higenamine and the phosphodiesterase type-5 (PDE-5) inhibitors was assessed. Higenamine induced relaxation of the CC and the aortic strips precontracted with PE in a dose-dependent manner. The CC was significantly more relaxed than the aortic rings in response to the same higenamine concentration (P<0.05). The CC relaxation reaction was suppressed by the β-receptor blocker propranolol. The cAMP concentration increased gradually with increased higenamine concentration (P<0.05). The ICP also increased with increased higenamine concentration in vivo (P<0.05). In the group pretreated with 10(-7) M higenamine, the relaxation reaction of CC induced by the PDE-5 inhibitor increased significantly, compared with CC exposed to the PDE-5 inhibitor but not pretreated with higenamine (P<0.05). In conclusion, higenamine induced relaxation of the rat CC in a dose-dependent manner. The effect may be mediated through β-adrenoceptors. The results suggest that higenamine may be valuable as a new lead compound for treating erectile dysfunction.

Sample size determination for testing equality in a cluster randomized trial with noncompliance

For administrative convenience or cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients rather than individual patients. Furthermore, because of ethical reasons or patient's decision, it is not uncommon to encounter data in which there are patients not complying with their assigned treatments. Thus, the development of a sample size calculation procedure for a CRT with noncompliance is important and useful in practice. Under the exclusion restriction model, we have developed an asymptotic test procedure using a tanh(-1)(x) transformation for testing equality between two treatments among compliers for a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 - β at a nominal α level. We have employed Monte Carlo simulation to evaluate the finite-sample performance of the proposed test procedure with respect to type I error and the accuracy of the derived sample size calculation formula with respect to power in a variety of situations. Finally, we use the data taken from a CRT studying vitamin A supplementation to reduce mortality among preschool children to illustrate the use of sample size calculation proposed here.

Test non-inferiority and sample size determination based on the odds ratio under a cluster randomized trial with noncompliance

Because the odds ratio (OR) possesses certain desirable statistical properties, the OR has been recommended elsewhere to measure the relative treatment effect in establishing non-inferiority. For cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients. Furthermore, it is not uncommon to encounter data in which there are patients not complying with their assigned treatment. Under the Dirichlet multinomial model, we have developed a test statistic for assessing non-inferiority based on the OR between two treatments under a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 - β of detecting non-inferiority with respect to the OR at a nominal α level. Using Monte Carlo simulation, we have evaluated the performance of the proposed test statistic and sample size formula. Finally, we use the CRT studying the effect of vitamin A supplementation on mortality among preschool children to illustrate the use of the sample size formula given here.

Test non-inferiority (and equivalence) based on the odds ratio under a simple crossover trial

For testing the non-inferiority (or equivalence) of a generic drug to a standard drug, the odds ratio (OR) of patient response rates has been recommended to measure the relative treatment efficacy. On the basis of a random effects logistic regression model, we develop asymptotic test procedures for testing non-inferiority and equivalence with respect to the OR of patient response rates under a simple crossover design. We further derive exact test procedures, which are especially useful for the situations in which the number of patients in a crossover trial is small. We address sample size calculation for testing non-inferiority and equivalence based on the asymptotic test procedures proposed here. We also discuss estimation of the OR of patient response rates for both the treatment and period effects. Finally, we include two examples, one comparing two solution aerosols in treating asthma, and the other one studying two inhalation devices for asthmatics, to illustrate the use of the proposed test procedures and estimators.

Surface X-ray speckles: coherent surface diffraction from Au(001)

We present coherent speckled x-ray diffraction patterns obtained from a monolayer of surface atoms. We measured both the specular anti-Bragg reflection and the off-specular hexagonal reconstruction peak for the Au(001) surface reconstruction. We observed fluctuations of the speckle patterns even when the integrated intensity appears static. By autocorrelating the speckle patterns, we were able to identify two qualitatively different surface dynamic behaviors of the hex reconstruction depending on the sample temperature.

Newer fluoroquinolones for treating respiratory infection: do they mask tuberculosis?

Possible masking of tuberculosis (TB) in treatment of community-acquired respiratory infection by newer fluoroquinolones has not been examined in randomised controlled trials. We undertook a randomised, open-label controlled trial involving adults with community-acquired pneumonia or infective exacerbation of bronchiectasis encountered in government chest clinics in Hong Kong. 427 participants were assigned by random permutated blocks of 20 to receive either amoxicillin clavulanate (n = 212) or moxifloxacin (n = 215). Participants were followed for 1 yr for active pulmonary TB. Excluding three participants with positive baseline culture, 13 developed active pulmonary TB: 10 (4.8%) out of 210 were given amoxicillin clavulanate, and three (1.4%) out of 214 were given moxifloxacin. The difference was significant by both proportion and time-to-event analysis. Post hoc analysis showed a significant decrease in the proportion with active pulmonary TB from 4.8% to 2.4% and 0% among participants given amoxicillin clavulanate (n = 210), moxifloxacin for predominantly 5 days (n = 127) and 10 days (n = 87), respectively. The log rank test for trend also showed a significant difference between the three subgroups. Regression models reaffirmed the linear effect; the adjusted odds ratio (95% confidence interval) of active pulmonary TB after moxifloxacin exposure up to predominantly 10 days was 0.3 (0.1-0.9). Newer fluoroquinolones appear to mask active pulmonary TB.

Analyses of fluoroquinolones and Clostridium difficile-associated diarrhoea in tuberculosis patients

SETTING

Systematic studies of fluoroquinolones (FQs) and Clostridium difficile-associated diarrhoea (CDAD) are scarce among tuberculosis (TB) patients, in whom fluoroquinolones (FQs) are increasingly used.

OBJECTIVE

To evaluate the relationship between FQs and CDAD among TB patients.

DESIGN

Retrospective cohort and nested case-control analyses were conducted among 3319 hospital patients on anti-tuberculosis treatment from 1999 to 2005. Each case of CDAD was matched by three sex- and age-matched controls randomly selected from the rest of the cohort. Not every case was confirmed by C. difficile cytotoxins.

RESULTS

Among 38 cases studied, the incidence of CDAD, which was 28.2 (95%CI 20.3-38.3) per 100 000 patient-days overall, increased from 12.9 (95%CI 5.8-25.3) for patients aged <60 years to 26.6 (95%CI 15.5-42.8) for those aged between 60 and 79 years, and 66.9 (95%CI 39.8-106.1) for those aged >79 years. Univariate analysis showed a significant association between CDAD and age, FQs, non-FQ antibiotics, serum albumin level, duration of hospital stay and nasogastric feeding. Only duration of hospital stay and nasogastric feeding remained significant on multivariable analysis.

CONCLUSION

The risk of CDAD due to FQs among TB patients is probably modest after controlling for sex, age, non-FQ antibiotics, serum albumin level, duration of hospital stay and nasogastric feeding.