Alternative Endoscopy Reading Paradigms Determine Score Reliability and Effect Size in Ulcerative Colitis.

OBJECTIVE: Central reading of endoscopy is advocated by regulatory agencies for clinical trials in ulcerative colitis [UC]. It is uncertain whether the local/site reader should be included in the reading paradigm. We explore whether using locally- and centrally-determined endoscopic Mayo subscores [eMS] provide a reliable final assessment and whether the paradigm used has an impact on effect size. METHODS: eMS data from the TURANDOT [NCT01620255] study were used to retrospectively examine seven different reading paradigms (using the scores of local readers [LR], first central readers [CR1], second central readers [CR2], and various consensus reads [ConCR]) by assessing inter-rater reliabilities and their impact on the key study endpoint, endoscopic improvement. RESULTS: More than 40% of eMS scores between two trained central readers were discordant. Central readers had wide variability in scorings at baseline (intraclass correlation coefficient [ICC] of 0.475 [0.339, 0.610] for CR1 vs CR2). Centrally-read scores had variable concordance with LR (LR vs CR1 ICC 0.682 [0.575, 0.788], and LR vs CR2 ICC 0.526 [0.399, 0.653]). Reading paradigms with LR and CR which included a consensus, enhanced ICC estimates to >0.8. At Week 12, without the consensus reads, the CR1 vs CR2 ICC estimates were 0.775 [0.710, 0.841], and with consensus reads the ICC estimates were >0.9. Consensus-based approaches were most favourable to detect a treatment difference. CONCLUSION: The ICC between the eMS of two trained and experienced central readers is unexpectedly low, which reinforces that currently used central reading processes are still associated with several weaknesses.

Efficacy and safety of topical brepocitinib cream for mild-to-moderate chronic plaque psoriasis: a phase IIb randomized double-blind vehicle-controlled parallel-group study.

BACKGROUND: Plaque psoriasis (PsO) is an inflammatory skin disease driven, in part, by the activation of Janus kinase (JAK) signalling pathways. OBJECTIVES: To assess the efficacy and safety of multiple doses of topical brepocitinib, a tyrosine kinase 2/JAK1 inhibitor, in participants with mild-to-moderate PsO. METHODS: This phase IIb multicentre randomized double-blind study was conducted in two stages. In stage 1, participants received one of eight treatments for 12 weeks: brepocitinib 0.1% once daily, 0.3% once or twice daily, 1.0% once or twice daily, 3.0% once daily, or vehicle once or twice daily. In stage 2, participants received brepocitinib 3.0% twice daily or vehicle twice daily. The primary endpoint was the change from baseline in Psoriasis Area and Severity Index (PASI) score at week 12, analysed using analysis of covariance. The key secondary endpoint was the proportion of participants who achieved a Physician Global Assessment response [score of clear (0) or almost clear (1) and an improvement of ≥ 2 points from baseline] at week 12. Additional secondary endpoints included the difference vs. vehicle in change from baseline in PASI, using mixed-model repeated measures, and the change from baseline in Peak Pruritus Numerical Rating Scale at week 12. Safety was monitored. RESULTS: Overall, 344 participants were randomized. Topical brepocitinib did not result in statistically significant changes compared with respective vehicle controls in the primary or key secondary efficacy endpoints for any dose group. At week 12, least squares mean change from baseline in PASI score ranged from -1.4 to -2.4 for the brepocitinib once-daily groups vs. -1.6 for vehicle once daily, and from -2.5 to -3.0 for the brepocitinib twice-daily groups vs. -2.2 for vehicle twice daily. From week 8, change from baseline in PASI score separated from vehicle in all brepocitinib twice daily groups. Brepocitinib was well tolerated, with adverse events (AEs) occurring at similar rates across groups. One participant in the brepocitinib 1.0% once-daily group developed a treatment-related AE of herpes zoster in the neck area. CONCLUSIONS: Topical brepocitinib was well tolerated but did not result in statistically significant changes compared with vehicle when administered at the doses evaluated to treat signs and symptoms of mild-to-moderate PsO.

Efficacy and safety of topical brepocitinib for the treatment of mild-to-moderate atopic dermatitis: a phase IIb, randomized, double-blind, vehicle-controlled, dose-ranging and parallel-group study.

BACKGROUND: Atopic dermatitis (AD) is a prevalent inflammatory, pruritic skin disease. The Janus kinase (JAK) pathway is a treatment target. OBJECTIVES: To assess the efficacy, safety and pharmacokinetics of topical cream brepocitinib, a small-molecule tyrosine kinase 2 (TYK2)/JAK1 inhibitor, in participants with mild-to-moderate AD. METHODS: In this phase IIb, double-blind, dose-ranging study, participants were randomized to receive one of eight treatments for 6 weeks: brepocitinib 0·1% once daily (QD), 0·3% QD or twice daily (BID), 1·0% QD or BID, 3·0% QD, or vehicle QD or BID. The primary endpoint was the percentage change from baseline in the Eczema Area and Severity Index (EASI) total score at week 6. Adverse events (AEs) were monitored. RESULTS: Overall, 292 participants were enrolled and randomized. The brepocitinib 1% QD and 1% BID groups achieved statistically significantly greater (with multiplicity-adjusted P < 0·05 due to Hochberg's step-up method) percentage reductions from baseline in EASI total score at week 6 [least squares mean (90% confidence interval, CI): QD: -70·1 (-82·1 to -58·0); BID: -75·0 (-83·8 to -66·2)] compared with respective vehicle [QD: -44·4 (-57·3 to -31·6); BID: -47·6 (-57·5 to -37·7)]. There was not a dose-dependent trend in AE frequency, and there were no serious AEs or deaths. CONCLUSIONS: Topical brepocitinib is effective and well tolerated in participants with mild-to-moderate AD. What is already known about this topic? Janus kinase (JAK) inhibitors are in development for treatment of atopic dermatitis (AD). The tyrosine kinase 2 and JAK 1 inhibition by brepocitinib may bring a new profile for topical JAK inhibitors for treatment of mild-to-moderate AD. What does this study add? Topical brepocitinib can provide rapid, effective symptom reduction, and could offer a novel alternative to current topical treatments for mild-to-moderate AD.

In Search of Ambiguity: A Three-Stage Workflow Design to Clarify Annotation Guidelines for Crowd Workers.

We propose a novel three-stage FIND-RESOLVE-LABEL workflow for crowdsourced annotation to reduce ambiguity in task instructions and, thus, improve annotation quality. Stage 1 (FIND) asks the crowd to find examples whose correct label seems ambiguous given task instructions. Workers are also asked to provide a short tag that describes the ambiguous concept embodied by the specific instance found. We compare collaborative vs. non-collaborative designs for this stage. In Stage 2 (RESOLVE), the requester selects one or more of these ambiguous examples to label (resolving ambiguity). The new label(s) are automatically injected back into task instructions in order to improve clarity. Finally, in Stage 3 (LABEL), workers perform the actual annotation using the revised guidelines with clarifying examples. We compare three designs using these examples: examples only, tags only, or both. We report image labeling experiments over six task designs using Amazon's Mechanical Turk. Results show improved annotation accuracy and further insights regarding effective design for crowdsourced annotation tasks.

Oral tyrosine kinase 2 inhibitor PF-06826647 demonstrates efficacy and an acceptable safety profile in participants with moderate-to-severe plaque psoriasis in a phase 2b, randomized, double-blind, placebo-controlled study.

BACKGROUND: Psoriasis treatments lack durable efficacy and have inconvenient administration, highlighting the need for new therapies. OBJECTIVE: To evaluate the efficacy and safety of tyrosine kinase 2 inhibitor, PF-06826647, in moderate-to-severe plaque psoriasis. METHODS: This phase 2b, double-blind study randomized participants to oral, once-daily PF-06826647 (1:1:2:2:2) 50:100:200:400 mg:placebo (16 weeks), then 200 or 400 mg (24 weeks) (NCT03895372). The primary end point was a proportion of participants achieving psoriasis area severity index (PASI) 90 at week 16. Secondary end points (PASI50/75/90/100; Physician's Global Assessment) and safety were assessed to week 40. RESULTS: Overall, 178 participants were treated. A significantly greater proportion of participants (risk difference % [90% CI]) achieved PASI90 in the 200-mg (33.0 [18.0, 47.1], P = .0004) and 400-mg (46.5 [30.6, 60.6], P < .0001; week 16) groups versus placebo. Significant increases from placebo were observed for all secondary end points (200 and 400 mg; weeks 6-16; P < .05); increases were evident to week 40 (categorical data). PF-06826647 was well tolerated and most treatment-emergent adverse events were mild/moderate. Eighteen participants discontinued due to treatment-emergent adverse events (14 arising from laboratory abnormalities). LIMITATIONS: Limitations included the large proportion of White males and non-placebo-controlled extension. CONCLUSION: PF-06826647 200 and 400 mg once daily showed significant efficacy versus placebo at week 16 and was well tolerated over 40 weeks.

Safety and Pharmacokinetics of the Oral TYK2 Inhibitor PF-06826647: A Phase I, Randomized, Double-Blind, Placebo-Controlled, Dose-Escalation Study.

Selective inhibition of tyrosine kinase 2 (TYK2) may offer therapeutic promise in inflammatory conditions, with its role in downstream pro-inflammatory cytokine signaling. In this first-in-human study, we evaluated the safety, tolerability, and pharmacokinetics (PK) of a novel TYK2 inhibitor, PF-06826647, in healthy participants. This phase I, randomized, double-blind, placebo-controlled, parallel-group study included two treatment periods (single ascending dose (SAD) and multiple ascending dose (MAD)) in healthy participants and a cohort of healthy Japanese participants receiving 400 mg q.d. or placebo in the MAD period (NCT03210961). Participants were randomly assigned to PF-06826647 or placebo (3:1). Participants received a single oral study drug dose of 3, 10, 30, 100, 200, 400, or 1,600 mg (SAD period), then 30, 100, 400, or 1,200 mg q.d. or 200 mg b.i.d. for 10 days (MAD period). Safety (adverse events (AEs), vital signs, and clinical laboratory parameters), tolerability, and PK were assessed. Overall, 69 participants were randomized to treatment, including six Japanese participants. No deaths, serious AEs, severe AEs, or AEs leading to dose reduction or temporary/permanent discontinuation were observed. All AEs were mild in severity. No clinically relevant laboratory abnormalities or changes in vital signs were detected. PF-06826647 was rapidly absorbed with a median time to maximum plasma concentration of 2 hours in a fasted state, with modest accumulation (< 1.5-fold) after multiple dosing and low urinary recovery. PF-06826647 was well-tolerated, with an acceptable safety profile for doses up to 1,200 mg q.d. for 10 days, supporting further testing in patients.

Safety, tolerability, efficacy, pharmacokinetics, and pharmacodynamics of the oral TYK2 inhibitor PF-06826647 in participants with plaque psoriasis: a phase 1, randomised, double-blind, placebo-controlled, parallel-group study.

BACKGROUND: Blockade of tyrosine kinase 2 (TYK2) signalling has previously shown therapeutic potential in the treatment of psoriasis. The primary objective of this study was to assess the safety and tolerability of the TYK2 inhibitor PF-06826647. METHODS: This phase 1, randomised, double-blind, placebo-controlled, parallel-group study assessed once daily oral dosing of PF-06826647 in participants with plaque psoriasis, at a single clinical research site in the USA. Eligible participants (aged 18-65 years) had plaque psoriasis covering at least 15% of total body surface area and a psoriasis area and severity index (PASI) score of at least 12 at baseline. Participants received PF-06826647 (100 mg or 400 mg), or placebo once daily for 28 days. Using a computer-generated randomisation schedule with a block size of 3, participants were sequentially randomly assigned into two cohorts by the investigator; in the first cohort, participants were randomly assigned in a 2:1 ratio to receive either oral PF-06826647 400 mg or placebo once daily, whereas participants in the second cohort were randomly assigned in a 2:1 ratio to receive either oral PF-06826647 100 mg or placebo once daily. Site, investigator, Pfizer personnel, and participants, were masked to treatment. The primary endpoint was the safety of multiple-dose PF-06826647 in participants with plaque psoriasis. Secondary endpoints were the characterisation of the pharmacokinetics of multiple-dose PF-06826647 in plasma and the change in PASI score at day 28. Safety analysis was done in all participants who received at least one dose of study drug. Efficacy analysis was done in all participants who received at least one dose of randomised study drug, and had a baseline and at least one post-baseline measurement. This study is registered as a randomised, controlled trial with ClinicalTrials.gov, NCT03210961 and is completed. FINDINGS: The trial was done between July 14, 2017, and Jan 25, 2019. Overall from 91 participants assessed, 40 participants with moderate-to-severe psoriasis were randomly assigned to treatment (placebo 14 [35%] of 40; PF-06826647 100 mg, 11 [28%] of 40; PF-06826647 400 mg, 15 [38%] of 40). Treatment-emergent adverse events (TEAEs) were reported in 12 (80%) of 15 participants in the PF-06826647 400 mg group, seven (50%) of 14 in the placebo group and five (45%) of 11 in the 100 mg group. All TEAEs were mild in severity, except one moderate TEAE of vomiting reported in the placebo group. There were no deaths, serious TEAEs, severe TEAEs, dose reductions, or temporary discontinuations. Compared with placebo, the change from baseline in PASI score at day 28 showed a significant reduction in least squares mean difference for the PF-06826647 400 mg group (-13·05; 90% CI -18·76 to -7·35; p=0·00077) but not for the PF-06826647 100 mg group (-3·49; -9·48 to 2·50; p=0·33). Both the area under the concentration-time curve over the dosing interval and the maximum concentration increased in a less than dose proportional manner with increasing dose from 100 mg to 400 mg PF-06826647. INTERPRETATION: PF-06826647 showed significant improvement in disease activity within 4 weeks of dosing with an acceptable safety profile. PF-06826647 holds promise over conventional oral treatments for psoriasis that have shown limited efficacy or unfavourable safety profiles. FUNDING: Pfizer.

Molecular Profiling of Ulcerative Colitis Subjects from the TURANDOT Trial Reveals Novel Pharmacodynamic/Efficacy Biomarkers.

BACKGROUND AND AIMS: To define pharmacodynamic and efficacy biomarkers in ulcerative colitis [UC] patients treated with PF-00547659, an anti-human mucosal addressin cell adhesion molecule-1 [MAdCAM-1] monoclonal antibody, in the TURANDOT study. METHODS: Transcriptome, proteome and immunohistochemistry data were generated in peripheral blood and intestinal biopsies from 357 subjects in the TURANDOT study. RESULTS: In peripheral blood, C-C motif chemokine receptor 9 [CCR9] gene expression demonstrated a dose-dependent increase relative to placebo, but in inflamed intestinal biopsies CCR9 gene expression decreased with increasing PF-00547659 dose. Statistical models incorporating the full RNA transcriptome in inflamed intestinal biopsies showed significant ability to assess response and remission status. Oncostatin M [OSM] gene expression in inflamed intestinal biopsies demonstrated significant associations with, and good accuracy for, efficacy, and this observation was confirmed in independent published studies in which UC patients were treated with infliximab or vedolizumab. Compared with the placebo group, intestinal T-regulatory cells demonstrated a significant increase in the intermediate 22.5-mg dose cohort, but not in the 225-mg cohort. CONCLUSIONS: CCR9 and OSM are implicated as novel pharmacodynamic and efficacy biomarkers. These findings occur amid coordinated transcriptional changes that enable the definition of surrogate efficacy biomarkers based on inflamed biopsy or blood transcriptomics data.ClinicalTrials.gov identifierNCT01620255.

Effect of PF-00547659 on Central Nervous System Immune Surveillance and Circulating ß7+ T Cells in Crohn's Disease: Report of the TOSCA Study.

BACKGROUND AND AIMS: Progressive multifocal leukoencephalopathy [PML], a brain infection associated with anti-integrin drugs that inhibit lymphocyte translocation from bloodstream to tissue, can be fatal. Decreased central nervous system [CNS] immune surveillance leading to this infection has been reported in patients with multiple sclerosis or Crohn's disease treated with anti-integrin antibody natalizumab. PF-00547659 is an investigational human monoclonal antibody for inflammatory bowel disease, targeted against α4ß7-mucosal addressin cell-adhesion molecule-1 [the integrin ligand selectively expressed in the gut]. We hypothesised that this selective agent would not affect central nervous system immune surveillance. METHODS: Cerebrospinal fluid from five healthy volunteers, and from 10 patients with Crohn's disease previously treated with immunosuppressants, was evaluated to assess the feasibility of the study. Subsequently, 39 patients with active Crohn's disease and previous immunosuppression were evaluated over 12 weeks of PF-00547659-induction therapy. We measured total lymphocytes, T cell subsets in cerebrospinal fluid, and circulating ß7+ memory cells. Disease activity was assessed using the Harvey-Bradshaw Index. RESULTS: Patients treated with PF-00547659 had no reduction of cerebrospinal fluid lymphocytes, T-lymphocyte subsets, or CD4:CD8 ratio, whereas circulating ß7+ memory cells increased significantly. A total of 28/35 [80%] patients had a clinical response and 27/34 [79%] had disease remission. Treatment-related adverse events, none serious, were reported in 23/49 [47%] patients. CONCLUSIONS: In patients with active Crohn's disease, natalizumab therapy increases the risk for PML, and the increased risk is thought to be associated with iatrogenic leukopenia within the CNS. PML under PF-00547659 may be a lesser concern, as this agent did not reduce lymphocytes or T cell subsets in the cerebrospinal fluid.

Normal intrathecal leukocyte cell number and composition do not decrease the incidence of post-lumbar puncture headache.

The pathogenesis of post-lumbar puncture headache (PLPH) has remained unclear. A beneficial role of CSF cells in the repair of a post-traumatic dural CSF leak has been suggested. The primary purpose of this study was to investigate the effects of 8weeks of induction therapy with high-dose PF-00547659 on the cellular elements of CNS immune surveillance in patients with active Crohn's Disease and a history of immunosuppressive therapy (Clinicaltrials.govNCT01387594). PF-00547659 is a human monoclonal antibody that binds to mucosal addressin-cell adhesion molecule 1 (MAdCAM-1) on endothelial cells and blocks its interaction with beta7-integrin expressing lymphocytes. The study was executed in three parts or cohorts under two protocols. The incidence of a PLPH was 35% after the initial lumbar puncture, and 26% following the second lumbar puncture. After initiation of PF-00547659 anti-MAdCAM-1 therapy, there was a small and non-significant increase in the numbers of overall CSF leukocytes, and in lymphocyte subsets (CD3+, CD4+, and CD8+ T cells). The lymphocyte composition was unaltered by PF-00547659 anti-MAdCAM-1 therapy. Our observations suggest that normal numbers and composition of intrathecal leukocytes do not decrease the incidence of PLPH.

Anti-MAdCAM antibody (PF-00547659) for ulcerative colitis (TURANDOT): a phase 2, randomised, double-blind, placebo-controlled trial.

BACKGROUND: PF-00547659 is a fully human monoclonal antibody that binds to human mucosal addressin cell adhesion molecule-1 (MAdCAM-1) to selectively reduce lymphocyte homing to the intestinal tract. We aimed to assess the efficacy and safety of PF-00547659 in patients with moderate to severe ulcerative colitis. METHODS: This phase 2, randomised, double-blind, placebo-controlled clinical trial recruited patients aged 18-65 years from 105 centres in 21 countries, with a history (≥3 months) of active ulcerative colitis extending more than 15 cm beyond the anal verge (with a total Mayo score ≥6 and a Mayo endoscopic subscore ≥2) who had failed or were intolerant to at least one conventional therapy. Patients were stratified by previous anti-TNFα treatment, and randomly assigned by a computer-generated randomisation schedule to receive a subcutaneous injection of 7·5 mg, 22·5 mg, 75 mg, or 225 mg PF-00547659 or placebo at baseline, then every 4 weeks. Patients, investigators, and sponsors were blinded to the treatment. The primary endpoint was the proportion of patients achieving remission (total Mayo score ≤2 with no individual subscore >1 and rectal bleeding subscore ≤1) at week 12. The efficacy analysis included all patients who received at least one dose of the randomised treatment; the safety analysis was done according to treatment received. All p values were one-sided and multiplicity-adjusted. This study is registered with ClinicalTrials.gov, number NCT01620255. FINDINGS: Between Nov 2, 2012, and Feb 4, 2016, we screened 587 patients; 357 were eligible and randomly assigned to receive placebo (n=73) or PF-00547659 at doses of 7·5 mg (n=71), 22·5 mg (n=72), 75 mg (n=71), or 225 mg (n=70). Remission rates at week 12 were significantly greater in three of four active-treatment groups than in the placebo group (2·7% [two of 73]): 7·5 mg (11·3% [eight of 71]), 22·5 mg (16·7% [12 of 72]), 75 mg (15·5% [11 of 71]), and 225 mg (5·7% [four of 70]). These rates corresponded to a stratum-adjusted (anti-TNFα-naive and anti-TNFα-experienced) risk difference versus placebo of 8·0% for 7·5 mg (90% CI 1·9 to 14, p=0·0425), 12·8% for 22·5 mg (5·6 to 19·9, p=0·0099), 11·8% for 75 mg (4·8 to 18·8, p=0·0119), and 2·6% for 225 mg (-1·2 to 6·4, p=0·1803). Four of 73 (5·5%) patients had a serious adverse event in the placebo group, ten of 71 (14·1%) in the 7·5 mg group, one of 70 (1·4%) in the 22·5 mg group, three of 73 (4·1%) in the 75 mg group, and three of 70 (4·3%) in the 225 mg group. No safety signal was observed for the study drug. INTERPRETATION: PF-00547659 was safe and well tolerated in this patient population, and better than placebo for induction of remission in patients with moderate to severe ulcerative colitis. The greatest clinical effects were observed with the 22·5 mg and 75 mg doses. FUNDING: Pfizer.

Safety, Pharmacokinetic, and Pharmacodynamic Evaluation After Single and Multiple Ascending Doses of a Novel Selective Androgen Receptor Modulator in Healthy Subjects.

PURPOSE: Tolerability, pharmacokinetic (PK), and pharmacodynamic (PD) properties of single ascending doses (SADs) and multiple ascending doses (MADs) of PF-06260414, a novel selective androgen receptor modulator, were assessed after oral administration in healthy subjects. METHODS: Range of SAD and MAD levels tested were 1 to 400 mg and 3 to 100 mg BID, respectively (n = 8 per cohort). In addition, a 60-mg once-daily (n = 8) cohort and a Japanese cohort receiving 30 mg BID (n = 7) also received PF-06260414. Plasma was collected to study PK properties and hypothalamic-pituitary-gonadal (HPG) axis hormones. Tolerability was evaluated from adverse events (AEs), physical examinations, vital signs, ECGs, and clinical laboratory results. FINDINGS: PF-06260414 was well tolerated with no serious AEs. The most frequently reported AEs were increase in alanine aminotransferase and headache, which were reported by 7 and 3 subjects, respectively. PF-06260414 had fast absorption (median Tmax, approximately 1-2 hours), a mean t½ of approximately 6.9 to 12.8 hours, time-independent PK properties and dose proportionality. Cmax and AUCτ geometric means in Japanese subjects were 98.6% and 79.5% higher than in Western subjects, respectively, but had similar HPG axis modulation. Changes in HPG axis hormones monitored in SADs were similar to placebo. Maximum placebo-corrected modulations were observed for total testosterone and sex hormone-binding globulin in the MAD 100-mg BID regimen. IMPLICATIONS: This study was the first to compare a number of different factors of PF-06260414, including tolerability, PK and PD properties, and ethnic differences between Japanese and Western healthy subjects. PF-06260414 had favorable PK properties and found that sex hormone-binding globulin, total testosterone, and HDL were most sensitive to modulation. ClinicalTrials.gov identifier: NCT02070939.

Binomial confidence intervals for testing non-inferiority or superiority: a practitioner's dilemma.

In testing for non-inferiority or superiority in a single arm study, the confidence interval of a single binomial proportion is frequently used. A number of such intervals are proposed in the literature and implemented in standard software packages. Unfortunately, use of different intervals leads to conflicting conclusions. Practitioners thus face a serious dilemma in deciding which one to depend on. Is there a way to resolve this dilemma? We address this question by investigating the performances of ten commonly used intervals of a single binomial proportion, in the light of two criteria, viz., coverage and expected length of the interval.

Weighted profile likelihood-based confidence interval for the difference between two proportions with paired binomial data.

Inference on the difference between two binomial proportions in the paired binomial setting is often an important problem in many biomedical investigations. Tang et al. (2010, Statistics in Medicine) discussed six methods to construct confidence intervals (henceforth, we abbreviate it as CI) for the difference between two proportions in paired binomial setting using method of variance estimates recovery. In this article, we propose weighted profile likelihood-based CIs for the difference between proportions of a paired binomial distribution. However, instead of the usual likelihood, we use weighted likelihood that is essentially making adjustments to the cell frequencies of a 2 × 2 table in the spirit of Agresti and Min (2005, Statistics in Medicine). We then conduct numerical studies to compare the performances of the proposed CIs with that of Tang et al. and Agresti and Min in terms of coverage probabilities and expected lengths. Our numerical study clearly indicates that the weighted profile likelihood-based intervals and Jeffreys interval (cf. Tang et al.) are superior in terms of achieving the nominal level, and in terms of expected lengths, they are competitive. Finally, we illustrate the use of the proposed CIs with real-life examples.

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.

Bias reduction and a solution for separation of logistic regression with missing covariates.

Logistic regression is an important statistical procedure used in many disciplines. The standard software packages for data analysis are generally equipped with this procedure where the maximum likelihood estimates of the regression coefficients are obtained iteratively. It is well known that the estimates from the analyses of small- or medium-sized samples are biased. Also, in finding such estimates, often a separation is encountered in which the likelihood converges but at least one of the parameter estimates diverges to infinity. Standard approaches of finding such estimates do not take care of these problems. Moreover, the missingness in the covariates adds an extra layer of complexity to the whole process. In this article, we address these three practical issues--bias, separation, and missing covariates by means of simple adjustments. We have applied the proposed technique using real and simulated data. The proposed method always finds a solution and the estimates are less biased. A SAS macro that implements the proposed method can be obtained from the authors.

A comparative study of the bias corrected estimates in logistic regression.

Logistic regression is frequently used in many areas of applied statistics. The maximum likelihood estimates (MLE) of the logistic regression parameters are usually computed using the iterative Newton-Raphson method. It is well known that these estimates are biased. Several methods are proposed to correct the bias of these estimates. Among them Firth (1993) and Cordeiro and McCullagh (1991) proposed two promising methods. The conditional exact method (CMLE) is popular for small-sample estimates, and is available in many software packages. In this article we compare these methods in terms of their bias. In general, our extensive simulations show that the methods proposed by Cordeiro and McCullagh and by Firth work well, though Cordeiro and McCullagh is slightly better in our simulations. In case of separation, Firth or CMLE can be used; however, a judicious approach is required when there is a wide variation in results. Two real data analyses are given exhibiting these properties. The data analysis also includes bootstrap results.