Sample size graphs for “proving the null hypothesis”

doi:10.1016/0197-2456(84)90116-8

Controlled Clinical Trials

Volume 5, Issue 2, June 1984, Pages 97-105

https://doi.org/10.1016/0197-2456(84)90116-8 Get rights and content

Abstract

Sample size graphs are given for clinical trials designed to test whether an experimental therapy is as effective as a standard therapy. We assume a dichotomous outcome variable and a one-sided test of the hypothesis that the probability of success with standard therapy is greater than the probability of success with experimental therapy by at least some specified amount δ. Graphs are given for significance level α = 0.01, 0.025, 0.05; type II error β = 0.10, 0.20; and δ = 0.10, 0.20.

References (1)

WC Blackwelder
“Proving the null hypothesis” in clinical trials
Controlled Clin Trials
(1982)

Cited by (72)

Lower and extended dosage of misoprostol for cervical ripening in 1st trimester miscarriage (MISO200): A randomized clinical trial
2022, European Journal of Obstetrics and Gynecology and Reproductive Biology
Citation Excerpt :
Uterine bleeding was determined when additional measures were taken by the end of the procedure, e.g., use of intramuscular methylergometrine; cervical laceration was determined when sutures were required. Sample size was calculated according to the literature for a non-inferiority trial [18]. We expected that cervical dilatation would be achieved in 96% of the cases using 400 µg of misoprostol and 86% in the 200 µg group.
To compare the efficacy of priming the uterine cervix before Manual Vaccum Aspiration (MVA) using 200 µg or 400 µg of vaginal misoprostol, inserted a mean time of 6 h before MVA in first trimester miscarriage.
Randomized, triple-blind, non-inferiority clinical trial. Patients between 18 and 50 years old, with a diagnosis of miscarriage, were eligible for the study. Patients were allocated to receive either 200 μg or 400 µg of misoprostol before the MVA. The primary outcome was the need to dilate the uterine cervix with mechanical dilators (Hegar dilators). As a secondary outcome, cervical dilatation ≥8 mm before the procedure was considered successful. A difference of <25% was considered as non-inferior.
Between December 21, 2016 and October 6, 2019, 269 women were screened. After screening, 105 and 106 women received 200 µg and 400 µg of misoprostol, respectively. Mechanical cervical dilatation was not necessary in 84.8% (95%CI 77% to 90%) and 96.2% (95%CI 91% to 99%), in the 200 µg and 400 µg groups, respectively [difference = 11.5% (95%CI 3.7% to 19.2%). Cervical dilatation of ≥8 mm was 52.4% (95%CI 42.9% to 61.7%) in the 200 µg misoprostol group, while in the 400 µg group was 71.7% (95%CI 62.5% to 79.4%) [difference = 19.3% (95%CI 6.5 to 32.2).
After a mean time of 6 h, 200 µg of vaginal misoprostol is not inferior to 400 µg of misoprostol for cervical priming before MVA, in first trimester miscarriage. This non-inferiority was not observed when the ≥8 mm criterion was considered.
Home Management Versus Primary Care Physician Follow-up of Patients With Distal Radius Buckle Fractures: A Randomized Controlled Trial
2021, Annals of Emergency Medicine
Citation Excerpt :
All costs and unit prices are given in Canadian dollars (Table E1, available online at http://www.annemergmed.com). The sample size was determined with methods appropriate for noninferiority trials (ie, trials with nonzero null hypotheses).31-34 The sample size of 110 patients was based on testing the null hypothesis that home management is greater than or equal to 5% less effective than primary care physician follow-up according to the modified ASKp-38 scores at 3 weeks, α=2.5%, and having a 90% probability of rejecting the null hypothesis if home management and primary care physician follow-up are equally effective.
In patients with a distal radius buckle fracture, we determine whether home removal of a splint and physician follow-up as needed (home management) is noninferior to primary care physician follow-up in 1 to 2 weeks with respect to functional recovery. We also compare groups with respect to health care and patient-level costs.
This was a noninferiority randomized controlled trial conducted at a tertiary care children’s hospital. Eligible patients were randomized to home management versus primary care physician follow-up and received telephone contact at 3 and 6 weeks after the index ED visit. Functional recovery was measured with the Activities Scale for Kids–performance, and participants reported wrist-injury-related health care interventions and expenses. The primary outcome was a comparison of the performance score between groups at 3 weeks.
We enrolled 149 patients with mean age 9.5 years (SD 2.7 years), and 81 (54.4%) were male patients. Of the 133 patients (89.3%) with completed 3-week follow-up, the mean Activities Scale for Kids–performance score was 95.4% in the home management group (n=66) and 95.9% in the primary care physician follow-up group (n=67) (mean difference –0.4%; lower bound of the 95% confidence interval –2.4%). There was a mean costs savings of –$100.10 (95% confidence interval –$130.0 to –$70.20) in health care and –$28.2 (95% confidence interval –$49.6 to –$7.0) in patient costs in the home management versus primary care physician follow-up group.
In patients with distal radius buckle fractures, home management is at least as good as primary care physician follow-up with respect to functional recovery. Implementation of the home management strategy also demonstrated significant cost savings.
Randomized noninferiority field trial comparing 2 first-generation cephalosporin products at dry off in quarters receiving an internal teat sealant in dairy cows
2016, Journal of Dairy Science
Citation Excerpt :
The minimum difference in cure rate to declare noninferiority of CF compared with CP was 10% (i.e., the delta for an important difference was 10%). To demonstrate noninferiority, 275 infected quarters at S1 were needed in each group assuming α = 0.05, β = 0.1, and 80% success in the reference group (Blackwelder and Chang, 1984). Assuming 30% prevalence of infections at S1 and 10% loss to follow-up, a minimum of 255 cows per group (1,019 quarters per group) would need to be enrolled.
The study objective was to compare 2 commercial dry cow mastitis products at the quarter level, with concurrent internal teat sealant application, evaluating the cure risk difference, odds of a cure, odds of a new intramammary infection (NIMI) during the dry period, and risk for a clinical mastitis (CM) case between calving and 60 d in milk (DIM). A total of 590 cows (2,360 quarters) from 8 commercial dairy herds in Italy were enrolled and randomized to 1 of the 2 treatments at dry off: Cefovet A (CF; 250 mg of cephazoline; Merial Italia SpA, Milan, Italy), and Cepravin (CP; 250 mg of cephalonium dehydrate MSD Animal Health Srl, Segrate, Italy). Quarter milk samples were collected before dry cow therapy treatment at dry off, 2 to 9 DIM, and 10 to 17 DIM. Quarter milk samples from CM cases were collected during the first 60 DIM. Noninferiority analysis was used to evaluate the effect of treatment on the risk difference of a bacteriological cure during the dry period, the primary outcome. The odds of cure, developing a NIMI during the dry period, and the risk of a CM event within 60 DIM were evaluated with multivariable logistic regression and hazard analysis, respectively. The overall crude quarter-level prevalence of NIMI at dry off was 15.3%. The most common pathogen isolated from milk samples at dry-off was coagulase-negative staphylococci. Noninferiority analysis showed no effect of treatment on the risk difference for a cure between dry off and both postpartum samples, difference was 0.013. The least squares means from the multivariable model evaluating the odds of cure was 94% for CF and 95%for CP. We observed no effect of treatment on the odds for the presence of a NIMI at 2 to 9 DIM (least squares means: CF = 0.09 and CP = 0.07), nor did we note a difference in risk of experiencing a CM event between calving and 60 DIM (hazard ratio = 0.8). In conclusion, no difference was observed between the 2 products evaluated when assessing the aforementioned outcomes in quarters also receiving an internal teat sealant.
Comparison of antibiotic-only and antibiotic-steroid combination treatment in corneal ulcer patients: Double-blinded randomized clinical trial
2011, Canadian Journal of Ophthalmology
Objective: To determine the benefit of early addition of corticosteroids to antibiotics in the treatment of corneal ulcers.
Design: Randomized clinical trial.
Participants: Thirty eyes of 30 patients, over the age of 12 years, with bacterial corneal ulcer confirmed by culture.
Methods: Patients were randomized before enrollment; 15 were treated with gatifloxacin (Zymar) and a masked placebo and the other 15 were treated with gatifloxacin and masked dexamethasone 0.1% (Maxidex). Primary outcome was residual ulcer size at 10 weeks based on digital photographs. Secondary outcomes included residual ulcer area by clinician estimate, visual acuity, VF-14 score, and time to healing.
Results: All subjects (n = 30) demonstrated a reduction in ulcer size over the study period. There was no significant difference between the 2 groups in terms of the primary outcome. There was a significant difference between the 2 groups in 1 of the secondary outcomes. The mean residual ulcer size compared with the baseline by clinician estimate (slit-lamp) was −0.789 mm² for the antibiotic-only group and −4.206 mm² for the antibiotic-steroid group (p = 0.05). Among the other secondary outcomes there were no significant differences between the 2 groups.
Conclusions: No benefit was demonstrated in our primary outcome for using steroids in combination with antibiotic therapy in treatment of corneal ulcers. This study suggests that the early addition of steroids to the antibiotic treatment of corneal ulcers does not seem to be harmful when employed in a closely monitored clinical setting.
Objet: [Établir l’avantage de l’ajout rapide des corticostéroïdes aux antibiotiques dans le traitement des ulcères cornéens.
Nature: Essais cliniques randomisés.
Participants: Trente yeux de 30 patients de plus de 12 ans, ayant un ulcère bactérien de la cornée, confirmé par culture.
Méthodes: Les patients ont été randomisés avant l’inscription; 15 ont été traités la gatifloxacine (Zymar) avec placébo masqué et 15 autres le furent avec gatifloxacine et dexaméthasone masquée 0,1% (Maxidex). Le premier résultat a porté sur la taille résiduelle de l’ulcère après 10 semaines selon les photographies numériques. Les résultats secondaires ont porté sur l’aire résiduelle de l’ulcère selon l’estimation du clinicien, l’acuité visuelle, le score VF-14 et le délai de guérison.
Résultats: Tous les sujets (n = 30) ont montré une réduction de la taille de l’ulcère pendant l’étude. Il n'y eut pas d’écart significatif entre les 2 groupes quant au premier résultat. Les seconds résultats ont présenté un écart important entre les 2 groupes au niveau d’un des résultats. La taille résiduelle moyenne comparativement l’estimation de base du clinicien (biomicroscopie) était −0,789 mm² pour le groupe antibiotique seulement et −4,206 mm² pour le groupe antibiotique stéroïde (p = 0,05). Quant aux autres résultats secondaires, il n'y eut pas d’écarts significatifs entre les 2 groupes.
Conclusions: Nos premiers résultats n'ont pas démontré qu'il était avantageux d’utiliser des stéroïdes en combinaison avec la thérapie antibiotique pour traiter les ulcères de la cornée. Cette étude suggère que l’ajout rapide de stéroïdes au traitement antibiotique des ulcères cornéens ne semble pas nuire dans un encadrement clinique suivi de près.
Prospective, randomized, multicenter Food and Drug Administration investigational device exemption study of lumbar total disc replacement with the CHARITÉ artificial disc versus lumbar fusion: Five-year follow-up
2009, Spine Journal
The CHARITÉ artificial disc, a lumbar spinal arthroplasty device, was approved by the United States Food and Drug Administration in 2004 based on two-year safety and effectiveness data from a multicenter, prospective, randomized investigational device exemption (IDE) study. No long-term, randomized, prospective study on the CHARITÉ disc or any other artificial disc has been published to date.
The purpose of this study was to compare the safety and effectiveness at the five-year follow-up time point of lumbar total disc replacement using the CHARITÉ artificial disc (DePuy Spine, Raynham, MA) with that of anterior lumbar interbody fusion (ALIF) with BAK cages and iliac crest autograft, for the treatment of single-level degenerative disc disease from L4 to S1, unresponsive to nonoperative treatment.
Randomized controlled trial—five-year follow-up.
Ninety CHARITÉ patients and 43 BAK patients.
Self-reported measures: visual analog scale (VAS); validated Oswestry disability index (ODI version 1.0); Short-Form 36 Questionnaire, and patient satisfaction. Physiologic measures: radiographic range of motion, disc height, and segmental translation. Functional measures: work status.
Of the 375 subjects enrolled in the CHARITÉ IDE trial, 277 were eligible for the five-year study and 160 patients thereof completed the five-year follow-up. The completers included 133 randomized patients. Overall success was defined as improvement≥15 pts in ODI vs. baseline, no device failure, absence of major complications, and maintenance or improvement of neurological status. Additional clinical outcomes included an ODI questionnaire as well as VAS, SF-36, and patient satisfaction surveys. Work status was tracked for all patients. Safety assessments included occurrence and severity of adverse events and device failures. Radiographic analyses such as index- and adjacent-level range of motion, segmental translation, disc height, and longitudinal ossification were also carried out.
Overall success was 57.8% in the CHARITÉ group vs. 51.2% in the BAK group (Blackwelder's test: p=0.0359, Δ=0.10). In addition, mean changes from baseline for ODI (CHARITÉ: −24.0 pts vs. BAK: −27.5 pts), VAS pain scores (CHARITÉ: −38.7 vs. BAK: −40.0), and SF-36 questionnaires (SF-36 Physical Component Scores [PCS]: CHARITÉ: 12.6 pts vs. BAK: 12.3 pts) were similar across groups. In patient satisfaction surveys, 78% of CHARITÉ patients were satisfied vs. 72% of BAK patients. A total of 65.6% patients in the CHARITÉ group vs. 46.5% patients in the BAK group were employed full-time. This difference was statistically significant (p=0.0403). Long-term disability was recorded for 8.0% of CHARITÉ patients and 20.9% of BAK patients, a difference that was also statistically significant (p=0.0441). Additional index-level surgery was performed in 7.7% of CHARITÉ patients and 16.3% of BAK patients.
Radiographic findings included operative and adjacent-level range of motion (ROM), intervertebral disc height and segmental translation. At the five-year follow-up, the mean ROM at the index level was 6.0° for CHARITÉ patients and 1.0° for BAK patients. Changes in disc height were also similar for both CHARITÉ and BAK patients (0.7 mm for both groups, p=0.9827). Segmental translation was 0.4 and 0.8 mm in patients implanted with CHARITÉ at L4–L5 vs. L5–S1, respectively, and 0.1 mm in BAK patients.
The results of this five-year, prospective, randomized multicenter study are consistent with the two-year reports of noninferiority of CHARITÉ artificial disc vs. ALIF with BAK and iliac crest autograft. No statistical differences were found in clinical outcomes between groups. In addition, CHARITÉ patients reached a statistically greater rate of part- and full-time employment and a statistically lower rate of long-term disability, compared with BAK patients. Radiographically, the ROMs at index- and adjacent levels were not statistically different from those observed at two-years postsurgery.
Designing bioequivalence studies-how much of a difference is acceptable?
2007, Fertility and Sterility

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^∗: Address reprint requests to: Dr. William C. Blackwelder, National Institute of Allergy and Infectious Diseases, Westwood Building, Room 739, Bethesda, MD 20205.

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Sample size graphs for “proving the null hypothesis”

Abstract

Controlled Clin Trials