Introduction to sample size determination and power analysis for clinical trials

doi:10.1016/0197-2456(81)90001-5

Controlled Clinical Trials

Volume 2, Issue 2, June 1981, Pages 93-113

https://doi.org/10.1016/0197-2456(81)90001-5 Get rights and content

Abstract

The importance of sample size evaluation in clinical trials is reviewed and a general method is presented from which specific equations are derived for sample size determination or the analysis of power for a wide variety of statistical procedures. The method is discussed and illustrated in relation to the t test, tests for proportions, tests of survival time, and tests for correlations as they commonly occur in clinical trials. Most of the specific equations reduce to a simple general form for which tables are presented.

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Accelerometers and patient-reported outcomes (PRO) are used to assess physical activity (PA) in people with multiple sclerosis (pwMS). So far it is unknown, however, whether these assessments represent mobility limitations in pwMS with mild and moderate to severe disability alike. The primary aim of the study was to assess the correlation between accelerometry and International Physical Activity Questionnaire (IPAQ) scores in pwMS with different degrees of ambulatory impairment. Taken its frequent use into account, the Godin Leisure Time Exercise Questionnaire (GLTEQ) was investigated as additional PRO.
In a prospective cohort of pwMS, correlational analyses were performed between the number of daily steps, time spent in light, moderate to vigorous PA (MVPA) and time spent sitting as assessed using accelerometry (ActiGraph®-GT3X), and the respective IPAQ and GLTEQ scores. Additionally, associations of PA with disease-specific characteristics, aerobic capacity (VO2_peak), walking assessments (Timed 25-Foot Walk, T25FW; 2-Minute Walk Test, 2MWT) and walking perception (Multiple Sclerosis Walking Scale-12; MSWS-12) were explored. Patient subgroups with mild (Expanded Disability Status Scale; EDSS score <4.0) and moderate to severe disability (EDSS ≥4.0) were analysed for the impact of ambulatory impairment on PA. Multiple linear regression was used to determine predictors of PA.
A total of 56 pwMS completed the study, with a mean (standard deviation, SD) age of 48.4 (10.3) years, disease duration of 14.8 (9.6) years and median (interquartile range) EDSS score of 3.5 (2.0 – 4.4). Moderate to weak correlations were found between daily step count and IPAQ total metabolic equivalent (MET) minutes/week (p < 0.001; r = 0.506), MVPA MET-minutes/week (p < 0.01; r = 0.479) and walking MET-minutes/week (p < 0.05; r = 0.372) in the total cohort. Time spent sitting was inversely correlated with total MET-minutes/week and MVPA MET-minutes/week (p < 0.05; r = -0.358 and r = -0.365). Subgroup analysis revealed, that daily step count was significantly correlated with total MET-minutes/week, MVPA MET-minutes/week and walking MET-minutes/week (p < 0.01, r = 0.569; p < 0.01, r = 0.531 and p < 0.05, r = 0.480, respectively) in the “mild disability” subgroup only, whereas time spent sitting was inversely correlated with total MET-minutes/week (p < 0.05; r = -0.582) in the “moderate to severe disability” subgroup. There was no association between objectively assessed PA and GLTEQ scores in any group. In the total cohort, moderate to weak correlations were found between daily step count and walking assessments (T25FW: p < 0.01, ρ = -0.508; 2MWT: p < 0.01, ρ=0.463) and MSWS-12 (p < 0.001; ρ = -0.609). Moderate to weak correlations were also observed between VO2_peak and walking assessments (T25FW: p < 0.01; ρ = -0.516; 2MWT: p < 0.01, ρ=0.480). Multiple linear regression analysis identified disability and VO2_peak as predictors of PA (p = 0.045; β=0.25 and p < 0.001; β=0.49).
Significant associations of objective PA measurements using accelerometry with IPAQ were found only in pwMS with “mild disability”. In pwMS with “moderate to severe disability”, IPAQ did not reflect the objectively assessed amount of PA. In our cohort, GLTEQ showed no association with objectively assessed PA. Thus, an MS-specific self-reported questionnaire for assessing PA is warranted.
Sample size determination for time-to-event endpoints in randomized selection trials with generalized exponential distribution
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Randomized selection trials are frequently used to compare experimental treatments that have the potential to be beneficial, but they often do not include a control group. While time-to-event endpoints are commonly applied in clinical investigations, methodologies for determining the required sample size for such endpoints, except exponential distribution, are lacking. In recent times, there has been a shift in clinical trials, with a growing emphasis on progression-free survival as a primary endpoint. However, the utilization of this measure has typically been restricted to specific time points for both sample size determination and analysis. This alteration in approach could wield a substantial influence on the clinical trial process, potentially diminishing the capacity to discern variances between treatment groups. In the calculation of sample sizes for randomized trials, this investigation operates under the assumption that the time-to-event endpoint conforms to either an exponential, Weibull, or generalized exponential distribution.
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Raman imaging has been employed for a wide range of biological sample analyses, is often chosen for its non-invasiveness, and ability to provide rich information from samples with minimal preparation requirements. In this paper we give a brief overview of the applications of spontaneous Raman imaging in bioanalysis and then consider what Raman imaging in 2050 might look like. We discuss the state of Raman imaging around its inception, then provide a snapshot of current technology, then look towards 2050. We then discuss some of the potential bottlenecks for the continuing development of Raman imaging for biological sample analysis and, where appropriate, outline approaches to overcome these challenges.
Neuropathy 10–15 years after Roux-en-Y gastric bypass for severe obesity: A community-controlled nerve conduction study
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We searched for long-term peripheral nerve complications 10–15 years after Roux-en-Y gastric bypass surgery (RYGB), using a comprehensive nerve conduction study (NCS) protocol.
Patients (n = 175, mean age 52.0, BMI 35.2) and 86 community-controls (mean age 56.8, BMI 27.2) had NCS of one upper and lower limb. New abnormality scores from 27 polyneuropathy-relevant (PNP27s) and four carpal tunnel syndrome-relevant NCS-measures (CTS4s) were compared between groups with non-parametric statistics. Estimated prevalences were compared by 95 % confidence limits. The clinical neurophysiologist’s diagnosis was retrieved from hospital records (PNP-ncs, CTS-ncs, other).
Abnormality score did not differ between RYGB and control groups (PNP27s: 1.9 vs 1.7, CTS4s: 0.7 vs 0.6, p > 0.29). BMI correlated weakly with CTS4s in patients (rho = 0.19, p = 0.01), and less with PNP27s (rho = 0.12, p = 0.12). Polyneuropathy (PNP-ncs) prevalence was 12 % in patients and 8 % in controls. CTS-ncs prevalence was 21 % in patients and 10 % in controls (p = 0.04).
NCS-based abnormality scores did not differ between patients 10–15 years after RYGB and community-recruited controls, neither for PNP nor CTS.
Long-term polyneuropathic complications from RYGB have probably been avoided by modern treatment guidelines. NCS-diagnosed CTS is common in overweight RYGB patients. RYGB-patients with significant neuropathic symptoms need clinical evaluation.
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2024, Cancer Treatment and Research Communications
Accumulating evidence showed that inflammation contributes markedly to cancer progression, with C-reactive protein (CRP) being one of the lengthily studied inflammation marker. For breast cancer (BCa), pre-treatment elevated CRP upon diagnosis was linked with increased mortality. This study aimed to identify factors predictive of elevated CRP in pre-treatment BCa population that can serve as potential therapeutic targets to reduce inflammation.
This is a cross-sectional study using multiple logistic regression to identify predictors of elevated CRP among pre-treatment, newly diagnosed BCa patients. Studied variables were socio-demographic and medical characteristics, anthropometric measurements [body weight, Body Mass Index, body fat percentage, fat mass/fat free mass ratio, muscle mass, visceral fat], biochemical parameters [albumin, hemoglobin, white blood cell (WBC), neutrophil, lymphocyte], energy-adjusted Dietary Inflammatory Index, handgrip strength (HGS), scored Patient Generated-Subjective Global Assessment, physical activity level and perceived stress scale (PSS).
A total of 105 participants took part in this study. Significant predictors of elevated CRP were body fat percentage (OR 1.222; 95 % CI 1.099–1.358; p < 0.001), PSS (OR 1.120; 95 % CI 1.026–1.223; p = 0.011), low vs normal HGS (OR 41.928; 95 % CI 2.155–815.728; p = 0.014), albumin (OR 0.779; 95 % CI 0.632–0.960; p = 0.019), and WBC (OR 1.418; 95% CI 1.024–1.963; p = 0.036).
Overall, predictors of elevated CRP in pre-treatment, newly diagnosed BCa population were body fat percentage, PSS, HGS category, albumin and WBC.
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2023, Archives of Physical Medicine and Rehabilitation
To quantify therapy-attributable effects of a comprehensive inpatient rehabilitation program for lower limb lymphedema (LLL) and to compare the levels of health-related quality of life (HRQL) to population-based norms.
Naturalistic prospective cohort study with intra-individual control of effects.
Rehabilitation hospital.
Patients with LLL (N=67; 46 women).
Comprehensive, multidisciplinary inpatient rehabilitation with 45-60 hours of therapy.
Short Form 36 (SF-36) for HRQL, lymphedema-specific Freiburg Quality of Life Assessment for lymphatic disorders, Short Version (FLQA-lk), knee-specific Knee Outcome Survey Activities of Daily Living Scale (KOS-ADL), and Symptom Checklist-90Standard (SCL-90S). Observed pre/post rehabilitation effects were individually corrected by subtracting the home waiting-time effects and expressed as standardized effect sizes (ESs) and standardized response means (SRMs). Score differences to norms were quantified by standardized mean differences (SMDs).
Participants were on average aged 60.5 years, not yet obese, and had 3 comorbidities (n=67). The greatest improvement was in HRQL on the FLQA-lk with ES=0.767/SRM=0.718, followed by improvements in pain and function with ES/SRM=0.430-0.495 on the SF-36, FLQA-lk, and KOS-ADL (all P<.001). Vitality, mental health, emotional well-being, and interpersonal sensitivity improved most by ES/SRM=0.341-0.456 on all 4 measures (all P≤.003). Post rehabilitation scores were significantly higher than population norms on SF-36 bodily pain (SMD=1.140), vitality (SMD=0.886), mental health (SMD=0.815), and general health (SMD=0.444) (all P<.001), and comparable on the other scales.
Those affected by LLL stages II and III benefited substantially from the intervention, attaining equal or higher levels of HRQL than expected compared with the general population norms. Multidisciplinary, inpatient rehabilitation should be recommended for LLL management.

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View full text

Introduction to sample size determination and power analysis for clinical trials

Abstract

J Chronic Dis

J Chronic Dis

Sample size considerations for clinical trials of potentially hepatotoxic drugs

Statistical inference in clinical trials

Statistical problems in the design of clinical trials and interpretation of results

The importance of Beta, the Type II error and sample size in the design and interpretation of the randomized controlled trial

N Engl J Med

Statistical Methods

Statistical Methods for Rates and Proportions

Sample sizes for medical trials with special reference to long term therapy

J Chron Dis