Tables for Tolerance Limits for a Normal Population Based on Sample Mean and Range or Mean Range

1958 ◽  
Vol 12 (64) ◽  
pp. 288
Author(s):  
F. E. Grubbs ◽  
S. K. Mitra
Keyword(s):  
Normal Population ◽  
Population Based ◽  
Tolerance Limits ◽  
Sample Mean

scholarly journals Admissible and minimax estimation of the parameters of the selected normal population in two-stage adaptive designs under reflected normal loss function

2019 ◽  
Vol 39 (2) ◽  
pp. 361-383
Author(s):  
Hasan Mazarei ◽  
Nader Nematollahi
Keyword(s):  
Loss Function ◽  
Adaptive Design ◽  
Normal Population ◽  
Sufficient Conditions ◽  
Real Data ◽  
Population Based ◽  
Two Stage ◽  
Sample Mean ◽  
Data Application ◽  
Minimax Estimators

In clinical research, one of the key problems is to estimate the effect of the best treatment among the given k treatments in two-stage adaptive design. Suppose the effects of two treatments have normal distributions with means θ1 and θ2, respectively, and common known variance σ2. In the first stage, random samples of size n1 with means X1 and X2 are chosen from the two populations. Then the population with the larger or smaller sample mean XM is selected, and a random sample of size n2 with mean YM is chosen from this population in the second stage of design. Our aim is to estimate the mean θM or θJ of the selected population based on XM and YM in two-stage adaptive design under the reflected normal loss function. We obtain minimax estimators of θM and θJ, and then provide some sufficient conditions for the inadmissibility of estimators of θM and θJ. Theoretical results are augmented with a simulation study as well as a real data application.

scholarly journals Effects of between-person differences and within-person changes in symptoms of anxiety and depression on older age cognitive performance

2017 ◽  
Vol 48 (8) ◽  
pp. 1350-1358 ◽  
Author(s):  
E. J. Laukka ◽  
D. Dykiert ◽  
M. Allerhand ◽  
J. M. Starr ◽  
I. J. Deary
Keyword(s):  
Cognitive Function ◽  
Cognitive Performance ◽  
Negative Mood ◽  
Depression Scale ◽  
Population Based ◽  
Older Age ◽  
Anxiety And Depression ◽  
Sample Mean ◽  
Assessment And Treatment ◽  
Lothian Birth Cohort

AbstractBackgroundAnxiety and depression are both important correlates of cognitive function. However, longitudinal studies investigating how they covary with cognition within the same individual are scarce. We aimed to simultaneously estimate associations of between-person differences and within-person variability in anxiety and depression with cognitive performance in a sample of non-demented older people.MethodsParticipants in the Lothian Birth Cohort 1921 study, a population-based narrow-age sample (mean age at wave 1 = 79 years, n = 535), were examined on five occasions across 13 years. Anxiety and depression were measured with the Hospital Anxiety and Depression Scale (HADS) and cognitive performance was assessed with tests of reasoning, logical memory, and letter fluency. Data were analyzed using two-level linear mixed-effects models with within-person centering.ResultsDivergent patterns were observed for anxiety and depression. For anxiety, between-person differences were more influential; people who scored higher on HADS anxiety relative to other same-aged individuals demonstrated poorer cognitive performance on average. For depression, on the other hand, time-varying within-person differences were more important; scoring higher than usual on HADS depression was associated with poorer cognitive performance relative to the average level for that participant. Adjusting for gender, childhood mental ability, emotional stability, and disease burden attenuated these associations.ConclusionsThe results from this study highlight the importance of addressing both between- and within-person effects of negative mood and suggest that anxiety and depression affect cognitive function in different ways. The current findings have implications for assessment and treatment of older age cognitive deficits.

scholarly journals Prevalence of isolated gastrocnemius tightness in patients with foot and ankle pathology – a population based study

2018 ◽  
Vol 3 (3) ◽  
pp. 2473011418S0033
Author(s):  
Karan Malhotra ◽  
Oliver Chan ◽  
Nicholas Cullen ◽  
Matthew Welck ◽  
Andrew Goldberg ◽  
...  
Keyword(s):  
Normal Population ◽  
Population Based ◽  
Activity Level ◽  
Control Group ◽  
Power Calculation ◽  
Foot And Ankle ◽  
Population Based Study ◽  
The Difference ◽  
A Prospective Study ◽  
Gastrocnemius Tightness

Category: Other Introduction/Purpose: Gastrocnemius tightness (GT) is thought to predispose patients to multiple musculoskeletal pathologies including back pain, plantar fasciitis, and metatarsalgia. It is thought to be especially prevalent in patients with foot and ankle pathology (FAP) and consequently there is an emerging trend to perform lengthening / release procedures in this patient group. However, it is not clear what proportion of the normal population has GT and how this differs in patients with FAP. We set out to investigate what the incidence and degree of GT in the foot and ankle population is compared to the normal population. Methods: This was a prospective study comparing GT in a cohort of patients with FAP with GT in controls matched for age, gender, and ethnicity. The control group consisted of healthy adult volunteers and the FAP group consisted of patients presenting to our Foot & Ankle unit. Patients with previous surgery, tendoachilles tightness, or ankle arthritis were excluded. GT was measured using a digital inclinometer and the lunge test. It was calculated as the difference between maximal ankle dorsiflexion with the knee extended and with the knee flexed. Data on the control group was collected first and a power calculation suggested a FAP cohort size of 91 feet was required to detect a 2° difference in GT (a= 0.05, ß = 0.05, Ratio 3:1). Results: After case-matching 97 FAP cases were paired with 291 controls for analysis. Mean GT was 8.0° ±5.7° (range: 0-21°) in FAP patients versus 6.0° ±3.5° (range: 0-16°) in controls (p<0.001). Regression analysis demonstrated demographics including BMI and activity level were not significant determinants of GT in the FAP group (r=0.141, p=0.599). Subgroup analysis of the FAP group revealed a mean GT of 10.3° ±6.0° in patients with forefoot pathology (FoP) versus 6.9° ±5.3° in the other FAP patients (NFoP) (p=0.008). When comparing the NFoP group to the controls, there was no difference in GT (p=0.188). In total 21 FAP patients (21.6%) and 12 FoP patients (37.5%) had GT greater than 2 standard deviations of the control group (Figure 1). Conclusion: This population based study demonstrates increased GT in the FAP population versus the normal population; however, in patients without forefoot pathology, this difference may not be clinically relevant. Over a third of patients with forefoot pathology have GT which is greater than the normal population range. We conclude that not all patients with foot and ankle pathology have inherently increased GT, compared with the normal population, but it is reasonably common in patients with forefoot pathology. Further work is required to define what degree of GT may be considered significant, to determine which patients will benefit from surgical treatment.

Multiple Myeloma and Infections: A Population-Based Study Based On 9,610 Multiple Myeloma Patients

Blood ◽  
2012 ◽  
Vol 120 (21) ◽  
pp. 945-945
Author(s):  
Cecilie Blimark ◽  
Ulf-Henrik Mellqvist ◽  
Ola Landgren ◽  
Magnus Björkholm ◽  
Malin L Hultcrantz ◽  
...  
Keyword(s):  
Multiple Myeloma ◽  
Bacterial Infections ◽  
Viral Infections ◽  
Normal Population ◽  
Large Population ◽  
Population Based ◽  
First Year ◽  
Population Based Study ◽  
Prophylactic Measures ◽  
Increased Risk

Abstract Abstract 945 Background Infections are a major cause of morbidity and mortality in patients with multiple myeloma (MM). No large population-based evaluation has been made to assess the risk of infections in MM patients compared to the normal population. Therefore, we performed a large study, using population-based data from Sweden, to estimate the risk of bacterial and viral infections among 9,610 MM patients compared to 37,718 matched controls. Methods We gathered information on all MM patients reported to the nationwide Swedish Cancer Registry from 1988 to 2004, with follow-up to 2007. For each MM patient, four population-based controls (matched by age, sex, and county of residence) were identified randomly from the Swedish population database. Information on occurrence and date of infections was obtained from the centralized Swedish Patient registry that captures information on individual patient-based discharge diagnosis from inpatient (with very high coverage) and outpatient care (since 2000). Cox proportional hazard models were used to estimate the overall, one- and five-year risk of infections. In addition, the effect of gender, age and calendar period of diagnosis was evaluated. Hazard ratios (HRs) and confidence intervals (CIs) were calculated for the occurrence of different infections. Results Overall, MM patients had a 6-fold (HR= 5.9; 95% CI=5.7-6.1) risk of developing any infection compared to matched controls (Figure). The increased risk of developing a bacterial infection was 6-fold (HR=5.9; 95%; CI=5.6-6.1), and for viral infections 9-fold (HR=9.0; 95% CI=8.0-10.1), compared to controls. More specifically, MM patients had an increased risk (p<0.05) of the following bacterial infections: cellulitis (HR=2.6; 95% CI =2.2-3.1), osteomyelitis (HR=3.0; 95% CI 2.0–4.4), endocarditis (HR=4.4; 95% CI 2.9–6.6), meningitis (HR=14.5; 95% CI 9.1–23.0), pneumonia (HR=6.2; 95% CI 5.9–6.5), pyelonephritis (HR=2.5; 95% CI 2.1–3.0), and septicaemia (HR=13.7; 95% CI 12.5–14.9) and for the viral infections influenza (HR=5.4; 95% CI 4.4–6.7) and herpes zoster (HR=12.8; 95% CI 10.5–15.5). The risk of infections was highest during the first year after diagnosis; the risk of bacterial infections was 11-fold (95% CI 10.7–12.9) and the risk of viral infections was 18-fold (95% CI 13.5–24.4) higher compared to controls during the first year after diagnosis. MM patients diagnosed in the more recent calendar periods had significantly higher risk of infections, reflected in a 1.6-fold (95% CI=1.5-1.7) and 2-fold (95% CI=1.9-2.1) increased risk in patients diagnosed during 1994–1999 and 2000–2004, compared to patients diagnosed 1986–1993. Females had a significantly lower risk of infections compared to males (p<0.001). Increasing age was significantly associated with a higher risk of infections (p<0.001). Discussion In this large population-based study including over 9,000 MM patients and 35,000 matched controls, we found that bacterial and viral infections represent a major threat to myeloma patients. We found the risk of specific infections like pneumonia, and septicemia to be over ten times higher in patients than in controls during the first year after MM diagnosis. Importantly, the risk of infections increased in more recent years. The effect on infectious complications due to novel drugs in the treatment of MM needs to be established and trials on prophylactic measures are required. Disclosures: Mellqvist: Janssen, Celgene: Honoraria.

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