Theil Slope Estimate

Author(s):  
Clifford E. Lunneborg
Keyword(s):  
1984 ◽  
Vol 56 (2) ◽  
pp. 536-539 ◽  
Author(s):  
D. L. Sherrill ◽  
G. D. Swanson

The ventilatory response to changes in alveolar (arterial) CO2 is widely used as an index of respiratory control behavior. Methods for estimating these response slopes should incorporate the possibility that there may be errors in both the independent (partial pressure of CO2) and dependent (ventilation) variables. In a recent paper Daubenspeck and Ogden (J. Appl. Physiol. Respirat. Environ. Exercise Physiol. 45:823–829, 1978) have suggested problems inherent in the traditional technique of reduced major axis and have suggested a more contemporary technique of directional statistics. We have previously analyzed both techniques and developed a method to overcome the problems of reduced major axis and problems inherent in the use of directional statistics. Under the assumption of a bivariate normal distribution, we demonstrate that our slope estimate is similar to the maximum likelihood estimate proposed by Mardia et al. (J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 54: 309–313, 1983) for this problem. In addition, we demonstrate a bootstrap statistical approach when the distributions are not normally distributed. These concepts are illustrated using O2-CO2 interaction data.


2020 ◽  
Author(s):  
Emranul Sarkar ◽  
Alexander Kozlovsky ◽  
Thomas Ulich ◽  
Ilkka Virtanen ◽  
Mark Lester ◽  
...  

Abstract. For two decades meteor radars have been routinely used to monitor temperatures around the 90 km altitude. A common method, based on a temperature-gradient model, is to use the height dependence of meteor decay time to obtain a height-averaged temperature in the peak meteor region. Traditionally this is done by fitting a linear regression model in the scattered plot of log10(1 / τ) and height, where τ is the half-amplitude decay time of the received signal. However, this method was found to be consistently biasing the slope estimate. The consequence of such bias is that it produces a systematic offset in the estimated temperature, and thus requiring calibration with other colocated measurements. The main reason for such a biasing effect is thought to be due to the failure of the classical regression model to take into account the measurement error in τ or the observed height. This is further complicated by the presence of various geophysical effects in the data, which are not taken into account in the physical model. The effect of such biasing is discussed on both theoretical and experimental grounds. An alternative regression method that incorporates various error terms in the statistical model is used for line fitting. This model is used to construct an analytic solution for the bias-corrected slope coefficient for this data. With this solution, meteor radar temperatures can be obtained independently without using any external calibration procedure. When compared with colocated lidar measurements, the temperature estimated using this method is found to be accurate within 7 % or better and without any systematic offset.


Blood ◽  
2009 ◽  
Vol 114 (22) ◽  
pp. 1681-1681 ◽  
Author(s):  
Barbara Pro ◽  
Bertrand Coiffier ◽  
Steven M. Horwitz ◽  
Adam Boyd ◽  
Ellen Neylon ◽  
...  

Abstract Abstract 1681 Poster Board I-707 Background The rationally designed antifolate, pralatrexate, has high affinity for reduced folate carrier-1 (RFC-1) and was designed to be retained longer within cancer cells due to efficient polyglutamation by folylpolyglutamyl synthetase (FPGS). Prophylactic vitamin supplementation with folic acid and vitamin B12 is often used by physicians to minimize toxicities seen with antifolate chemotherapy (Scagliotti GV, JCO 2003; 21:1556). Nutritional status is a concern for cancer patients in general, and particularly for patients with aggressive disease that have been treated previously. In the PROPEL study, a pivotal international multi-center Phase 2 study of pralatrexate in patients with relapsed or refractory peripheral T-cell lymphoma (PTCL), patients were treated with pralatrexate and received folic acid and vitamin B12 supplementation. Patients in PROPEL had been treated with a median of three prior regimens, and an overall response rate of 28% by independent central review was observed. The most common grade 3-4 toxicities were thrombocytopenia (32%) and mucositis (22%). This report includes analyses of baseline MMA, Hcy, and RBC folate levels and their association with thrombocytopenia or mucositis in the PROPEL trial. Methods Patients received pralatrexate 30 mg/m2 IV weekly for 6 weeks in 7-week cycles and supplementation with vitamin B12 (1 mg IM q8-10 wks) and folic acid (1.0-1.25 mg PO daily). Eligibility criteria included histologically confirmed PTCL, disease progression after ≥ 1 prior treatment, and ECOG performance status £ 2. MMA, Hcy and RBC folate levels were measured at baseline, prior to vitamin initiation. A linear model was used to estimate the relationship (slope) between each of these baseline values and the maximum grade of mucositis and thrombocytopenia. Results Of the 115 patients enrolled, 111 were evaluable for safety and 109 were evaluable for response. Eighty-nine had baseline MMA levels, 91 had baseline Hcy levels, and 75 had baseline RBC folate levels before initiation of vitamin supplementation. Baseline values are summarized by the highest grade of thrombocytopenia or mucositis in the Table. The linear relationship between maximum mucositis grade on study (0 vs 1-2 vs 3-4) and baseline MMA was statistically significant (slope estimate = 43.3 nmol/L, p = 0.039). In addition, there was a trend for increasing MMA and increasing severity of thrombocytopenia that did not meet statistical significance (slope estimate = 17.6 μmol/L, p = 0.267). No other significant relationships were noted. Conclusions In the subset of relapsed or refractory PTCL patients tested for MMA levels in the PROPEL study, higher levels of baseline MMA were associated with increased severity of mucositis. There was an association between MMA and severity of thrombocytopenia that did not reach statistical significance. RBC folate and Hcy were not predictive of the severity of mucositis and thrombocytopenia in this analysis. Because patients with relapsed or refractory PTCL may have poor nutritional status, all patients treated with pralatrexate, including those with elevated MMA, should be supplemented with vitamins. Additional studies may be warranted to define the relationship between MMA levels and the development of mucositis and thrombocytopenia among patients treated with pralatrexate. Disclosures Pro: Allos Therapeutics, Inc: Research Funding. Horwitz:Allos Therapeutics, Inc: Consultancy, Research Funding. Boyd:Allos Therapeutics, Inc.: Employment. Fruchtman:Allos Therapeutics, Inc.: Employment.


Neurology ◽  
2018 ◽  
Vol 91 (7) ◽  
pp. e635-e642 ◽  
Author(s):  
Adriano Chiò ◽  
Letizia Mazzini ◽  
Sandra D'Alfonso ◽  
Lucia Corrado ◽  
Antonio Canosa ◽  
...  

ObjectiveAmyotrophic lateral sclerosis (ALS) incidence rates are consistent with the hypothesis that ALS is a multistep process. We tested the hypothesis that carrying a large effect mutation might account for ≥1 steps through the effect of the mutation, thus leaving fewer remaining steps before ALS begins.MethodsWe generated incidence data from an ALS population register in Italy (2007–2015) for which genetic analysis for C9orf72, SOD1, TARDBP, and FUS genes was performed in 82% of incident cases. As confirmation, we used data from ALS cases diagnosed in the Republic of Ireland (2006–2014). We regressed the log of age-specific incidence against the log of age with least-squares regression for the subpopulation carrying disease-associated variation in each separate gene.ResultsOf the 1,077 genetically tested cases, 74 (6.9%) carried C9orf72 mutations, 20 (1.9%) had SOD1 mutations, 15 (1.4%) had TARDBP mutations, and 3 (0.3%) carried FUS mutations. In the whole population, there was a linear relationship between log incidence and log age (r2 = 0.98) with a slope estimate of 4.65 (4.37–4.95), consistent with a 6-step process. The analysis for C9orf72-mutated patients confirmed a linear relationship (r2 = 0.94) with a slope estimate of 2.22 (1.74–2.29), suggesting a 3-step process. This estimate was confirmed by data from the Irish ALS register. The slope estimate was consistent with a 2-step process for SOD1 and with a 4-step process for TARDBP.ConclusionThe identification of a reduced number of steps in patients with ALS with genetic mutations compared to those without mutations supports the idea of ALS as a multistep process and is an important advance for dissecting the pathogenic process in ALS.


Author(s):  
Seung Kyu LEE ◽  
Truong An Dang

Purpose This study aims to investigate aspects related to the changing trends of the rainfall extremes in the entire Mekong Delta in the period of 32 years (1984-2015) applying rainfall extreme indices. First, the homogeneity tests were applied to assess the quality of observed rainfall data series. The authors, then, investigated three rainfall indices including the number of very heavy rainfall days 20 mm (R20), number of days above 50 mm (R50) and number of days above 100 mm (R100) applying the Mann-Kendall test and Sen’s slope estimate. Design/methodology/approach First, the homogeneity tests were applied to assess the quality of observed rainfall data series. The authors, then, investigated three rainfall indices including the number of very heavy rainfall days 20 mm (R20), number of days above 50 mm (R50) and number of days above 100 mm (R100) applying the Mann-Kendall test and Sen’s slope estimate. Findings The results of R20 pointed out that an insignificant upward tendency was found in the coastal provinces, whereas an insignificant downward tendency was also recorded in the inland provinces. Regarding the number of R50, a similar trend to R20 was recorded with five stations slightly increased and five stations slightly decreased. For the number of R100, the results recorded an absence of significant trends over the entire study area. Approximately 58.5% of stations show a slightly decreasing trend, while 41.5% of the remaining stations recorded a slightly increasing trend. Originality/value For the number of R100, the results recorded an absence of the significant trends over the entire study area. Approximately 58.5% of stations show a slightly decreasing trend, while 41.5% of the remaining stations recorded a slightly increasing trend. Of note is the fact that the number of R100 occurred more frequently in the northern provinces, which means the northern region is facing a high risk of flooding.


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