scholarly journals Bayesian Analysis of an Optimal Five Period Cross-over Design

2021 ◽  
pp. 123-130
Author(s):  
Cornelious Omwando Nyakundi ◽  
Isaac Kipkosgei Tum
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Method ◽  
Repeated Measurements ◽  
Unbiased Estimation ◽  
Experimental Unit ◽  
Carryover Effects ◽  
Significant Treatment ◽  
Analysis Methods ◽  
Carry Over ◽  
Highest Posterior Density

A crossover design is a repeated measurements design such that each experimental unit receives different treatments during the different time periods. In a majority of bioequivalence studies, design and analysis of cross-over using classical methods such as analysis of variance (ANOVA) and test are normally associated with erroneous results. The Bayesian method is desirable in the analysis of crossover designs to eliminate errors associated with carryover effects. The objective of this study was to compare the Bayesian and the - test analysis methods on treatments and carryover effects for an optimal two treatments, five periods and four sequence C (2, 5, 4) design. The treatments and residual estimates were obtained using Best Linear Unbiased Estimation (BLUE) method. In the Bayesian method of analysis, the posterior quantities were obtained for the mean intervals of treatments and carry-over effects and the highest posterior density (HPD) graphs were plotted and interpreted using conditional probability statements. For validation purposes, the Bayesian method results were compared with the existing -tests results. From the Bayesian analysis, the probability of significant treatment difference in the presence of carryover effects was 1, while from the -test, the calculated value of 11.73 was greater than the two sided tabulated value at 95  level of significance. The two analysis methods implied significant differences in the treatment effects. In conclusion, it was established that Bayesian method of analysis can be used for bioequivalence analysis even when the carry-over effects are present and hence it is highly recommended for bioequivalence studies.

scholarly journals Mathematical Analysis of a Five Periods Crossover Design for Two Treatments

2021 ◽  
Author(s):  
Cornelious Omwando Nyakundi ◽  
Joseph Kipsigei Koske ◽  
John Muindi Mutiso ◽  
Isaac Kipkosgei Tum
Keyword(s):  
Estimation Method ◽  
Simulated Data ◽  
Higher Order ◽  
Repeated Measurements ◽  
Unbiased Estimation ◽  
Experimental Unit ◽  
Best Linear Unbiased Estimation ◽  
Best Linear Unbiased ◽  
Carry Over

Introduction: A cross-over design is a repeated measurements design such that each experimental unit receives different treatments during different time periods. Lower order cross-over designs such as the two treatments, two periods and two sequences C (2, 2, 2) design have been discovered to be inefficient and erroneous in their analysis of treatments efficacy. In this regard, higher order cross-over designs have been recommended and developed like: the two treatments, three periods and four sequence C (2, 3, 4) design; and the two treatments, four periods and four sequence C (2, 4, 4) designs. However, there still exists more efficient higher order cross-over designs for two treatments which can be used in bioequivalence experiments. This study gives a new design and analysis for two treatments, five periods and four sequence C (2, 5, 4) cross-over design that gives more precise estimates and provides estimates for intra subject variability. Method: A hypothetical case study was considered on 160 experimental units which are assumed to be randomly selected from a given population. A cross over design of two treatments (A, B) in five periods whose sequences are given by BABAA, ABABB, BAABA and ABBAB were used. Each of the experimental units was used as its own control. The estimates for both direct treatments and treatments carry-over effects were obtained using best linear unbiased estimation method (BLUE). We simulated data for two treatments in five periods and four sequences and used it to test the null hypotheses of no significant differences in both the direct treatments and treatments carry-over effects using the

scholarly journals Effect of a Commercial Bentonite Clay (Smectite Clay) on Dairy Cows Fed Aflatoxin-Contaminated Feed

Dairy ◽  
2020 ◽  
Vol 1 (2) ◽  
pp. 135-153
Author(s):  
Antonio Gallo ◽  
Gabriele Rocchetti ◽  
Fiorenzo Piccioli Cappelli ◽  
Saverio Pavone ◽  
Anna Mulazzi ◽  
...  
Keyword(s):  
Dairy Cows ◽  
Latin Square ◽  
Bentonite Clay ◽  
Repeated Measurements ◽  
Adaptation Period ◽  
The European Union ◽  
Smectite Clay ◽  
Carry Over ◽  
Dairy Milk ◽  
The Impact

We evaluated the impact of dietary supplementation with a commercially available smectite clay (TOXO® MX, Trouw Nutrition, Amersfoort, The Netherlands), that binds to aflatoxins (AFs), on the performance and health status of multiparous lactating Holstein dairy cows that received dietary AFB1 (the main AF). The carry-over of AFB1 was determined by measuring AFM1 (the main metabolite) in dairy milk. Performance values, blood markers, and liver inflammatory markers were also measured. Nine multiparous mid-lactation Holstein cows (parity: 2.67 ± 0.86; days in milk: 91 ± 15 days; milk yield: 40.4 ± 2.7 kg/cow/day) were assigned to one of three treatments in a 3 periods × 3 treatments Latin square design (n = 3). In particular, three cows each received the CTR-0 diet (total mixed ration (TMR) with normal corn meals), the CTR-AFLA diet (CTR-0 diet with 17.53 ± 6.55 µg/kg DM AFBI), or the TRT diet (CTR-AFLA diet with 100 ± 1 g/cow/day of smectite clay). The AFB1 level was 0.63 ± 0.50 µg/kg DM in the CTR-0 diet, 2.28 ± 1.42 µg/kg DM in the CTR-AFLA diet, and 2.13 ± 1.11 µg/kg DM in the TRT diet. The experiment consisted of an adaptation period (21 days) and three 17-day experimental periods, each consisting of a 10-day intoxication period and 7-day clearance period. Data were analyzed using the MIXED procedure of SAS (SAS Inst. Inc., Cary, NC, USA) with or without repeated measurements. Overall, the addition of AFB1 reduced the DM intake, but the groups had no significant differences in milk yields. The highest feed efficiency was in the TRT group. Measurement of AFM1 in milk indicated a “plateau” period, from day 4 to day 10 of the intoxication period, when the AFM1 level exceeded the guidelines of the European Union. The commercial smectite clay reduced milk AFM1 concentration by 64.8% and reduced the carry-over by 47.0%. The CTR-0 and TRT groups had similar carry-over levels of AFM1, although the absolute concentrations differed. The groups had no significant differences in plasma biomarkers. These results indicate that the commercially available smectite clay tested here was effective in adsorbing AFs in the gastro-intestinal tracts of cows, thus reducing the excretion of AFM1 into dairy milk.

scholarly journals Optimal Designs for Carry Over Effects the Case of Two Treatment and Four Periods

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1179
Author(s):  
Miltiadis S. Chalikias
Keyword(s):  
Experimental Designs ◽  
Optimal Designs ◽  
Experimental Unit ◽  
Carry Over ◽  
Carry Over Effect

The optimal cross-over experimental designs are derived in experiments with two treatments, four periods, and an experimental unit. The results are given for the values n = 0mod4, 1mod4, 2mod4 and 3mod4. The criterion being the minimization of the variance of the estimated carry over effect.

Investigating the Effect of Prior Distributions on Posterior Estimates of Common Cause Failure Parameters Using Bayesian Method

2020 ◽  
Vol 6 (3) ◽  
Author(s):  
Edward Shitsi ◽  
Emmanuel K. Boafo ◽  
Felix Ameyaw ◽  
H. C. Odoi
Keyword(s):  
Bayesian Analysis ◽  
Confidence Level ◽  
Bayesian Method ◽  
Jeffreys Prior ◽  
Uncertainty Interval ◽  
Prior Distributions ◽  
Common Cause ◽  
Common Cause Failure ◽  
Dirichlet Prior ◽  
The Mean

Abstract Quantification of common cause failure (CCF) parameters and their application in multi-unit PSA are important to the safety and operation of nuclear power plants (NPPs) on the same site. CCF quantification mainly involves the estimation of potential failure of redundant components of systems in a NPP. The components considered in quantification of CCF parameters include motor operated valves, pumps, safety relief valves, air-operated valves, solenoid-operated valves, check valves, diesel generators, batteries, inverters, battery chargers, and circuit breakers. This work presents the results of the CCF parameter quantification using check valves and pumps. The systems considered as case studies for the demonstration of the proposed methodology are auxiliary feedwater system (AFWS) and high-pressure safety injection (HPSI) systems of a pressurized water reactor (PWR). The posterior estimates of alpha factors assuming two different prior distributions (Uniform Dirichlet prior and Jeffreys prior) using the Bayesian method were investigated. This analysis is important due to the fact that prior distributions assumed for alpha factors may affect the shape of posterior distribution and the uncertainty of the mean posterior estimates. For the two different priors investigated in this study, the shape of the posterior distribution is not influenced by the type of prior selected for the analysis. The mean of the posterior distributions was also analyzed at 90% confidence level. These results show that the type of prior selected for Bayesian analysis could have effects on the uncertainty interval (or the confidence interval) of the mean of the posterior estimates. The longer the confidence interval, the better the type of prior selected at a particular confidence level for Bayesian analysis. These results also show that Jeffreys prior is preferred over Uniform Dirichlet prior for Bayesian analysis because it yields longer confidence intervals (or shorter uncertainty interval) at 90% confidence level discussed in this work.

scholarly journals PSVI-19 Evaluating the effects of day of iron injection after farrowing on nursery performance and hematological criteria

2019 ◽  
Vol 97 (Supplement_2) ◽  
pp. 209-210
Author(s):  
Hayden E Williams ◽  
Cierra Roubicek ◽  
Joel M DeRouchey ◽  
Jason C Woodworth ◽  
Steve S Dritz ◽  
...  
Keyword(s):  
Animal Health ◽  
Negative Control ◽  
Repeated Measure ◽  
Experimental Unit ◽  
Injection Timing ◽  
Growth Data ◽  
Significant Treatment ◽  
Randomized Design ◽  
Nursery Pig ◽  
Pig Performance

Abstract Weaned pigs (n = 311; 5.9 kg BW) were used in a 59-d study evaluating the effects of Fe injection timing after birth on nursery pig performance and hematological criteria. Pigs were weaned at 21 d and allotted to pens based on preweaning Fe treatment with BW balanced across pens within a treatment with 5 or 6 pigs/pen and 10 pens/treatment. The preweaning treatments were a negative control receiving no Fe injection or 200-mg of injectable Fe (Gleptoforte, Ceva Animal Health, Lenexa, KS) provided in a single injection on d 2, 4, 6, 8, or 10 after birth. All pigs were fed common diets after weaning that contained 110 mg/kg of added Fe as FeSO4 provided from the trace mineral premix. Growth data were analyzed as a completely randomized design with pen as the experimental unit. Hematological criteria were measured as a repeated measure with pig as the experimental unit. Overall, increasing the age of pigs receiving a 200-mg Fe injection from 2 to 4 or 6 d after birth increased (quadratic; P = 0.013) d 80 ending BW with a decrease in BW when Fe was provided on d 8 or 10 (Table 1). Not providing an Fe injection after birth worsened (P < 0.05) ADG, ADFI, and d 80 ending BW. Significant treatment×day interactions (P < 0.001) were observed for Hgb and Hct values. These interactions occurred because pigs not receiving an Fe injection after birth had values that increased from d 21 to 35 while pigs receiving an Fe injection had values that decreased from d 21 to 35. While it is common practice to provide an Fe injection within the first 48 hours of birth, these results suggest delaying injection until d 4 or 6 may increase nursery final weight.

scholarly journals PSV-13 Effects of increasing iron dosage in newborn pigs on subsequent nursery performance and hematological criteria

2019 ◽  
Vol 97 (Supplement_2) ◽  
pp. 196-197
Author(s):  
Hayden E Williams ◽  
Joel M DeRouchey ◽  
Jason C Woodworth ◽  
Steve S Dritz ◽  
Mike D Tokach ◽  
...  
Keyword(s):  
Growth Performance ◽  
Animal Health ◽  
Negative Control ◽  
Repeated Measure ◽  
Experimental Unit ◽  
Growth Data ◽  
Significant Treatment ◽  
D 63 ◽  
Nursery Pig ◽  
Pig Performance

Abstract Weaned pigs (n = 308; 5.7 kg BW) were used in a 42-d study evaluating the effects of increasing injectable Fe dose at processing (d 3 after farrowing) on subsequent nursery pig performance and hematological criteria. Pigs were weaned on d 21 and allotted to pens based on previous Fe treatment with BW balanced across pens within a treatment with 5 or 6 pigs/pen and 10 pens/treatment. Treatments applied at processing were a negative control receiving no Fe injection or increasing injectable Fe (Gleptoforte, Ceva Animal Health, Lenexa, KS) to provide 50, 100, 150, 200-mg, or 200-mg plus 100-mg on d 11 post-farrowing. All pigs were fed the same diets after weaning containing 110 mg/kg of Fe from FeSO4 provided from the trace mineral premix. Growth data were analyzed as a CRD with pen as the experimental unit. Hematological criteria were analyzed as a repeated measure with pig as the experimental unit. Overall, increasing injectable Fe improved (linear; P < 0.05) ADG and ADFI (Table 1). Increasing injectable Fe up to 150 mg improved (quadratic; P = 0.011) G:F with a worsening G:F thereafter. There was no evidence of difference in growth performance (P > 0.10) between the 200-mg and the 200 + 100 mg injectable Fe treatments. Significant treatment×day interactions (P < 0.001) were observed for Hgb and Hct because pigs receiving an Fe injection less than 150-mg had increasing values through nursery while all other pigs had values remaining constant until d 63 after birth with no evidence of difference (P > 0.10) amongst all treatments at d 63 after birth. These results suggest that providing a 200-mg Fe injection at processing provides the greatest growth performance in the nursery and Fe in the diet is sufficient to meet the pigs’ Fe requirement to restore blood Fe status at the end of the nursery.

scholarly journals Analysis of COSIMA spectra: Bayesian approach

2014 ◽  
Vol 4 (2) ◽  
pp. 563-588 ◽  
Author(s):  
H. J. Lehto ◽  
B. Zaprudin ◽  
K. M. Lehto ◽  
T. Lönnberg ◽  
J. Silén ◽  
...  
Keyword(s):  
Quantitative Analysis ◽  
Bayesian Method ◽  
Dead Time ◽  
Multivariate Analyses ◽  
Probability Density Functions ◽  
Density Functions ◽  
Mass Scaling ◽  
Tof Sims ◽  
Analysis Methods ◽  
Measured Line

Abstract. We describe the use of Bayesian analysis methods applied to TOF-SIMS spectra. The method finds the probability density functions of measured line parameters (number of lines, and their widths, peak amplitudes, integrated amplitudes, positions) in mass intervals over the whole spectrum. We discuss the results we can expect from this analysis. We discuss the effects the instrument dead time causes in the COSIMA TOF SIMS. We address this issue in a new way. The derived line parameters can be used to further calibrate the mass scaling of TOF-SIMS and to feed the results into other analysis methods such as multivariate analyses of spectra. We intend to use the method in two ways, first as a comprehensive tool to perform quantitative analysis of spectra, and second as a fast tool for studying interesting targets for obtaining additional TOF-SIMS measurements of the sample, a property unique for COSIMA. Finally, we point out that the Bayesian method can be thought as a means to solve inverse problems but with forward calculations only.

scholarly journals Carryover Effects of Prohexadione-calcium on Apples

HortScience ◽  
2005 ◽  
Vol 40 (5) ◽  
pp. 1340-1342 ◽  
Author(s):  
Duane W. Greene
Keyword(s):  
Fire Blight ◽  
Apple Scab ◽  
Growth Control ◽  
Leaf Fall ◽  
Carryover Effects ◽  
Potential Benefits ◽  
Physiological Resistance ◽  
Carry Over ◽  
The Individual ◽  
Prohexadione Calcium

Proheaxadione-calcium (ProCa) was applied to `Spencer' apple trees at rates between 250 to 750 mg·L–1 after harvest but before leaf fall. The following spring terminal growth was reduced linearly from early petal fall through the growing season to leaf fall. ProCa was applied after harvest and before leaf fall at 500 mg·L–1 to `Spigold' apples. The carryover effect on terminal growth persisted for about 2 weeks after bloom. A combination of 500 and 82.5 mg·L–1 ProCa on `Spigold' in the fall and spring, respectively, reduced terminal growth greater than the individual treatments for about 3 weeks after petal fall. Recent report have shown that ProCa can induce physiological resistance to fire blight and apple scab when applied near petal fall. These data support the suggestion that ProCa may be used as a fall application and the carryover effects may result in early growth control. Potential benefits of the carry-over effects of ProCa for early-season suppression of fire blight and apple scab are discussed.

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