Approaches to Modelling Heterogeneity in Longitudinal Studies

<p>This thesis is about estimation bias of longitudinal data when there is correlation between the explanatory variable and the individual effect. In our study, we firstly introduce what is longitudinal data, then we introduce the commonly used estimation methods for the general linear model: the least squares method and maximum likelihood method. We apply these estimation methods to three simple general models which are commonly used to analyse longitudinal data. Secondly, we use frequentist and Bayesian analysis to explore the estimation bias theoretically and empirically, with an emphasis on the heterogeneity bias. This bias occurs where random effect estimation is used to analyse data with nonzero correlation between explanatory variables and the individual effect. We then empirically compare the estimated value with the true value. In this way, we demonstrate and verify the theoretical formulation which can be used to determine the size of the bias [Mundlak, 1978]. In order to avoid the estimation bias, the fixed effect estimation should be used to get the better solution under nonzero correlation situation. The Hausman test is used to confirm this. However, the bias not only occurs when we use frequentist analysis, but also exist by using the Bayesian estimation of random effect model. Finally, we follow the Mundlak [1978] idea, then define the special Bayesian model which can be used as Hausman test and as a comparable model. We also prove that it is best fit model among the random effect, fixed effect and pooled model if there is correlation between explanatory variables and individual effect. Throughout this thesis, we illustrate this ideas using examples based on real and simulated data.</p>

Approaches to Modelling Heterogeneity in Longitudinal Studies

<p>This thesis is about estimation bias of longitudinal data when there is correlation between the explanatory variable and the individual effect. In our study, we firstly introduce what is longitudinal data, then we introduce the commonly used estimation methods for the general linear model: the least squares method and maximum likelihood method. We apply these estimation methods to three simple general models which are commonly used to analyse longitudinal data. Secondly, we use frequentist and Bayesian analysis to explore the estimation bias theoretically and empirically, with an emphasis on the heterogeneity bias. This bias occurs where random effect estimation is used to analyse data with nonzero correlation between explanatory variables and the individual effect. We then empirically compare the estimated value with the true value. In this way, we demonstrate and verify the theoretical formulation which can be used to determine the size of the bias [Mundlak, 1978]. In order to avoid the estimation bias, the fixed effect estimation should be used to get the better solution under nonzero correlation situation. The Hausman test is used to confirm this. However, the bias not only occurs when we use frequentist analysis, but also exist by using the Bayesian estimation of random effect model. Finally, we follow the Mundlak [1978] idea, then define the special Bayesian model which can be used as Hausman test and as a comparable model. We also prove that it is best fit model among the random effect, fixed effect and pooled model if there is correlation between explanatory variables and individual effect. Throughout this thesis, we illustrate this ideas using examples based on real and simulated data.</p>

Productivity and growth in cowpea inoculated with rhizobia under different light environments

The objective of this work was to verify the influence of light environments combined with rhizobia inoculation on cowpea growth and productivity. A completely random design was used in a 4x4 factorial scheme, with four light environments, four nitrogen sources and eight replicates in split plot parcels. Light environments were set by means of photo-conversion and thermo-conversion nettings (Aluminet®, red net and black net) and control treatment without shading (full sun). Nitrogen sources were constituted by the strains INPA 03-11B - SEMIA 6462 (Bradyrhizobium elkanni) and UFLA 03-84 - SEMIA 6461 (Bradyrhizobium viridifuturi), and two control treatments: with 70 kg ha-1 of mineral nitrogen and without N. Plant height, indices of chlorophyll a, b and total chlorophill, the number of leaves, number of nodules, dry matter of nodules, dry matter of the aerial portion, dry matter of roots and total dry matter, relative efficiency, gathering of nitrogen in the aerial portion, number, length and matter of pods per plant and dry matter of 100 grains, were evaluated. . There was interaction between light conditions and nitrogen sources for the number of nodules. Individual effect was observed in all other variables. Strain INPA 03-11B was able to promote higher nodulation in cowpea plants in light environments under full sun and Aluminet and the strain UFLA 03-84 only under full sun conditions. However, the efficiency of diazotrophic bacteria to promote vegetative growth, nitrogen gathering and production was not influenced by different light environments. Thus, full sun cultivation is recommended, independently of the nitrogen source used.

Evaluation of Opuntia ficus-indica potential as a natural coadjuvant for vinasse treatment

Agro-industrial waste is generated in large quantities, producing negative environmental impacts. For instance, in the distillation process of vinasses, up to 15 L are produced per alcohol produced. Therefore, it is necessary to search for ecological alternatives. Biological treatments are not recommended because vinasses contain compounds, such as melanoidins, which exert inhibitory activity against microorganisms. Thanks to this activity, melanoidins could be removed, recovered, and become a value-added product. In this study, Opuntia ficus-indica (OFI) mucilage, a natural biopolymer as coadjuvant, was used to improve the coagulation-flocculation process in the treatment of real samples of mezcal vinasses, after evaluating the individual effect of aluminum sulfate and ferric chloride. It was possible to eliminate 90% of color using ferric chloride, showing better removals than aluminum sulfate. However, the effect of ferric chloride plus OFI mucilage generated an adverse effect because the removal was under 17%. The individual effect of ferric chloride for chemical oxygen demand (COD) removal was 28%. This removal was improved by the addition of OFI mucilage, as it was able to increase removal to 84%. The natural coadjuvant was shown to be effective in the COD removal in the treatment of mezcal vinasse using the coagulation-flocculation process.

CFTR Modulators: Does One Dose Fit All?

For many people with cystic fibrosis (pwCF), CFTR modulators will be the cornerstone of their treatment. These modulators show robust treatment effects at group level in pwCF with specific mutations. The individual effect however, is variable. In this review we will explain reasons for reconsideration of dosing regimens of CFTR modulating therapy in order to improve treatment response and prevent side effects. Since the effect of a drug depends on pharmacodynamics and pharmacokinetics, pharmacodynamics and pharmacokinetic properties of CFTR modulators will be discussed. Pharmacokinetic-pharmacodynamic relationships will be used to gain insight in dosage response and exposure response relationships. To understand the cause of variation in drug exposure, pharmacokinetic properties that may change due to CF disease will be explained. We show that with current insight, there are conceivable situations that give reason for reconsideration of dosing regimens, however many questions need to be unravelled.

THE INFLUENCE OF EXPEDITED FABRICATION RATE, UNRELIABLE MACHINES, SCRAP, AND REWORK ON THE PRODUCTION RUNTIME DECISION IN A VENDOR-BUYER COORDINATED ENVIRONMENT

Transnational manufacturing firms operate in highly competitive marketplaces. This means that they are continuously seeking ways to reduce order response and fabrication cycle times, maintain the desired product quality, manage unanticipated machine failures, and provide timely delivery to effectively minimize overall operating cost and maintain a competitive advantage over their intra-supply chains. To assist firms in achieving these operational goals, we examine a buyer-vendor coordinated system with an expedited fabrication rate, unreliable machines, scrap, and rework, with the objective of minimizing the overall operating costs. An imperfect manufacturing process is assumed, which arbitrarily produces repairable and scrap items, with the latter being reworked in each fabrication cycle. Additionally, the process is subject to a Poisson-distributed machine breakdown. The corrective action is undertaken immediately when the machine fails, and the production of unfinished/interrupted lot resumes when the process is restored. The expedited fabrication rate option is used at an extra cost to reduce the cycle length. We built a fabrication-shipment model to characterize the problem’s features explicitly. Mathematical and optimization approaches assist us in determining the optimal fabrication runtime policy. A numerical example illustrates the capability/applicability of our outcomes. Furthermore, it exposes a diverse set of information relating to the collective/individual effect of differences in the expedited rates, mean-time-to-breakdown, frequency of shipment, and rework/disposal rates of defective items on the optimal policy, utilization, total operating cost, and various cost contributors. This information can contribute to facilitating better decision-making.

The interaction on hypertension between family history and diabetes and other risk factors

To explore the individual effect and interaction of diabetes and family history and other risk factors on hypertension in Han in Shanghai China. The method of case–control study with l:l matched pairs was used, 342 cases of hypertension and 342 controls were selected and investigate their exposed factors with face-to-face. The method of epidemiology research was used to explore the individual effect and interaction of diabetes and family history and other risk factors on hypertension. The individual effect of family history (OR = 4.103, 95%CI 2.660–6.330), diabetes (OR = 4.219, 95%CI 2.926–6.083), personal taste (OR = 1.256, 95%CI 1.091–1.593), drinking behavior (OR = 1.391, 95%CI 1.010–1.914) and smoking behavior (OR = 1.057, 95%CI 1.00–1.117) were significant (p < 0.05). But individual effect of sex, education, occupation, work/life pressure, environmental noise, sleeping time and sports habit were not significant (p > 0.05). The OR of interaction between FH and DM to hypertension was 16.537 (95%CI 10.070–21.157), between FH and drinking behavior was 4.0 (95%CI 2.461–6.502), FH and sport habit was 7.668 (95%CI 3.598–16.344), FH and personal taste was 6.521 (95%CI 3.858–11.024), FH and smoking behavior was 5.526 (95%CI 3.404–8.972), FH and work/life pressure was 4.087 (95%CI 2.144–7.788). The SI of FH and DM was 2.27, RERI was 8.68, AP was 52.48% and PAP was 55.86%. FH and DM, personal taste, smoking behavior had positive interaction on hypertension, but FH and sport habits, drinking behavior, work/life pressure had reverse interaction on hypertension. FH and diabetes were very important risk factors with significant effect for hypertension. FH and diabetes, personal taste, smoking behavior had positive interaction on hypertension, but FH and sport habits, drinking behavior, work/life pressure had reverse interaction on hypertension.