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PubMed2005

Bounding causal effects under uncontrolled confounding using counterfactuals.

Common sensitivity analysis methods for unmeasured confounders provide a corrected point estimate of causal effect for each specified set of unknown parameter values. This article reviews alternative methods for generating deterministic nonparametric bounds on the magnitude of the causal effect using linear programming methods and potential outcomes models. The bounds are generated using only the observed table. We then demonstrate how these bound widths may be reduced through assumptions regarding the potential outcomes under various exposure regimens. We illustrate this linear programming approach using data from the Cooperative Cardiovascular Project. These bounds on causal effect under uncontrolled confounding complement standard sensitivity analyses by providing a range within which the causal effect must lie given the validity of the assumptions.

Adrenergic beta-Antagonists↗
PubMed1987

A non-linear regression program in BASIC for estimating Km and Vmax.

This paper gives a program in BASIC for calculating the kinetic parameters Km and Vmax for an enzyme reaction from a set of paired values of reaction velocity at given substrate concentrations. An initial estimate of the two parameters is made using a weighted linear regression, these values are then used in an iterative process to fit the data to the Michaelis-Menten equation and give final values of Km and Vmax with their associated standard errors.

Algorithms↗
PubMed2004

Solving and analyzing side-chain positioning problems using linear and integer programming.

MOTIVATION: Side-chain positioning is a central component of homology modeling and protein design. In a common formulation of the problem, the backbone is fixed, side-chain conformations come from a rotamer library, and a pairwise energy function is optimized. It is NP-complete to find even a reasonable approximate solution to this problem. We seek to put this hardness result into practical context. RESULTS: We present an integer linear programming (ILP) formulation of side-chain positioning that allows us to tackle large problem sizes. We relax the integrality constraint to give a polynomial-time linear programming (LP) heuristic. We apply LP to position side chains on native and homologous backbones and to choose side chains for protein design. Surprisingly, when positioning side chains on native and homologous backbones, optimal solutions using a simple, biologically relevant energy function can usually be found using LP. On the other hand, the design problem often cannot be solved using LP directly; however, optimal solutions for large instances can still be found using the computationally more expensive ILP procedure. While different energy functions also affect the difficulty of the problem, the LP/ILP approach is able to find optimal solutions. Our analysis is the first large-scale demonstration that LP-based approaches are highly effective in finding optimal (and successive near-optimal) solutions for the side-chain positioning problem.

Algorithms↗
PubMed2006

Design of optimal food-based complementary feeding recommendations and identification of key "problem nutrients" using goal programming.

The WHO is urging countries to promote improved complementary feeding practices to ensure optimal health, growth, and development of young children. To help achieve this, a rigorous 4-phase approach for designing optimal population- specific food-based complementary feeding recommendations (CFRs) was developed and is illustrated here. In phase I, an optimized diet is selected, using goal programming (Model #1), which aims to provide a desired nutrient content with respect to habitual diet patterns and cost. Based on its food patterns, a set of draft CFRs is designed. In phase II, their success for ensuring a nutritionally adequate diet is assessed via linear programming (Model type #2) by sequentially minimizing and maximizing the level of each nutrient (i.e., worst and best-case scenarios) while respecting the CFRs. For nutrients that are <70% of desired levels, the best food sources are identified via linear programming in phase III (Model #3). Different combinations of these foods are incorporated into the original draft of the CFRs to produce alternative CFRs, which are then compared on the basis of their cost, flexibility, and "worst-case scenario" nutrient levels (Model type #2) to select, in phase IV, a final set of CFRs. A hypothetical example is used to illustrate this approach. Outcomes include a set of optimal, population-specific CFRs and practical information regarding key "problem nutrients" in the local diet. Such information is valuable for nutrition promotion, as well as nutrition program planning and advocacy, to help achieve global initiatives for improving the complementary feeding practices of young children living in disadvantaged environments.

Breast Feeding↗
PubMed2005

Interval fuzzy modeling applied to Wiener models with uncertainties.

This correspondence addresses the problem of interval fuzzy model identification and its use in the case of the robust Wiener model. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion which minimizes the maximum estimation error between the data and the proposed fuzzy model output is used. The min-max optimization problem can then be seen as a linear programming problem that is solved to estimate the parameters of the fuzzy model in each fuzzy domain. This results in lower and upper fuzzy models that define the confidence interval of the observed data. The model is called the interval fuzzy model and is used to approximate the static nonlinearity in the case of the Wiener model with uncertainties. The resulting model has the potential to be used in the areas of robust control and fault detection.

Algorithms↗
PubMed1990

From food basket to food security. The food factor in nutritional surveillance.

One important indicator of nutritional surveillance is the one devoted to monitor food security. The experience toward the development of one of such indicators is presented. This includes the development of a food basket, defined as the group of foods that meet the characteristics such as is now consumed by important population segments of the community; it contributes a substantial portion of the calories and proteins purchased, and is responsible for an important proportion of the food budget. The concept implies a dynamic food basket, the quantities of which are calculated in a way that simulates the behavior of the consumer and the best nutrition knowledge. For this purpose we use linear program techniques. A measure of the risk of being unable to buy the foods needed for a family is presented, and is used as a proxy for food security risk. In the appendix, the mathematical expressions of the model used for a linear program is also presented.

Colombia↗
PubMed2002

Linear and nonlinear programming to optimize the nutrient density of a population's diet: an example based on diets of preschool children in rural Malawi.

BACKGROUND: Food consumption surveys are often used to detect inadequate nutrient intakes but not to determine whether inadequate nutrient intakes are due to suboptimal use of locally available foods or to insufficient availability of nutrient-dense foods. OBJECTIVES: The objectives were to describe the use of linear programming as a method to design nutrient-adequate diets of optimal nutrient density and to identify the most stringent constraints in nutritional recommendations and food consumption patterns in a population's diet. DESIGN: This analysis was conducted with the use of food consumption data collected during 2 seasons from rural Malawian children aged 3-6 y. Linear programming was used to select diets based on local foods that satisfied a set of nutritional constraints while minimizing the total energy content of the diet. Additional constraints on daily intakes of foods and food groups were also introduced to ensure that the diets were compatible with local food patterns. The strength of the constraints was assessed by analyzing nonlinear programming sensitivity. RESULTS: In the harvest season, it was possible to satisfy nutritional recommendations with little departure from the local diet. In the nonharvest season, nutritional adequacy was impaired by the low availability of riboflavin- and zinc-rich animal or vegetable foods and by the high phytate content of other foods. CONCLUSIONS: This analysis suggests that nutrition education may help improve the diets of children in the harvest season, whereas changes in the range of available foods might be needed in the nonharvest season. Linear and nonlinear programming can be used to formulate recommendations with the use of data from local food consumption surveys.

Child↗
PubMed2006

Meeting adequate intake for dietary calcium without dairy foods in adolescents aged 9 to 18 years (National Health and Nutrition Examination Survey 2001-2002).

BACKGROUND: In the United States, >50% of dietary calcium is provided by milk and milk products. Calcium intakes in the United States are inadequate for many children, and a large proportion do not drink milk or consume dairy products. However, no studies have addressed whether dairy-free diets can provide adequate calcium while meeting other nutrient recommendations. OBJECTIVE: To determine the highest calcium intake for adolescents obtained from dairy-free diets, and to examine the relationship between intakes of calcium-fortified foods, using citrus juice as an example, and maximal calcium intakes. DESIGN: In the National Health and Nutrition Examination Survey 2001 to 2002, 65 females and 62 males, aged 9 to 18 years, reported no intake of dairy. We used linear programming to generate diets with maximal calcium intake, while meeting Dietary Reference Intakes for a set of nutrients, limiting energy and fat intakes, and not selecting food quantities exceeding amounts usually eaten in the population. RESULTS: With food use and energy and fat constraints, diets formulated by linear programming provided 1,150 and 1,411 mg/day of calcium for girls and boys, respectively. With the Dietary Reference Intakes constraints, these decreased to 869 and 1,160 mg/day. When we introduced 1.5 servings of fortified juice to the diets, the highest calcium intake increased to 1,302 mg/day for girls and to 1,640 mg/day for boys. CONCLUSIONS: Adequate intake for calcium cannot be met with dairy-free diets while meeting other nutrient recommendations. To meet the adequate intake for calcium without large changes in dietary patterns, calcium-fortified foods are needed. In addition, greater physical activity and responsible sunlight exposure should be encouraged to promote vitamin D adequacy.

Adolescent↗
PubMed2006

Exact and approximation algorithms for DNA tag set design.

In this paper, we propose new solution methods for designing tag sets for use in universal DNA arrays. First, we give integer linear programming formulations for two previous formalizations of the tag set design problem. We show that these formulations can be solved to optimality for problem instances of moderate size by using general purpose optimization packages and also give more scalable algorithms based on an approximation scheme for packing linear programs. Second, we note the benefits of periodic tags and establish an interesting connection between the tag design problem and the problem of packing the maximum number of vertex-disjoint directed cycles in a given graph. We show that combining a simple greedy cycle packing algorithm with a previously proposed alphabetic tree search strategy yields an increase of over 40% in the number of tags compared to previous methods.

Algorithms↗
PubMed2002

Multiple-objective (goal) programming model for feed formulation: an example for reducing nutrient variation.

A multiple-objective programming (MOP) model was applied to the feed formulation process with the objectives of minimizing nutrient variance and minimizing ration cost. A MOP model was constructed for a broiler grower ration (3 to 6 wk) and formulated with a Microsoft Excel solver. Twenty-one ingredients with 17 nutrients were included in the formulation. Amino acids were based on digestible values. The following objectives were considered as soft constraints: (1) meeting the nutrient requirements; (2) meeting the ingredient restrictions; and (3) meeting nutrient ratios, including calcium to phosphorus and the relationship of amino acids to lysine (ideal amino acid ratios). Hard constraints considered were (1) a least-cost ration and (2) minimal nutrient variances for protein, methionine, and lysine. It was found that (1) the MOP model was more flexible in providing a compromise solution than a traditional feed formulation with a linear program, (2) the MOP model was able to handle several conflicting objectives simultaneously as compared to the traditional linear programming approach that could handle only one objective, and (3) the MOP model gave the best compromise solution that would satisfy multiple decision makers when trade-offs were made between the ration cost and minimum variances of protein and methionine. The MOP model is an efficient tool to assist the decision-making process through solving a series of linear/nonlinear programs and by interacting with decision-makers.

Amino Acids↗
PubMed2002

Maximum feasibility guideline in the design and analysis of protein folding potentials.

Protein folding potentials are expected to have the lowest energy for the native shape. The Linear Programming (LP) approach achieves exactly that goal for a training set, or indicates that this goal is impossible to obtain. If a solution cannot be found (i.e., the problem is infeasible) two possible routes are possible: (a) choosing a new functional form for the potential, (b) finding the best potential with a feasible subset of the data, and (or) detecting inconsistent subset of the data in the training set. Here, we explore option (b). A simple heuristic for finding an approximate solution to an infeasible set of linear inequalities is outlined. An approximately feasible solution is obtained iteratively, starting from a certain initial guess, by computing a series of analytic centers of the polyhedra defined by all the inequalities satisfied at the subsequent iterations. Standard interior point algorithms for Linear Programming can be used to compute efficiently the analytic center of a polyhedron. We demonstrate how this procedure can be used for the design of folding potentials that are linear in their parameters. The procedure shows an improvement in the quality of the potentials and sometimes points to flaws in the original data.

Algorithms↗
PubMed2006

A simple approach to optimal control of invasive species.

The problem of invasive species and their control is one of the most pressing applied issues in ecology today. We developed simple approaches based on linear programming for determining the optimal removal strategies of different stage or age classes for control of invasive species that are still in a density-independent phase of growth. We illustrate the application of this method to the specific example of invasive Spartina alterniflora in Willapa Bay, WA. For all such systems, linear programming shows in general that the optimal strategy in any time step is to prioritize removal of a single age or stage class. The optimal strategy adjusts which class is the focus of control through time and can be much more cost effective than prioritizing removal of the same stage class each year.

Plant Development↗
PubMed1982

Structural analysis for the forces in the human spinal column and its musculature.

A method of structural analysis is proposed for a model of the thoracic and lumbar spine which involves body weight, external load, muscle forces, intervertebral reactions and disc and ligament elasticity. The procedure consists of three phases: (i) for an initial position the equations of equilibrium are solved using a linear programming technique which minimizes the total force in the system and produces intervertebral reactions and muscle forces, (ii) for an incremental change in configuration a structural analysis is performed to obtain a further set of intervertebral reactions, (iii) with the net values of intervertebral reactions, from combining the results of the previous two phases, a further application of the linear programming technique is made to obtain the muscle forces in the deformed positions. The results are presented for a subject, in a single step of forward flexion.

Biomechanical Phenomena↗
PubMed2006

The maximal amount of dietary alpha-tocopherol intake in U.S. adults (NHANES 2001-2002).

The current study was designed to determine the maximal amount of alpha-tocopherol intake obtained from food in the U.S. diet, and to examine the effect of different food group intakes on this amount. Data from 2138 men and 2213 women aged >18 y were obtained from the National Health and Nutrition Examination Survey (NHANES) 2001-2002. Linear programming was used to generate diets with maximal alpha-tocopherol intake, with the conditions of meeting the recommended daily allowances or adequate intakes for a set of nutrients, sodium and fat recommendations, and energy limits, and that were compatible with the observed dietary patterns in the population. With food use and energy constraints in models, diets formulated by linear programming provided 19.3-24.9 mg alpha-tocopherol for men and women aged 19-50 or >50 y. These amounts decreased to 15.4-19.9 mg with the addition of the sodium, dietary reference intake, and fat constraints. The relations between maximal alpha-tocopherol intake and food group intakes were influenced by total fat restrictions. Although meeting current recommendations (15 mg/d) appears feasible for individuals, dramatic dietary changes that include greater intakes of nuts and seeds, and fruit and vegetables, are needed. Careful selection of the highest vitamin E source foods within these groups could further increase the likelihood of meeting the current recommended daily allowance.

Adult↗
PubMed1989

Estimation of blood flow distribution in skeletal muscle from inert gas washout.

A new method is evaluated for the estimation of blood flow-to-volume distribution in skeletal muscle from inert gas washout kinetics. Acetylene washout from the isolated, blood-perfused canine gracilis muscle was measured continuously with a blood gas catheter in combination with a mass spectrometer. The washout curves were transformed to flow-to-volume ratio distributions by means of a 50-compartment model. The algorithm fits the expression for the washout curve derived from the model by a least-squares method with enforced smoothing. The algorithm was evaluated using computer simulations in which artificial washout curves were generated by a multicompartment model with a known flow distribution. A wide range of given flow distributions could be recovered from the simulated data. The data were also analyzed using a linear programming technique. Analysis of the experimental data with the least-squares method showed that there is considerable heterogeneity in the distribution of perfusion in resting gracilis muscle. The distribution is characterized by at least two modes and a single compartment with a very low perfusion-to-volume ratio. Experimental noise made it impossible to obtain feasible flow distributions by means of linear programming.

Acetylene↗
PubMed1998

Financial incentives and primary care provision in Britain: do general practitioners maximise their income?

The system of remunerating general practitioners (GPs) in Britain underwent significant changes in April 1990 with the implementation of a new contract between individual GPs and health authorities. The changes were a precursor to a wide-ranging programme of reforms of the British National Health Service. This paper investigates the relationship between financial incentives and the provision of primary health care services in Britain. A comprehensive anonymized data set was used, comprising information on 208 general practices in Scotland which serve just under one million people. An econometric model was tested to identify the determinants of cross-practice variation in the magnitude of the changes in GPs' remuneration levels between the two contracts. A linear programming model was used to examine the GPs' response to the financial incentives built into the new contract. The results of the econometric model indicated that the main beneficiaries of the 1990 contract were the practices which had expanded over the 1989-92 period, re-structured the GPs' partnership and made use of managerial skills by employing a practice manager; those practices also had larger lists in 1992 and relatively more patients attracting deprivation payments. The linear programming model showed that only a small minority of the practices (4.8%) maximised the remuneration from the new contract. Optimal solutions concerning income maximization strategies identified financial disincentives in the fee structure of the remuneration system associated with the provision of selected services and the care of particular groups of patients. The successful adoption of these strategies would involve cream skimming and selective service provision. However, there is no conclusive evidence of British GPs engaging in such activities.

Age Factors↗
PubMed2003

Do economic constraints encourage the selection of energy dense diets?

Economic constraints, by inducing the selection of low cost energy dense diets, could indirectly be responsible for the high prevalence of obesity in low socio-economic status groups. Diet optimisation by linear programming was used to test this hypothesis, by examining the relationship between the cost and the energy density (ED) of modelled diets. Models were developed that minimized the departure from the mean adult French diet estimated from a cross-sectional dietary survey. Palatability constraints were introduced into all models. The impacts of cost on ED and of ED on cost were explored by introducing and strengthening first a constraint on cost and then a constraint on ED. Forcing the cost of the linear programming diets to decrease induced a strong increase in their EDs. In contrast, forcing the ED to increase induced only a moderate decrease in diet costs. These results suggest that, although an energy dense diet can be selected at a relatively high cost, when cost is not influencing food choices, an energy dense diet will be preferentially selected to maintain habitual French dietary patterns when the budget for food is low. This supports the hypothesis that economic constraints play a role in the high prevalence of obesity in low-income people.

Adult↗
PubMed2003

Effect of feeding protein supplements of differing degradability on omasal flow of microbial and undegraded protein.

Ten ruminally cannulated lactating Holstein cows that were part of a larger trial studying the effects of feeding different proteins on milk production were used in a replicated 5 x 5 Latin square to quantify flows of microbial and rumen-undegradable protein (RUP) in omasal digesta. Cows were fed total mixed rations containing (dry matter basis) 44% corn silage, 22% alfalfa silage, 2% urea, and 31% concentrate. The basal diet contained 31% high-moisture corn; equal N from one of four protein supplements was added to the other diets at the expense of corn: 9% solvent soybean meal (SSBM), 10% expeller soybean meal (ESBM), 5.5% blood meal (BM), and 7% corn gluten meal (CGM). Omasal sampling was used to quantify total AA N (TAAN) and nonammonia N (NAN) flows from the rumen. Estimates of RUP were made from differences between total and microbial N flows, including a correction for RUP in the basal diet. Modifying a spectrophotometric assay improved total purine recovery from isolated bacteria and omasal samples and gave estimates of microbial TAAN and NAN flows that were similar to a standard HPLC method. Linear programming, based on AA patterns of the diet and isolated omasal bacteria and ruminal protozoa, appeared to overestimate microbial TAAN and NAN flows compared to the purine assays. Yields of microbial TAAN and NAN determined using any method was not affected by diet and averaged 32 to 35 g NAN per kilogram of organic matter truly digested in the rumen. On average, National Research Council (NRC) equations underpredicted microbial N flows by 152 g/d (vs. HPLC), 168 g/d (vs. spectrophotometry), and 244 g/d (vs. linear programming). Estimates of RUP (means from the HPLC and spectrophotometric methods) were: SSBM, 27%, ESBM, 45%, BM, 60%, and CGM, 73%. Except for CGM, RUP values averaged about 20 percentage units lower than those reported by the NRC.

Amino Acids↗