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Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
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Dosage Regimens: Partial Pharmacokinetic Parameters

It is not uncommon for complete drug pharmacokinetic profiles to remain elusive in pharmacokinetics. This necessitates certain educated assumptions by pharmacokineticists to determine appropriate dosage regimens without comprehensive pharmacokinetic data from animal or human studies. One prevalent assumption is setting the bioavailability factor, denoted as F, to 1 or 100%. This assumption caters to the scenario where a drug doesn't achieve full systemic absorption, resulting in the patient...
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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Midpoint Rule01:20

Midpoint Rule

Approximating areas under curved boundaries is a common problem in applied mathematics, particularly when an exact calculation is difficult or impractical. One effective numerical method for this purpose is the Midpoint Rule, which provides an estimate of the area under a curve by using rectangular approximations over a specified interval.Description of the Midpoint RuleThe Midpoint Rule begins by dividing the given interval into a number of equal subintervals. For each subinterval, the...
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In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
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Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...

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On approximations in treatment costing

D K Whynes1, A R Walker

  • 1Department of Economics, University of Nottingham, UK.

Health Economics
|January 1, 1995
PubMed
Summary

Economists can use crude costing for aggregate analysis of colorectal cancer surgical treatment costs, but reduced lists reduce accuracy. Total costs are predictable, though functional form specification is challenging.

Area of Science:

  • Health Economics
  • Surgical Oncology
  • Cost-Effectiveness Analysis

Background:

  • Detailed cost evaluations in healthcare are often time-consuming and resource-intensive.
  • Economists seek efficient methods for cost assessment in clinical evaluations.
  • Acute care costing for colorectal cancer surgery presents specific challenges.

Purpose of the Study:

  • To assess the accuracy and viability of cost-saving methods in acute care settings.
  • To compare detailed costing with reduced list costing and econometric estimation for colorectal cancer surgery.
  • To determine the reliability of different costing approaches for research and clinical sub-samples.

Main Methods:

  • Comparison of a detailed costing study with reduced list costing methodologies.

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  • Utilized econometric estimation techniques to model healthcare costs.
  • Analyzed colorectal cancer surgical treatment data within an acute care framework.

    • Main Results:

    • Reduced list costing offers research economies but significantly compromises accuracy.
    • Crude costing, using specialty averages, is acceptable for aggregate analysis but introduces bias for specific patient sub-samples.
    • Total costs demonstrate predictability from limited variables with high accuracy, despite challenges in ex ante functional form specification.

    Conclusions:

    • Simplified costing methods must be carefully evaluated for accuracy trade-offs.
    • Aggregate cost analysis can utilize crude costing, but patient-specific analyses require more detailed or refined methods.
    • Predictive modeling of total costs is feasible, highlighting potential for efficient cost management in surgical care.