M

in the

In the USA, managed care refers to a system of health care in which services are delivered through a network of contracting hospitals, physicians and other providers, and financed through a set fee. Some forms of managed care, such as Preferred Provider Organizations (PPOs) and Point of Service plans (POSs), allow patients to receive services outside the network but at a higher out-of-pocket price than for in-network services. Health Maintenance Organizations (HMOs) do not allow this. Ideally the managed care organization monitors the quality and appropriateness of care to guard against both over-and under-utilization, although sometimes cost containment or dumping the patient on another cost centre are said to be the most tangible motivations.

204 Mandated Cover

Typically primary care physicians are either salaried or paid capitation rates in HMOs and POSs, but in PPOs they generally are paid on a fee-for-service basis. HMOs and POSs usually require that patients first see a primary care gatekeeper for referrals but this is rarely the case in PPOs. Managed care organizations rely more on supply-side than on demand-side controls (such as the provision only of services for which there is evidence of cost-effectiveness), although recent years have seen substantial increases in patient cost-sharing requirements.

In idealized form, managed health care will effectively control both the demand and the supply side of a local market, acting as agent for members, eliminating demand for ineffective care on the one hand, and negotiating lower prices and restricting provision to services deemed to be cost-effective on the other. In the figure, for example, the 'normal' demand curve D is shifted to the left (DM) and the price negotiated down from P to PM so that total expenditure falls from the amount indicated by the larger rectangle to that indicated by the smaller one. Although the figure does not show the (hoped for) impact on health, it indicates the potential that managed care has for cost control. Essentially the same reasoning often lies behind arguments for 'socialized' medical care.

Mandated Cover

Insurance benefits that are made compulsory by a regulatory or other governmental body.

Marginal Product 205

Manpower Planning

The art of projecting the future demand and supply of particular types of labour so that appropriate policies may be adopted in the short term as regards training and education to ensure that future supplies are adequate for the demands that are to be met. Also known as 'health human resource planning'.

Mantel-Haenszel Test

A form of %2 test. See Chi-squared Test.

Marginal Benefit

The additional benefit from increasing the rate or volume of an activity. Mathematically it is the first derivative of benefit with respect to the (continuous) variable in question.

Marginal Cost

The additional cost from increasing the rate or volume of an activity. Mathematically it is the first derivative of cost with respect to the (continuous) variable in question.

Marginal Cost-effectiveness Ratio

Same as incremental cost-effectiveness ratio.

Marginal Intertemporal Rate of Substitution

The rate at which present consumption will be traded for an increase in future consumption. See Time Preference.

Marginal Product

The increase in output rate obtained by increasing the rate of use of one input. See Production Function.

206 Marginal Rate of Return Marginal Rate of Return

The incremental gain over time (conventionally a year) from sacrificing a little more current consumption or resource. Cf. Rate of Return.

Marginal Rate of Substitution

The marginal rate of substitution in consumption is the (negative) slope of an indifference curve. It is the ratio of the marginal utilities of two goods as one is substituted for the other such as to leave the individual in question indifferent (ceteris paribus).

The marginal rate of substitution in production is the (negative) slope of an isoquant. It is the ratio of the marginal products of two inputs as one is substituted for the other such as to leave the output rate constant (ceteris paribus). Also known as the marginal rate of technical substitution.

Marginal Rate of Transformation

The slope of a production possibilities curve.

Marginal Social Cost

The sum of marginal private cost (costs internal to the decision maker) and marginal external costs.

Marginal Social Value

The sum of individual marginal values placed upon a good or service that all must consume if anyone does. See Public Goods.

Marginal Utility

The increase in utility gained from a small increase in the rate of consumption of the good yielding it. See Diminishing Marginal Utility, Utility.

Market Failure 207

Marginal Utility of Income

The marginal utility to be had from an increment in income. Marginal Value

The maximum value attached to a little more or less of a good, service or desired characteristic. See Demand Curve.

Market Failure

Markets in health care are notable, not because they fail to satisfy any one of the standard assumptions required for competitive markets to achieve Pareto optimality, but because they fail every single one of them: there is enormous asymmetry of information between producers (medical professionals of all kinds) and consumers (patients actual and potential); the agency relationship works imperfectly and can be distorted by systems of physician pay; there is little evidence that patients behave in accordance with the axioms of rational choice theory; markets, especially those for risk, are extremely incomplete; the medical care industry is riven with monopolistic organizations, from those in the pharmaceutical industry through those in the medical professions themselves, to the local monopolies held by hospitals and community-based primary care practices. In addition, much of health care has the character of a public good and generates externalities both physical (as with communicable disease) and psychic (as when you derive comfort from knowing that your neighbours are insured). Health care is also a field in which equity has always been regarded as of at least equal importance to efficiency (even if that is not how economists have allocated their effort).

This accounts for the extensive public intervention in health care and for the development of more or less economically informed methods of professional and other regulation, allocating resources to regions and institutions and conducting health technology appraisals. It also accounts for the substantial demand for health economists in both the private and the public sector beyond secondary and tertiary education.

208 Market Forces Factor

Market Forces Factor

An adjustment made to the national tariff in the National Health Service's commissioning arrangements to allow for local variations in wages and prices.

See Purchaser-provider Split.

Market Imperfections

Broadly, the reasons for market failure.

Market Mechanism

Same as price mechanism.

Market Prices

In national income accounting, Gross Domestic Product or Gross National Product at market prices means that the measure of each includes the effect of taxes and subsidies. Cf. Factor Cost.

Market Segmentation

The act of dividing an overall market into groups, or segments, of consumers with similar characteristics such as age, region of residence or average health status. It is usually done in order to engage in price discrimination in price-searchers' markets. Prices in the markets with less elastic demand tend to be higher. In order to work effectively, the segments need to be such that resale is not possible from low-price to high-price segments (parallel trade) so segmentation is likely to be seen when there is price-searching and the product is highly perishable, transport costs are high, or, where segments correspond to jurisdictions, suppliers have managed to 'capture' regulatory agencies.

Markov Chain

A Markov chain is a sequence of events whose probabilities at any one time interval depend upon previous values in the decision tree. See Markov Model.

Markov Model

Maternal Mortality Rate 209

A type of model used much in cost-effectiveness and cost-utility analyses in which the progress of a disease with and without interventions is modelled in a sequence of time periods, each being associated with a particular measure of health, and each having a probability of moving from it to the next state. The method is an extended form of the decision tree that is particularly suited to the analysis of chronic conditions when a normal decision tree might become uncontrollably complex. Named after the Russian mathematician Andrei Andreyevich Markov (1856-1922).

Markov Node

Decision points in a decision tree.

Markov System

Same as Markov model.

Masking

Same as blinding.

Matching

A process through which pairs of individuals are brought together in order to trade, share or otherwise engage in some mutual activity. There is also matching in biostatistics: selecting a control population that is matched on some characteristics that may influence the outcome of interest independently of the disorder in question.

Maternal Mortality Rate

The number of deaths in a year from puerperal causes divided by the number of live births in the same population in that year, all multiplied by 1000.

210 Matrix Matrix

An array of numbers (called 'elements') displayed in vectors: rows and columns. There is a special algebra for manipulating matrices.

Matrix Approach

A term sometimes used to describe the way in which the costs and benefits of an option are presented.

Maturation Effect

A change in a dependent variable that is due to the passage of time. Maxillofacial Surgery

A branch of dentistry specializing in the surgery of the jaw and mouth. Maximand

That which is to be maximized: for example, health, profit, utility or welfare. Maximin

An ethical rule of distributive fairness which stipulates that one should maximize the welfare of the least well-off person in a society.

Maximum Likelihood Estimation

A method of estimation in which joint probability is reinterpreted as a likelihood function that depends on the model's parameters, given the observed set of data. The parameter values that maximize this function are used as estimates.

Mean Survival 211

Maximum Price Law

A system established in 1966 in The Netherlands whereby a maximum price is set for pharmaceuticals of a particular class, based on comparisons with a selection of other European countries.

MBHC

Acronym for managed behavioral health care in the USA.

MBHO

Acronym for managed health care organization in the USA. See Managed Behavioral Health Care.

McCarran-Ferguson Act

The US McCarran-Ferguson Act was adopted in 1945 after extended controversy over the jurisdiction of state and federal governments in regulating the business of insurance. The principal objective of the Act was to establish the primacy of the states in regulating the industry. The purpose clause of the Act states that the continued regulation and taxation of the business of insurance by states are in the public's best interest and the Act explicitly empowers states to regulate and tax insurance.

Mean

A measure of the central tendency of a set of numbers. The average of a set of numbers. The sum of the observations divided by their number. Arithmetic mean = YXJN, where the Xi are the values of X and N is the total number of observations. The qualifier 'arithmetic' is usually dropped. See Geometric Mean.

Mean Survival

The average period for which a person having particular characteristics survives. See Survival Analysis.

212 Measurement

Measurement

Assigning numbers to entities according to a rule in order to indicate order, size or other characteristics of interest. Cf. Cardinal Scale, Ordinal Scale, Utility Measurement.

Measurement Bias

Bias arising from inaccuracy in measurements, coding or classification in clinical trials.

Median

The middle value of an ordered set of numbers.

Median Voter Model

A theorem in public choice theory states that the median voter determines the rate of output chosen for public goods that are publicly produced (or privately produced but publicly financed). In the figure there are five demand curves for a community of five taxpayers, who each pay the same amount of tax. Public output decisions are taken by simple majority vote. The marginal tax rate is indicated by MT and the demand curves, D1, D2 and so on are the marginal value curves for the five voters. Voter l's preferred output is Qb

Medicaid Notch 213

voter 2's is Q2, and so on. If Q1 is proposed, only voter 1 will support it, the others all preferring larger output rates. If Q2 is proposed, voters 3, 4 and 5 will outvote voters 1 and 2, preferring more. If Q4 is proposed voters 1, 2 and 3 will outvote voters 4 and 5 and voters 1, 2, 3 and 4 will outvote voter 5 in opposing output rate Q5. The rate that commands the majority is Q3, which just happens to be voter 3's preferred rate, and voter 3 is the median voter.

Medicaid

Medicaid is a US health plan developed by the federal government in 1965 as a companion to the Medicare programme. The programme is intended for low-income residents and is addressed particularly to families with children, pregnant women, children, the aged, the blind and the disabled. To be eligible for Medicaid, a person must belong to one of these groups and meet the financial criteria for that group. There are optional groups also, such as the 'medically needy'. Eligibility for the programme is through a means test that reviews the income and resources of the individual or family applying for coverage. Federal law provides that a state may qualify for federal Medicaid matching funds only if it designs its programme within specific federal requirements. These include eligibility for specific population groups, coverage for certain medical services and medical providers, and adherence to specific rules relating to payment methodologies, payment amounts, and cost sharing for Medicaid beneficiaries. To qualify for federal Medicaid matching funds, a state must obtain approval of its Medicaid State Plan.

Medicaid provides open-ended federal contributions according to a statutory formula to participating states with approved plans. The State Medicaid Agency will be reimbursed for a portion of actual expenditures made under the provisions of the state plan. Provided that the state plan meets the basic eligibility criteria, the portion is computed from a formula that takes into account the average per capita income for each state relative to the national average. By law, the portion (known as Federal Medical Assistance Percentage) cannot be less than 50 per cent. See Medicare.

Medicaid Notch

A discontinuity in the leisure-income trade-off for Medicaid beneficiaries that provides a disincentive to work more than a given amount (beyond which substantial benefits are lost).

214 Medical Savings Account

Medical Savings Account

A trust account established for the benefit of an employee (or, in some places, established by an individual) to pay for qualifying medical expenses. Where such trusts are permitted, contributions, interest accumulations and withdrawals applied to health costs are exempt from income tax. The employer is usually required to purchase catastrophic health insurance coverage with a high deductible which results in a reduced premium. The employee may also contribute up to a maximum equal to the health insurance deductible. Also known as a Health Care Savings Account in some jurisdictions.

Medical Services Advisory Committee

An Australian agency that advises the Minister for Health and Ageing on evidence relating to the safety and cost-effectiveness of medical technologies. Its web site is http://www.health.gov.au/msac/. See also Pharmaceutical Benefits Advisory Committee.

Medicare

A term used generally to describe publicly funded and provided health care in Australia, Canada and the USA. Medicare is the term used in Australia to describe its universal health insurance scheme. Introduced in 1984, it provides access to free treatment in a public hospital and free or subsidized treatment by primary practitioners (specified services only). It is funded through taxes and a special Medicare levy based on taxable income. In Canada, the term is used loosely to describe the provincially provided (but largely federally controlled) systems of public health care insurance, providing free access to hospital and doctors' (specialists and general practitioners) services. It is funded through provincial health insurance premiums and through provincial and federal general taxation.

In the USA the term refers explicitly to a federal programme that is the main health insurance programme for people aged 65 and older, the disabled and people with end-stage renal disease, regardless of income. People who qualify for social security benefits are automatically eligible for Medicare. It is funded via payroll taxes and members' payments: premiums, deductibles and coinsurance. Medicare coverage provides for acute hospital care, physician services, brief stays in skilled nursing facilities, short-term skilled home care related to a medical problem and prescription drugs. There are two major programmes: Hospital Insurance (Part A) and Supplementary Medical

Meta-analysis 215

Insurance (Part B). The Medicare coverage for Part A has no premium and pays 100 per cent of hospital costs for the first 60 days after payment of a deductible (currently about $876). Medicare Part B pays up to 80 per cent of doctors' bills for a monthly premium of about $66. Doctors may bill beneficiaries for an additional amount (the 'balance') not to exceed 15 per cent of the Medicare approved charge (see Balance Billing). Medicare currently has about 39 million beneficiaries. See Medicaid.

MEDLINE®

MEDLINE® (Medical Literature, Analysis and Retrieval System Online) is the US National Library of Medicine's (NLM) premier bibliographic database, containing over 12 million references to journal articles in life sciences with a concentration on biomedicine. MEDLINE is available on the Internet through the NLM home page at www.nlm.nih.gov and can be searched free of charge. No registration is required.

Merit Good

A good or service whose consumption is regarded (by someone influential) as being unusually meritorious. It is generally associated with the idea that people are not consuming enough of something and that it would be good for them (or society) if they consumed more. But the claim is not being made on externality grounds or because of market failure and seems inherently paternalist (for example, a belief that people are myopic or ignorant). Education is often cited as an example of a merit good; health care is rarely so cited. The grounds for this asymmetry are obscure.

Meta-analysis

'Meta-' has a Greek origin and indicates, amongst other things, that the subject matter (in this case 'analysis') has a second-order character: an analysis of analyses. A meta-analysis is a form of systematic review of literature in which the quantitative results of several studies are systematically combined to generate more precise estimates of the effects under investigation, improve on the power of individual studies to detect effects, and to raise and discuss matters that may not have been evident in the individual studies. Of course, meta-analysis cannot correct for any defects that run throughout a literature (for example, the use of the potentially less

216 Meta-analysis valid outcome 'change in tumour size' rather than 'postponed death' as the outcome of a screening programme).

Meta-analyses are usually presented in the form of a forest plot. This is constructed as follows. The horizontal axis in the figure measures the treatment effect, for example the probability of death, so that to the left of the vertical axis death is less likely and to its right it is more likely. Where the vertical axis meets the horizontal corresponds to a probability of 1 (better outcomes are usually but not always to the left.) The line ab shows the result of a single research study. The solid square in the middle of the line is the point estimate of the mean effect in this study. This is a measure of the effect of the treatment compared to a control group and is most often represented as an odds ratio. The square is small or large depending on the weight this study is to be given in the combined analysis. The length of the line around the point estimate is the confidence interval for the result. When a study has only a few patients, the line will be long and the size of the square in its middle will be small.

good effect bad effect

Suppose there are two other studies, shown by the lines cd and ef. The study represented by cd shows the opposite effect to that in the previous study (in this study, the experimental group does better than the control) and the confidence interval is narrower and the weight this study receives will be e

_f good effect bad effect

Modelling 217

larger. There is a third study also, which has relatively low statistical significance and a small weight. Taking all three together, the summary is represented by the diamond, whose height locates the best estimate of effect and whose width indicates its confidence interval. Its position relative to the vertical axis shows what the conclusion is, on balance, taking the whole literature (in this case a forest plot of three items) into account. If the diamond crosses the vertical line, the conclusion is that the literature as a whole does not yield a clear answer about the relative effectiveness of the procedure in question (conventionally at the 95 per cent confidence level).

MEWA

Acronym for multiple employer welfare arrangement.

Acronym for market forces factor.

Microeconomics

The economic study of individual units in society like persons, households and firms. Cf. Macroeconomics.

Mixed Economy

An economy in which the ownership of productive enterprises is variously private, charitable or public.

Mode

The most frequently occurring value of a single variable in a data set. Modelling

Two broad kinds of modelling are done in health economics. One is the general kind employed throughout economics, which might be termed 'theo-

218 Monopolistic Competition retical modelling', in which empirical characteristics are assumed (like transitivity of preferences) and general implications derived from an essentially analytical process of reasoning. The use of utility theory to model individual choices is a good example, from which is derived the implication that demand curves have a negative slope. The other is empirical modelling, where empirical relationships are postulated and interest focuses on simulating and quantifying the cause-and-effect relationships, elasticities and the like. Some modelling is relatively theory-free and is mainly concerned to forecast by the extrapolation of past trends, with due allowance for interaction between determining variables but without necessarily any prior notion of the nature of such interactions.

In health economics, modelling has assumed considerable importance in cost-effectiveness analysis (CEA) and related techniques. A distinction can be made between cohort modelling (where all modelled individuals share similar characteristics at the outset) and micropopulation simulation modelling (which can represent the mixed nature of real populations or communities).

Critical issues in modelling are that it should relate to relevant issues (for example, embody appropriate comparators), have an appropriate time horizon (for example, consequences should be modelled over a realistic time horizon), take a relevant perspective (for example, one relevant for decision makers), embody relevant outcomes (for example, final, not intermediate or surrogate), make realistic assumptions (for example, concerning adverse events) and have robust mathematical descriptions and appropriate modelling techniques (for example, use sensitivity analysis, discounting).

It is often necessary to construct an analytical framework within which to synthesize the available evidence in order to estimate both clinical effectiveness and cost-effectiveness. This framework will, in turn, usually require the development of a model. This may be a theoretical decision-analytic model using aggregated data or an empirical model using patient-level data.

Monopolistic Competition

A form of market in which sellers have to search out the best price for them.

See Competition, Price-searching.

Monopoly

A market in which there is a single seller. See Competition, Price-searching.

Moral Hazard 219

Monopsony

A situation in which a resource user is sufficiently dominant in the market for the price of resources to be affected as this user's demand rises or falls. See

Competition.

Monotonicity

The general property of a sequence of numbers that each successive number is greater than or equal (increasing monotonicity) or smaller than or equal (decreasing monotonicity) to its predecessor. The ordering is 'strong' if ties are not allowed. In economics, this property of choices generally means that if, x is preferred to y, then the utility of x > utility of y. In health economics, a special usage is that, if the health of one person increases, then the level of the community's health (or welfare) also increases (ceterisparibus). A weaker form of monotonicity requires only that the transformed entity does not fall, rather than that it should actually increase.

Monte-Carlo Simulation

A form of simulation, frequently used in cost-effectiveness and cost-utility analyses, in which random numbers drawn from a given probability distribution repeatedly stand for the values of uncertain variables. Confidence limits are placed on the most likely value after a large number of such simulations. Monte-Carlo simulation is named after Monte-Carlo, Monaco, where roulette wheels, dice, cards and slot machines replace the soberer games of economic modellers. See Simulation.

Moral Hazard

This is of two main types. Ex ante moral hazard refers to the effect that being insured has on behaviour, increasing the probability of the event insured against occurring. Ex post moral hazard derives from the price-elasticity of demand: being insured reduces the patient's price of care and hence leads to an increase in demand by insured persons. The basic economics of ex post moral hazard can be elucidated by considering the figure. The vertical axis shows the price of health care P (assumed - implausibly - to be set equal to marginal cost) and the marginal value placed upon health care consumption by an individual. The horizontal axis indicates the rate of consumption of

220 Moral Hazard

220 Moral Hazard

Quantity per time period

Quantity per time period

health care (so much per week, month and so on). The demand curve, or marginal value curve, is not perfectly inelastic, indicating that at lower prices more care (longer inpatient stays, for example) is demanded. The horizontal line is the (constant) marginal cost curve. In a world of no insurance, the individual faces a price OP at which OCl care will be consumed when ill. Let the individual (while healthy) consider buying insurance. Suppose neither the individual nor the insurer is in any doubt about the probability, p, of illness striking in any period (another tall order). Given that the insured, when uninsured, would consume OP x OQ, the actuarially fair premium (sometimes termed 'risk premium') is p times the cost of this amount of care. We assume also that there is zero loading: that is, the insurer adds nothing to the premium to cover the administrative costs of operating the insurance service. Now let the event insured against occur. Assuming that the premium payment has not had an effect on the individual's income sufficient to shift the demand curve, the amount demanded will now be OC2: being insured reduces the price of consuming care to zero. Expenditure by the insurer will be OPdC2, much larger than the amount upon which the premium was based. This is ex post moral hazard. It is held to be inefficient because the cost of producing C1C2 care is much larger than its value to the consumer: there is an excess burden or deadweight loss, or 'waste' of adC2. However, before rushing to the conclusion that moral hazard must be controlled through coinsurance, copayments and other forms of rationing, it needs to be borne in mind that there may be reasons for wanting individuals to consume more care than, given their personal circumstances, they would normally choose (see, for example, externality). If such grounds exist, then a second best optimum may

Mortality Rate 221

entail the need to do less to constrain demand (and even to encourage it further). Even more fundamentally, there may be reasons for entirely eschewing the idea that the demand curve reveals anything worth knowing about the value placed on health care. In that case, even if the behavioural account given of moral hazard may still stand, the ethical accusation of 'waste' entirely fails.

One behavioural effect of moral hazard in a market-based system is evidently to cause premiums to rise: in the example just considered, the increase in the premium is p(C1adC2). Premiums thus reflect both the inherent element of risk (the fair premium) and the additional costs generated through moral hazard. This may be sufficient not only to cause the insured to withdraw from insurance and self-insure; it may, as in the figure, actually exceed the cost of purchasing out-of-pocket the original planned consumption of care at price P. The welfare effects of moral hazard ought thus to be considered in terms of its impact both on health care utilization and on the take-up of health care insurance.

Another form of moral hazard has been held to be the effect that being insured in public programmes like the US Medicaid has on savings: because Medicaid will pay for, say, the nursing home care of the elderly with few savings, the poor have a smaller incentive to save. As with other forms of moral hazard, one needs to ask, of course, whether the consequence is intended or unintended, desirable or undesirable. See Market Failure.

Morbidity

A synonym for illness, often proxied by a patient's contact with a physician and the resultant diagnosis. Morbidity rates are calculated in a manner similar to that for mortality rates, especially cause- (or disease-) specific mortality rates.

Mortality Rate

The crude mortality rate is often described as the total number of deaths per year divided by the population at mid-year times 1000 (that is number of deaths per 1000 person-years of observation). The age-specific mortality rate is the mortality rate for a specific age group (such as '65 years and older'). The sex-specific mortality rate is the mortality rate for males or females. The age- and sex-adjusted rates are weighted according to the proportion of each group in the population. The disease- or cause-specific mortality rate is the annual number of deaths from the particular disease divided by the mid-year population times 1000.

222 MOS-20

MOS-20

Derives from Medical Outcomes Study, a RAND project. Better known as

MTU-FSIOS

See Swiss Network for Health Technology Assessment. Multi-attribute Valuation

The method commonly used to calculate quality-adjusted life-years. It is multi-attribute by virtue of the essential concept ('health') being considered to be a function of several attributes (absence of pain might be one such). The valuation part relates to the process of combining and scaling the attributes using the principles of utility (or expected utility) theory. The measurements involved are usually derived from sample surveys or formal experiments involving groups of the public deemed to be relevant for the purposes of the study in question.

Multicollinearity

When two or more independent variables are very closely linearly related, they convey essentially the same information in multiple regression analysis. When this happens, the independent variables are said to be highly collinear and the phenomenon is called multicollinearity. If two or more variables are highly correlated, one is not likely to contribute significantly to the model in the presence of the other(s). Also spelled 'multicolinearity'.

Multilevel Modelling

The analysis of data that have a hierarchical structure. Multinomial

Having the character of a polynomial, with a form like y = a + bx + cx2 + dx3 + ex4 + ..., where a, b, c and so on are constants and x and y are variables.

Multi-task Agency 223

Multinomial Logit Model

A statistical model for unordered multinomial outcomes.

Multiple Correlation

The correlation between a variable and more than one other variable. Cf.

Partial Correlation.

Multiple Employer Welfare Arrangement

A US trust arrangement for self-funding a corporate group benefit plan covering medical and dental insurance and pensions. Generally MEWAs are created by small employers.

Multiple (Linear) Regression

A statistical technique based on an assumed linear relationship (that is, of the formy = a + bx + cz + ... + e) between a dependent variable and a variety of explanatory or independent variables; e (epsilon) is an error term generated by the fact that the independent variables are unlikely to account for all the changes in the dependent variable. The parameters a, b, c can be estimated by finding the line that best fits the data to the hypothetical linear structure. The least-squares method does this by minimizing the sum of squares of the vertical distances of each actual observation from the fitted line (assuming the dependent variable to be on the vertical axis). The coefficients give a quantitative account of the relationship between y and x. Thus, if b = 7.4, this means that a one-unit increase in x (any other variables constant) is associated with a 7.4 increase in the mean or expected value of y.

Multi-task Agency

The agency relationship in medicine is typically multi-task in nature (as is, for example, vividly revealed in physician fee schedules) and different methods of remuneration tend to produce different mixes of these various tasks and different mixes of quality. The optimum solution is elusive and methods of payment (such as fee-for-service or capitation) tend to be complemented

224 Multivariate Analysis by organizational, legal and social assumptions and values that reinforce the agency relationship.

Multivariate Analysis

An analysis in which there is more than one independent variable. Non-economists often reserve this term for systems that have multiple dependent variables and use 'multivariable' for the case of multiple independent variables.

Multivariate Sensitivity Analysis

A form of sensitivity analysis that allows for the possibility that factors affecting incremental cost-effectiveness ratios are not independent of one another. Same as scenario analysis.

Mutatis Mutandis

A Latin tag meaning 'making the necessary changes'. Allowing for the impact on a variable of indirect consequential changes which might otherwise have been ignored or assumed to be unimportant. So a cost curve might be constructed either on the assumption that the activity of the firm whose cost curve it is does not affect anything going on in the outside world (ceteris paribus) or on the assumption that it affects local wages and the behaviour of other local employers with those consequences (mutatis mutandis) built into the cost curve.

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