L

This is a convenient visual scatter diagram used in meta-analysis that compares the outcomes (say) of an experimental group with those for a control group in a set of clinical trials. Each trial is located in the space of a figure such as the one here, where the size of the circles indicates the size of the trial. It is often used as an indicator of heterogeneity and hence as an indicator of the likelihood that results from different trials can be validly combined. Named after Kristin L'Abbé. See Kristin A. L'Abbé, Alan S. Detsky and K. O'Rourke (1987), 'Meta-analysis in clinical research', Annals of Internal Medicine, 107, 224-33.

Labour Force Participation

The proportion of a population (perhaps a subgroup of the total non-institutionalized population of a jurisdiction) that is above a certain age (usually 16) and willing to work (that is, either in work or actively looking for work).

Laspeyres Price Index

An index number where prices and quantities of goods and services over time are weighted according to their values in a specified base period:

Positive response with placebo

Positive response with placebo

192 Last Observation Carried Forward/Backward

PL = £ PnQJ £ P000, where PL is the Laspeyres index, Pn is the price per unit in period n and Q0 is the quantity produced in period 0. The Laspeyres index measures the change in cost of purchasing the same basket of goods and services in the current period as was purchased in a specified base period. Named after Etienne Laspeyres (1834-1913). Cf. Paasche Price Index.

Last Observation Carried Forward/Backward

A (not very good) method of dealing with incomplete data. Sometimes termed 'last value carried forward/backward'.

Last Value Carried Forward/Backward

Same as last observation carried forward/backward.

Law of Demand

This states that demand (in the sense of quantity demanded) rises as price falls. While for some economists the 'law' is an article of faith, its interpretation really depends on what is held constant along the demand curve. There are conceivable empirical exceptions if income in the sense of money income is held constant and the good in question is an inferior good. No empirical exception is permitted if income in the sense of utility is held constant for in this case the 'law' is merely another way of putting the standard axiom of convexity (or diminishing marginal rate of substitution in consumption). These ceteris paribus notions are precisely that, of course: notions. In empirical work they are included amongst the determining variables but they still need careful definition (the concept of 'real' income to be used particularly needs definition). See Demand Function.

Law of Diminishing Returns

A somewhat less satisfactory term than an alternative: Law of Variable Proportions.

Law of One Price

League Table 193

A regularity that is often predicted by economic theory, though less frequently observed in practice, to the effect that a good which can be cheaply transported (like pharmaceuticals) and which is sold in international markets (like pharmaceuticals) will sell at the same price in all markets. Pharmaceuticals notoriously are not sold at uniform prices, despite their trivial transport costs.

Law of Variable Proportions

This 'law' is a generalization about the nature of technology when factors of production are substitutable. It states that, as the rate of use of one factor is increased, the others remaining constant, the marginal product (increase in output) will eventually fall and the average product too will eventually fall. While this is suggested as a general characteristic of production functions, it is particularly applicable in the short run. The term 'law of diminishing returns' is sometimes met but ought probably to be discarded in that it focuses attention on the 'constancy' or otherwise of factors of production rather than what is critical: the proportions in which the different factors are used. The element in the definition that runs 'the others remaining constant' is not a literally descriptive characterization but rather an analytical one, describing one essentially mathematical property of a production function. See Diminishing Returns to Scale.

Lead-time Bias

A bias in screening programme evaluation taking the form of increased survival times arising solely from making a diagnosis earlier in the history of the disease.

League Table

The relative cost-effectiveness of various health care technologies is frequently presented in the form of 'league tables' based upon literature reviews. A common reason for doing this is the maximizing idea that, provided the data reflect the true incremental cost-effectiveness of each technology and the effectiveness measure is appropriate, then the health budget will have its maximum impact by working down the table until the budget is exhausted (and by not funding anything else). Amongst the dangers in using such tables

194 Least Squares in other than a broadly indicative way are the following: the list is probably incomplete (and omits some cost-effective technologies); the data are not actually marginal (incremental cost-effectiveness ratios) but averages; the perspective on cost and benefit may vary from one technology to another; the literature reviews may have had inappropriate inclusion or exclusion criteria; the cost-effectiveness ratios may be dependent on the scale of use of each technology; the circumstances of the evidence collection in the reviewed studies may make the transfer of conclusions to other settings and circumstances inappropriate. A (famous) example is the table.

League table

Cost per QALY

Technology

(£ sterling)

Pacemaker for atrioventricular heart block

700

Hip replacement

750

Valve replacement for aortic stenosis

900

CABG (severe angina; left main disease)

1 040

CABG (severe angina; triple vessel disease)

1 270

Coronary artery bypass graft (moderate angina; left main

1 330

disease)

CABG (severe angina; left main disease)

2 280

CABG (moderate angina; triple vessel disease)

2 400

CABG (mild angina; left main disease)

2 520

Kidney transplantation (cadaver)

3 000

CABG (moderate angina; double vessel disease)

4 000

Heart transplantation

5 000

CABG (mild angina; triple vessel disease)

6 300

Haemodialysis at home

11 000

CABG (mild angina; double vessel disease)

12 600

Haemodialysis in hospital

14 000

Source: Alan Williams (1985), 'The economics of coronary artery bypass grafting', British Medical Journal, 291, 326-9. Reproduced with permission of The BMJ Publishing Group.

Source: Alan Williams (1985), 'The economics of coronary artery bypass grafting', British Medical Journal, 291, 326-9. Reproduced with permission of The BMJ Publishing Group.

Least Squares

A method for estimating parameters in a regression analysis, so called on account of its minimizing the sum of the squared differences between each observation and its estimated value.

Licence 195

Left-censored Data

Data from patients for whom follow-up did not begin at the same time as for other patients in a trial.

Length Bias

The mistaken attribution of increased survival times to a screening programme that arises from a tendency for insidious, slow-developing diseases to be more easily detected by screening than fast-developing, aggressive diseases. See Bias.

Length of Stay

A term usually referring to the time a patient of a particular type (or patients in general) spends in hospital. Mean length of stay (say, by diagnostic related group - DRG) is calculated by dividing the sum of inpatient days by the number of patients within the DRG. People entering and leaving a hospital on the same day have a length of stay of zero.

Liberty Principle

A principle of social justice associated with the name of John Rawls. It is a schedule of basic rights, including liberty of conscience and movement, and freedom of religion, which ought to be equally distributed and as complete as is consistent with each having the same freedom. See Fairness.

Licence

The legal (or other formal) permission granted to a professional person to practise their profession or for a pharmaceutical company to manufacture a product whose patent or other intellectual property right is owned by someone else.

196 Life Expectancy Life Expectancy

The statistically expected remaining years of life for a representative person (usually in a specific jurisdiction and by subgroup: male, female, ethnicity and so on) at a given age (say, at birth, or having already reached 65). The World Health Organization publishes variants called 'Healthy Life Expectancy' which includes an adjustment for time spent in poor health. Healthy Life Expectancy at birth measures the equivalent number of years in full health that a newborn child can expect to live based on the current mortality rates and prevalence distribution of health states in the population.

Unadjusted life expectancy data show enormous variations across the world. A child born in Japan in 2002 had an expectation of life of 81.9 years (85.3 if female) whereas one born in Sierra Leone had an expectation of life of 34.0 years (35.7 if female). In general, females have a longer expectancy than males. Much of the disparity is attributable to high infant mortality rates. In Africa around 40 per cent of deaths occur amongst infants under five years of age. Poor sanitation and associated disease characteristics of grinding poverty - malnutrition, diarrhoea, malaria and infections of the lower respiratory tract - are principal causes. While the past decades have seen a general rise in expectation of life in all countries, in some regions, especially in Africa (for example Botswana, Lesotho, Swaziland and Zimbabwe) life expectation is actually falling thanks to HIV/AIDS. See The World Health Report 2004 -Changing History, Geneva: World Health Organization.

Life Table

A table showing how many people survive for a variety of periods of time. 'Survive' need not mean 'merely remain alive' (the table may be about surviving in a particular condition) and the periods do not have to be years, though life tables frequently embody both. Another name for them is survival tables.

Likelihood

Same as probability in the frequentist sense. Likelihood Function

A function that represents the joint probability of all the points in a data set.

Likelihood Ratio

Linear Programming 197

The likelihood that a particular test result is expected in a patient with the target condition compared with the likelihood that this same result would be expected in a patient without that condition. The link between the likelihood ratio (LR) and sensitivity and specificity is as follows:

Positive LR = sensitivity/(1-specificity) Negative LR = (1-sensitivity)/specificity.

Likert Scale

An ordinal scaling of health states based upon ordinal rankings derived from surveys. A typical approach will pose a statement and ask the respondent whether they Strongly Agree, Agree, are Undecided, Disagree or Strongly Disagree. See Renis Likert (1932), 'A technique for the measurement of attitude scales', Archives of Psychology, 140, 44-53.

Line Item Budget

Same as global budget.

Line of Equality

A line in a graph that indicates a completely equal distribution of whatever is measured on the vertical axis. See Concentration Curve, Lorenz Curve.

Linear Probability Model

A model of binary dependent variables based on the linear regression model.

See binary variable and multiple regression.

Linear Programming

A mathematical technique for finding the maximum or minimum value taken on by a given function (the objective function) that satisfies a set of linear constraints in the form of equalities and inequalities.

198 Linear Transformation Linear Transformation

The transforming of a variable, A, into another, B, by use of a linear equation of the form:

Linearity

A process or equation that can be expressed in a linear equation having the form

X = a + bY, where b, the slope of the straight line relating X and Y, is a constant and a is a constant intercept.

Loading

A term indicating that an insurance premium has administrative and other costs 'loaded' onto it over and above the actuarially fair premium, which in principle is the expected cost of health care multiplied by the probability of that care being utilized. Because loading is unlikely to be systematically related to the risk of events, one of its consequences is that for-profit free market insurers are unlikely to offer policies for either very likely or very unlikely adverse events, where potential insurance clients' willingness to pay to avoid the consequences of risk is relatively low and the fraction of the premium taken up by loading is consequently higher. See Insurance.

LOCF/B

Acronym for last observation carried forward/backward. Logical Positivism

A twentieth-century philosophical movement in which, in its most extreme form (which had considerable impact on economics), the only statements deemed to be meaningful are those that (a) are analytically true or (b) can be empiri-

Long Run 199

cally verified (sometimes, which is not, of course, the same thing, 'refuted') by the evidence of one's senses as in controlled scientific experiments.

Logistic Distribution

A continuous probability distribution that is the basis of the logit model of binary choice.

Logistic Regression

Regression between a binary dependent variable and one or more independent variables using a logit model. Cf. Discriminant Function Analysis.

Logit Model

A model with binary dependent variables based on the logistic distribution. Lognormal Distribution

A variable has a lognormal distribution if the log of the variable has a normal distribution. It is a distribution that is skewed to the right (so the mean is larger than the median). Like the normal distribution, the lognormal is characterized by two parameters: the mean and standard deviation. Values cannot be negative.

Long Run

A theoretical idea that has to do with the speed with which factors of production can be adjusted. A context for decision making (rather than a time period) in which all the inputs in a process can be treated as variable. In reality, nearly all inputs can be varied within any time period but the costs of doing so rise as the period shortens or is to begin at an earlier date, so whether to treat an input as fixed or variable is actually a choice for a decision maker rather than something fixed by 'nature'. Inputs treated as fixed may not necessarily be literally fixed in any technological sense (for example, the organization may be bound by a contract not to vary them). In general, the faster one seeks to make any change in input use, the more costly

200 Longevity such changes will be. Some inputs are costlier, for many reasons, than others to alter and those that are costliest will tend to number amongst those most frequently treated as fixed. The real point, however, is that what to treat as fixed and what as variable is itself a question of choice and any decision about this will confine the scope of inputs to be varied. See Production Function, Short Run, Time.

Longevity

Length of life.

Longitudinal Data

Data that relate to successive periods of time. Cf. Cross-sectional Data. Longitudinal Study

Any study using time series data. In econometric studies, the object is often to analyse the determinants of (the growth of) income, expenditure (for example, national health care expenditures) or consumption. Increasingly there are micro data sets available as well as macro data sets. Clinical trials, when individual people are followed, are called longitudinal cohort studies or follow-up studies (the two terms are substitutable). If individual people are not followed, but classes of people (usually age classes) are restudied, one has a longitudinal cross-sectional study.

Lorenz Curve

The Lorenz curve was developed by Max Lorenz (1880-1962), a US economist who developed it to describe income inequalities. It shows the cumulative percentage of income, health care expenditures and so on held by successive percentiles of the population. The percentage of individuals or households is plotted on the horizontal axis, the percentage of income, health care expenditures and so on on the vertical axis. A perfectly equal distribution, where each has the same, appears as a straight line, called the 'line of equality'. A completely unequal distribution, where one person has everything, appears as a mirror L shape. This is a line of perfect inequality. See Concentration Index, Gini Coefficient.

Luxury Good 201

0 100 Cumulative % of persons or households

Acronym for length of stay.

Loss Function

Also known as 'criterion function'. It is a function that is minimized to achieve a desired objective. For example, econometricians minimize the sum of squared errors in making an estimate of a function or a slope; in this case the loss function is the sum of squared errors.

Loss to Follow-up

A common cause of missing data, especially in long-term studies, loss to follow-up occurs when researchers lose contact with participants in a trial through death, migration or any other cause. Planned data collection efforts are incomplete as a result.

Luxury Good

An economic good with an income-elasticity greater than 1.0. Because the term has pejorative overtones and also because the elasticity condition defines as 'luxuries' many things (apparently including many forms of health care) that are not generally regarded as luxuries, it is a term better avoided

202 Luxury Good and 'good with an income elasticity greater than 1.0' used instead, which has the advantage of saying directly what the characteristic is that matters without overtones of approval or disapproval, importance or unimportance.

Macroeconomics

The study of aggregate entities in the economy, like money supply, income, exports or unemployment, and the links between them.

Magnitude Estimation

A method of deriving a ratio scale by asking raters of alternative states of health to think of them in terms of multiples (for example, state A may be 'twice as bad' as state B).

Malpractice

Mistaken, careless or unethical (legally negligent) medical practice for which the practitioner may be sued.

Managed Behavioral Health Care

A form of managed care provided stance abuse care.

Managed Care

USA for mental health and sub-

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