**LARGE-SAMPLE METHOD **(Syn: asymptotic method) Any statistical method based on an approximation that becomes more accurate as sample size increases. Examples include chi-square tests on a set of frequencies and normal tests of estimates from frequency data.

**LATE MATERNAL DEATH **See maternal mortality.

**LATENT CLASS ANALYSIS **A type of statistical analysis used to group variables or observations into distinct clusters, based on the assumption that there are underlying “latent classes” within the data. Analysis can be cross-sectional or longitudinal, i.e., it can identify clusters of distinct variables at a point in time or patterns in a variable over a period of time.

**LATENT HETEROGENEITY **Epidemiological data that are too heterogeneous to be described by a simple mathematical model such as the binomial or Poisson distribu- tion, suggestive of the effect of unidentified risk factors.

**LATENT IMMUNIZATION **See immunization, latent.

**LATENT INFECTION **Persistence of an infectious agent within the host without symptoms (and often without demonstrable presence in blood, tissues, or bodily secretions of the host).

**LATENCY PERIOD **(Syn: latent period, latency) Two mutually incompatible definitions are commonly used in the health and life sciences:

1. The interval from initiation of the disease to clinical emergence of the disease (e.g., appearance of manifestations) or to disease detection. Thus, according to this definition, the latency period begins when the induction period ends, at the initiation of the disease. In infectious disease epidemiology, the period between exposure and the onset of infectiousness (which may be shorter or longer than the incubation period).

2. The interval between initiation of exposure to the causal agent and appearance or detection of the health process; e.g., from onset of exposure to the disease- causing agent to appearance of manifestations of the disease. Thus, according to this definition, the latency period begins when the induction period begins, at the initiation of exposure to the disease-causing agent.

The two definitions agree that the latency period ends when the disease becomes clinically apparent and/or detectable; in the first definition, the induction period is followed by the latency period (there is no overlap), whereas in the second definition the latency period includes the entire induction period. See also sojourn time.

**LATIN SQUARE **One of the basic statistical designs for experiments that aim at removing from the experimental error the variation from two sources, which may be identified with the rows and columns of the square. In such a design, the allocation of *k *experi- mental treatments in the cells of a *k *by *k *(Latin) square is such that each treatment occurs exactly once in each row and column.98 A design for a 5 × 5 square is as follows:

This law, enunciated by Jacob Bernoulli (1654–1705), states that the accuracy of a sample mean is increased (or the standard error of a statistic is reduced) as the numbers studied increase. The larger the sample, the more likely it is to be representative of the “universe” population. This law is valid only with unbiased samples.

**LEAD TIME **The time gained in treating or controlling a disease when detection is earlier than usual (e.g., in the presymptomatic stage), as when screening procedures are used for early detection of disease.

**LEAD-TIME BIAS **(Syn: zero time shift) Overestimation of survival time, owing to the backward shift in the starting point for measuring survival that arises when diseases such as cancer are detected early, as by screening procedures. A systematic error arising when follow-up of groups does not begin at comparable stages in the natural history of a condition. For example, interventions for women whose breast cancer is detected by screening cannot be validly compared with interventions for women whose disease is first detected by clinical examination at a later stage of the disease.14,62,63 See also inception cohort; zero-time shift.

**LEAST SQUARES **A principle of estimation, attributed to Gauss and Legendre, in which the estimates of a set of parameters in a statistical model are those quantities that mini- mize the sum of squared differences between the observed values of the dependent variable and the values predicted by the model.

**LEDERMANN FORMULA **The observation by Ledermann270 that the frequency distribu- tion of alcohol consumption in the population of consumers may be log-normal; the curve is sharply skewed – approximately one-third of drinkers consume more than 60% of the total amount of alcohol. Among drinkers, the proportion of persons with alco- holism remains constant at around 7%–9%. The pattern of consumption of illicit drugs among users may also be log-normal. Questions have been raised, however, about the validity of some assumptions upon which the formula is based.

**LENGTH BIAS **

- A systematic error due to selection of disproportionate numbers of long-duration cases (patients who survive longest) in one group but not in another. This can occur when prevalent rather than incident cases are included in a case-control study.
- Given that biologically and clinically aggressive diseases often have a shorter asymptomatic pre-clinical period than less aggressive diseases, a screening program is more likely to detect slower progressing diseases (e.g., slow-growing tumors), which

**LAW OF LARGE NUMBERS **have better prognosis (e.g., survival).14,62,63 The screening program may thus falsely appear to improve survival as compared to a cohort including a wider spectrum of disease. See also inception cohort; latency period; screening.

**LENGTH OF THE GENERATION **Time required for the replacement of a female genera- tion by their daughters of reproductive age.

**LEVIN’S ATTRIBUTABLE RISK **See attributable fraction (population).

**LIFE COURSE **The natural history of human life. A term for conditions that evolve over a large part or all of the life span from infancy, or even from conception, through adolescence, adult life, and senescence, sometimes peaking in early adult life, sometimes in middle age, but generally progressing throughout life as a person grows older. The term arose in recognition of the fact that the natural history of many chronic diseases and the natural life span of humans are intertwined. *Life cycle *has been used in other scientific disciplines to describe a series of distinct, bounded life stages that are socially and/or biologically determined. The concept of *life span *used in psychology assumes that development and aging form a continuous process from birth to death. The distinction between *life span *and *life course *is mainly a matter of scientific history.16,113 See also accumulation of risk; developmental origins hypothesis; developmental and life

course epidemiology; ecological transition; social epidemiology.

**LIFE CYCLE **See life course.

**LIFE EVENTS **Aspects of the pattern of living that may be associated with or produce changes in health. The relationship of “life stress” and “emotional stress” to onset of sev- eral kinds of serious chronic disease, such as coronary heart disease and hypertension, has been the subject of epidemiological studies. The Rahe-Holmes Social Readjustment Rating Scale271 was the first to be developed to assign ranks or ratings to significant life events such as death of a spouse or other close relative, loss of regular job, relocation, marriage, divorce, etc. Many other rating scales have since been developed.

**LIFE EXPECTANCY **See expectation of life.

**LIFE EXPECTANCY FREE FROM DISABILITY (LEFD) **An estimate of life expectancy adjusted for activity-limitation (data for which are derived from hospital discharge statistics, etc.). See also disability-adjusted life years (DALYs); disability-free life expectancy; quality-adjusted life years (QALYs).

**LIFE EXPECTANCY WITH DISABILITY **The average number of years an individual is expected to live with disability if current patterns of mortality and disability continue to apply. See disability-free life expectancy.

**LIFE SPAN **See life course.

**LIFESTYLE **The set of habits and customs that is influenced, modified, encouraged, or constrained by the lifelong process of socialization. These habits and customs include use of substances such as alcohol, tobacco, tea, coffee; dietary habits; exercise; etc., which have important implications for health and are often the subject of epidemiological investigations.

**LIFE TABLE **(Syn: actuarial table) A summarizing technique used to describe the pattern of mortality and survival in populations. The survival data are time-specific and cumulative probabilities of survival of a group of individuals subject, throughout life, to the age-specific death rates in question. The life-table method can be applied to the study not only of death but also of any defined endpoint, such as the onset of disease or the occurrence of specific complication(s) of disease. The survivors to age *x *are denoted by the symbol *l**x*, the expectation of life at age *x *is denoted by the symbol *e* ̊*x*, and the proportion alive at age *x *who die between age *x *and *x *+ 1 years is denoted by the symbol *nq**x*. The life table method is used in public health and in assessments of treat- ment regimens in clinical practice.

The first rudimentary life tables were published in 1693 by the astronomer Edmund Halley. These made use of records of the funerals in the city of Breslau. In 1815 in England, the first actuarially correct life table was published, based on both population and death data classified by age.

Two types of life tables may be distinguished according to the reference year of the table: the current, or period, life table and the generation, or cohort, life table.

The current life table is a summary of mortality experience over a brief period (1 to 3 years), and the population data relate to the middle of that period (usually close to the date of a census). A current life table therefore represents the combined mortality experience by age of the population in a particular short period of time.

The cohort, or generation, life table describes the actual survival experience of a group, or cohort, of individuals born at about the same time. Theoretically, the mortality experience of the persons in the cohort would be observed from their moment of birth through each consecutive age in successive calendar years until all of them die.

The clinical life table describes the outcome experience of a group, or cohort, of individuals classified according to their exposure or treatment history.

Life tables are also classified according to the length of age interval in which the data are presented. A complete life table contains data for every single year of age, from birth to the last applicable age. An abridged life table contains data by intervals of 5 or 10 years of age. See also expectation of life; survivorship study.

**LIFE TABLE, EXPECTATION OF LIFE FUNCTION, ***e* ̊*x *(Syn: average future lifetime) The expectation of life function is a statement of the average number of years of life remaining to persons who survive to age *x*.

**LIFE TABLE, SURVIVORSHIP FUNCTION, ***l**x *The survivorship function is a statement of the number of persons out of an initial population of defined size (e.g., 100,000 live births) who would survive or remain free of a defined endpoint condition to age *x *under the age-specific rates for the specified year. The value of *l**40*, for example, is determined by the cumulative operation of the specific death rates for all ages below 40.

**LIFETIME RISK **The risk to an individual that a given health effect will occur at any time after exposure without regard for the time at which that effect occurs.

**LIKELIHOOD FUNCTION **A function constructed from a statistical model and a set of observed data that gives the probability of the observed data for various values of the unknown model parameters. Values for the parameters that maximize this function are called maximum likelihood estimates of the parameters.

**LIKELIHOOD INTERVAL **An interval containing all parameter values that have a value of the likelihood function greater than a certain proportion of the maximum; e.g., one seventh of the maximum, which roughly corresponds to a 95% confidence interval in most cases.

**LIKELIHOOD RATIO **

1. The ratio of the values of the likelihood function at two different parameter values or under two different data models. Usually, one of the two values is taken to be the maximum of the function (the value of the function at the maximum-likelihood estimates). See likelihood-ratio test.

2. The probability that a given test result would occur in a person with the target disorder divided by the probability that the same result would occur in a person without that disorder. It can be calculated for any level of a test result (for continuous diagnostic tests with many possible cutoff values) as the ratio of the probability of that test result among individuals with the target disorder to the probability of that same test result among individuals who are free of the target disorder. For a positive result, the likelihood ratio equals the ratio sensitivity/(1 – specificity). For a negative test result the likelihood ratio equals (1 – sensitivity)/specificity.

Likelihood ratios are used to appraise screening and diagnostic tests. See also sensitivity and specificity.

**LIKELIHOOD-RATIO TEST **A statistical test based on the ratio of the maximum value of the likelihood function under one statistical model to the maximum value under another statistical model; the models differ in that one includes and the other excludes one or more parameters.

**LIKERT SCALE **An ordinal scale of responses to a question or statement ordered in a hierarchical sequence, such as from “strongly agree” through “no opinion” to “strongly disagree.” Rensis Likert, a social psychologist, developed an empirical method for assigning numerical scores to such a scale.

**LINEAR MODEL **A statistical model in which the average value of a dependent variable *y *at a given value of a factor,*x*,is assumed to be equal to a + b*x*,where a and b are unknown constants.

**LINEAR REGRESSION **Regression analysis using linear models.

**LINKAGE **See genetic linkage; record linkage.

**LINKAGE DISEQUILIBRIUM **A condition in which alleles at two loci or genes are found together in a population at a greater frequency than predicted simply by the product of their individual allele frequencies. Alleles at markers near disease-causing genes tend to be in linkage disequilibrium in the affected individuals.23

**LIVE BIRTH **WHO definition adopted by the Third World Health Assembly, 1950: “Live birth is the complete expulsion or extraction from its mother of a product of conception, irrespective of the duration of the pregnancy, which, after such separation, breathes or shows any other evidence of life, such as beating of the heart, pulsation of the umbili- cal cord, or definite movement of voluntary muscles, whether or not the umbilical cord has been cut or the placenta is attached; each product of such a birth is considered live born.”

In the *Report of WHO Expert Committee on Prevention of Perinatal Mortality and Morbidity *(Technical Report Series 457, 1970), it is noted that the above definition requires the inclusion as live births of very early and patently nonviable fetuses and that accordingly it is not strictly applied. The committee suggested, therefore, that the WHO should introduce a viability criterion into the definition so that very immature fetuses surviving for very short periods were excluded, even though they showed one or more of the transitory signs of life. The Conference for the Tenth Revision of the International Classification of Diseases (*ICD-10) *recommended that the above definitions, adopted for *ICD-9*, should remain unchanged.

**LOCUS **

1. The position of a point, as defined by the coordinates on a graph 2. The position that a gene occupies on a chromosome

**LOD SCORE **In genetics, the log odds ratio of observed to expected distribution of genetic markers.

**LOGIC **The branch of philosophy and science that deals with canons of thought and crite- ria of validity in reasoning. Logic relies on precise definition of tangible objects, terms, and concepts; rational classification; application of fundamental principles of the under- lying field of scholarship (mathematics, physics, ethics, etc.); and minimal use of axioms and assumptions. Properly done, epidemiology applies logic to arrive at conclusions about cause-and-effect relationships.180,263 See also hypothetico-deductive method.

**LOGICAL FRAMEWORK (LOGFRAME) ANALYSIS **A method of project or program planning that uses a matrix of the goal, purpose, expected results, and activities on the vertical axis and the performance indicators, means of verification, and assumptions on the horizontal axis. The approach is often conducted in a group setting with facilitation, so as to promote teamwork and ownership of the plan. The matrix can be used also for project monitoring and evaluation and may be updated in response to changes in the timetable, performance, or feasibility of component activities. Logframe planning is favored by some international development agencies.

**LOG-LINEAR MODEL **A statistical model that uses a linear model for the logarithms of frequency counts in contingency tables.

**LOG-NORMAL DISTRIBUTION **If a variable *Y *is such that the natural log of *Y *is normally distributed, it is said to have log-normal distribution. This is a skew distribution. See also normal distribution.

**LONGITUDINAL STUDY **See cohort study.

**LOST TO FOLLOW-UP **Study subjects in a cohort study whose outcomes are unknown (e.g., because they could not or did not wish to attend follow-up visits). See also attri- tion; censoring; cohort.

**LOW BIRTH WEIGHT **See birth weight.

**“LUMPING AND SPLITTING” **Derisive term describing the propensity of some researchers to group related phenomena or to separate phenomena that hitherto had been grouped.