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Ymuch of the last century (but attaining much higher fi gures in some years) down to below 10 in many countries today. It has been very dependent on general social conditions: low wages, poor housing, and bad nutrition, all having shown close correlation with high IMRs. When infections were rife, and brought into the home by older children, the rate was higher. But with the improvement of infection preven-tion and treatment, much related to sanitation, vaccination, and antibiotics, infant mortality has occurred close to the time of birth. For this reason, the national neonatal mortality rate (NMR) has been used, a neonate being defi ned as up to the age of 28 days. The same denominator is used as for the IMR, and the difference between them is known as the postneonatal mortality rate. Defi ned in this way, as it is, it contravenes the proper defi nition of a rate, which should refer to the ratio of the number to whom some event has happened (e.g., death) to all those who were at risk for that event. The denominator of the postneonatal mortality rate is the number of live births, just as it is for the IMR and the NMR. But all those who succumbed as neonates are no longer at risk in the postneonatal period, and thus should be excluded from the denominator. The difference, however, is usually small, and it is more convenient to use two rates, which add to the overall IMR. Further reductions in the deaths at this period of life have focused attention nearer to the time of birth. Deaths in the fi rst week of life (up to the age of 7 days) have been recorded for many years now, as well as separately for each of those 7 days, and even for the fi rst half hour of life. Clearly many of the causes of those very early deaths will have orig-inated in the antenatal and intrauterine period. They will share causes with those born dead (stillbirths), and indeed they are combined together in the prenatal mortality rate. This includes both stillbirths taken together. The stillbirth rate (SBR) alone must of course use the same denomina-tor, since all births were at risk of death in the process of birth, to which the stillbirths fall victim. All of these rates have been devised to highlight specifi c areas of importance, especially in pediatrics. Closely related is the measurement of the material morbidity rate (MMR). Here the numerator is the deaths of women from maternal or puerperal causes, and the denominator, interestingly, is the total number of births, live and still. A moment’s refl ection will show that it is the occasion of birth (whether live or still) that puts a woman at risk of this cause of death, and that if she has twins—or higher orders of multiple births—she is at risk at the birth of each, so that the correct denominator must include all births. FERTILITY RATES The information collected on the birth certifi cate usually permits the tabulation of fertility rates by age and number of previous children. Age-specifi c fertility rates are defi ned as the number of live births (in a calendar year) to a thousand women of a given age. If they are expressed for single years of age, and they are separated into male and female births, then we add together all the rates for female births to give what is known as the gross reproduction rates (GRRs). If this quantity is close to unity, then it implies that the number of girl children is the same as the number of women of repro-ductive age, and the population should thus remain stable in number. But no allowance has been made for the number of women who die before the end of their reproductive life, and thus will fail to contribute fully to the next generation. When this allowance is made (using the female mortality rates for the appropriate ages) we obtain the net reproductive rates (NNRs). Note, however, that there remains an assumption that may not be fulfi lled—that the age-specifi c rates remain unchanged throughout the reproductive age range (usually taken as 15 to 45), that is, for a period of 30 calendar years. Indices such as the NRR were devised as attempts to pre-dict or forecast the likely future trends of populations. The crude birth rates (CBRs), defi ned as the ratio of the number of births to the total of the population, is like the crude death rate in being very sensitive to the age structure of the pop-ulation. Nonetheless, their difference is called the rates of natural increase (RNI) and provides the simplest measure of population change: CBR ⫺ CDR ⫽ RNI The measure excludes the net effect of migration in changing the population numbers: in some countries it is very rigidly controlled, and in others it may be estimated by a sampling process at airports, seaports, and frontier towns. POPULATION TRENDS Previously it has been noted that both the GRR and NRR make the assumption of projecting the rates observed in 1 calendar year to cover a 30-year period (15 to 45). It would of course be possible to follow a group of women, all of the same age, from when they were 15 up to the age of 45 in the latest year for which fi gures are available. Such a group would be called a “cohort”—the term used in epidemiology for a group defi ned in a special way. To cover this cohort would necessitate obtaining fertility rates for up to 30 years back, and in any case that cohort would of course have com-pleted its reproductive life. The highest fertility rates are commonly found at younger ages: it is possible to show graphically a set of “cohort fertility rates” by age labeled by their year of birth (often a central year of birth, since the cohort may be more usefully defi ned as a quinquennial group). If they are expressed in cumulative form (i.e., added together) and refer only to female birth, it will become clear how nearly they approach unity, from below or above, if the population is increasing. No adjustment for female mortality in the period is required, since the rates are, for each year (or quinquennium), calculated for those women of that cohort alive at that time. The method therefore represents the most useful prediction of future population trends, which can be projected further forward by assumptions that can be made explicit in their graphical depiction. C005_011_r03.indd 376C005_011_r03.indd 376 11/18/2005 10:25:41 AM11/18/2005 10:25:41 AM
Y 377 COHORT ANALYSIS OF MORTALITY A similar breakdown of age-specifi c mortality rates can be made, in order to reveal different patterns of relationship to the passage of time. Figure 1, for instance, shows mortality rates by sex and age in a single calendar year—the age in which death took place. Mortality rates are given for 5-year age groups, which is the usual practice, so that if a similar curve were to be drawn on the same graph for the calendar year 5 years earlier, you could join together the point rep-resenting, say, the age group 60–64 on the original curve to the point for 55–59 5 years earlier. This line would then represent a short segment of the cohort age-specifi c mortal-ity curve born in the period 60–64 years before the date of the fi rst curve. By repeating the process, it is clearly pos-sible to extend the cohort curves spaced 5 years apart in their birth years. Figure 6 shows how the cohort mortality makes clear the rising impact of cigarette smoking in the causation of lung cancer, since successive later-born cohorts show increases in the rates, until those of 1916 and 1926, which begin to show diminishing rates. The cohort method is thus of particular relevance where there have been secular changes similar to that of cigarette smoking. MEASUREMENT OF SICKNESS (MORBIDITY) If, instead of death, you look for ways of measuring sickness in the population, once again you are confronted by several major differences in both interpretation and presentation. In the fi rst place, illness has a duration in a sense that is absent from death. Secondly, the same illness can repeat in the same individual, either in a chronic form or by recurrence after complete remission or cure. And thirdly, there are grades of illness or of its severity, which at one extremity may make its recognition by sign or symptom almost impossible without the occurrence of the individual. The tolerance of pain or dis-ability, or their threshold, differ widely between people, and therefore complicate its measurement. In the case of absence from work, where a certifi cate specifying a cause may (or may not) be required, various measures have been used. A single period of absence is known as a “spell,” and thus the number of spells per employee in a year, for instance, can be quoted, as well as the mean length of spell, again per employee, or perhaps more usefully, by diagnosis. Inception rate, being the proportion of new absences in a given period (1 year, or perhaps less) is another measure, which again would be broken down into diagnostic groups. Prevalence is yet another measure, intended to quantify the proportion of work by sickness (perhaps by separate diagnostic groups) at a particular time. This may be, for instance, on one particular day, when it is known as “point prevalence,” or in a certain length of time (e.g., 1 month), which is known as “period prevalence.” Most prevalence rates are given for a year, and the defi nition often referred to is the number of cases that exist within that time frame. On the other hand, incidence is the number of cases that arose in the time period of interest, again usually a year. When sickness-absence certifi cates are collected for the purpose of paying sickness benefi ts, they have been analyzed to present rates and measures such as those discussed here, often against a time base, which can show the effect of epidemics or extremes of weather—or may indicate the occurrence of popular sports events! But such tabulations are either prepared for restricted circulation only, or if published are accompanied by a number of cave-ats concerning their too-literal interpretation. Incidence and prevalence rates are related to each other, and it is not unusual to have both reported in a single study (Mayeux et al., 1995). An example of prevalence and inci-dence for Parkinson’s disease for the total population and different ethnic groups is shown in Tables 2 and 3. For prevalence, the study identifi ed 228 cases of the diseases (Parkinson’s) for the time period 1988–1989, with the fi nal date of inclusion being December 31, 1989. Not included in the table is the mean age of cases (prevalence) (73.7 years, standard deviation 9.8) for patients having ages 40 to 96 years. Mayeux also reported that the mean age of occur-rence (symptoms) was 65.7 (standard deviation 11.3), with differing ages for men (64.6, standard deviation 12.7) and women (67.4, standard deviation 10.6), with these differ-ences having a p value of 0.06, or 6%. It should be noted that if a statistical signifi cance of 5% is used for establish-ing a difference, the age difference in years between men and women when symptoms of Parkinson’s disease were fi rst observed (occurrence or onset of diseases), thus, is not different. However, this raises an important issue that using a cutoff value, say 5%, does not provide a defi nitive deter-mination for evaluating data, in this case the importance of 35 40 4550 55 606570 758085Age0100200300400500600700Mortality rate per 100,000192618861916191118911901FIGURE 6 Lung-cancer incidence in birth cohorts.C005_011_r03.indd 377C005_011_r03.indd 377 11/18/2005 10:25:41 AM11/18/2005 10:25:41 AM
378
Ydisease occurrence between the two sexes. Most when exam-ining these data would suggest that even though the differ-ence is not signifi cant, an important difference between men and women appears to exist for the onset of disease, with men’s being much earlier. This would indicate, for example, that screening for this disease be initiated at an earlier time period for men. Table 2, by Mayeux et al. (1995), also indicates a dif-ference of disease onset by age. There is a dramatic preva-lence rate (total) for populations under 45 (1.3 per 100,000) as compared to those over (e.g., 99.3 per 100,000 for the age group 45–64 years). The prevalence also overall increases with age. There are also differences in prevalence among ethnic groups and sex within these groups. This demonstrates the importance of studies examining race and sex as impor-tant factors in disease (Ness et al., 2004; Lange et al., 2003b). This study (Mayeux et al., 1995) examined the age-adjusted prevalence rate for combined men and women by ethnic group (race), and a signifi cant difference ( p value ⬍ 0.01) was observed among blacks (57 per 100,000), whites (116 per 100,000), and Hispanics (130 per 100,000). This indicates that there is not only a difference in the onset of Parkinson’s TABLE 2Prevalence of idiopathic Parkinson’s disease in a New York neighborhood based on a community diseases registry, 1988–1989Ethnic group and sex Age group (years) Total ⬍45 45–64 65–74 75–84 ⭓85 Crude Age-adjustedBlack men No. 0 1 7 6 1 15 —Population 19,395 4,265 1,216 530 150 25,556 —Prevalence rate 0 23.4 575.7 666.7 58.7 92.0(29.0–88.4)‡92.0(54.7–129.0)White menNo. 0 1 7 8 3 19 —Population 20,285 6,020 2,296 1,305 443 30,349 —Prevalence rate 0 16.6 304.9 613.0 667.0 62.6(34.5–90.7)54.7(28.4–81.0)White womenNo. 1 14 12 34 12 73 —Population 26,447 7,036 2,446 1,710 636 38,275 —Prevalence rate 3.8 199.0 490.6 1,074.7 1,886.8 167.3(147.0–234.0)86.0(131.0–114.0)Hispanic menNo. 0 1 7 6 1 15 —Population 19,395 4,265 1,216 530 150 25,556 —Prevalence rate 0 23.4 575.7 666.7 58.7 92.0(29.0–88.4)92.0(54.7–129.0)Hispanic womenNo. 0 1 7 6 1 15 —Population 19,395 4,265 1,216 530 150 25,556 —Prevalence rate 0 23.4 575.7 666.7 58.7 92.0(29.0–88.4)92.0(54.7–129.0)TotalNo. 0 1 7 6 1 15 —Population 19,395 4,265 1,216 530 150 25,556 —Prevalence rate 0 23.4 575.7 666.7 58.7 92.0(29.0–88.4)92.0(54.7–129.0)Source: From Mayeux et al. (1995), The frequency of idiopathic Parkinson’s disease by age, ethnic group and sex in northern Manhattan, 1988–1993, American Journal of Epidemiology, 142:820–27; with permission from Oxford Press.C005_011_r03.indd 378C005_011_r03.indd 378 11/18/2005 10:25:42 AM11/18/2005 10:25:42 AM
Y 379disease by age and sex, but by ethnic group as well. These differences in Table 2 illustrate the importance of controlling for various confounders such as sex, age, and race in epidemio-logical studies. When examining the incidence rate of Parkinson’s dis-ease (Table 3), this study reports 83 new cases during the 3-year period. For the incident cases, the mean age was 76.3 years, with a standard deviation of 9.5 and a time period of symptoms (duration of 1.4 years). There was reported no dif-ference in the mean age (75.2 years) for men and women for the onset of symptoms. From Table 3, the annual inci-dence of Parkinson’s disease in New York City is 13 per 100,000. Unlike that reported for prevalence, there were no incidences of Parkinson’s diseases below the age of 45 years during this study period. However, as noted for prevalence, the incidence rate of disease increases with age. There is also a difference in the rates for men and women and among ethnic groups evaluated. The data in Tables 2 and 3 can be used to evaluate the numbers of cases and the occurrence of disease in a TABLE 3 Annual incidence of idiopathic Parkinson’s disease over a 3-year period in a community diseases registry, New York City, 1988–1989 Ethnic group And sex Age group (years) Total 45–64 65–74 75–84 ⭓85 Crude Age-adjustedBlack men No. 1 7 6 1 15 — —Population 4,265 1,216 530 150 25,556 — —Prevalence rate — 23.4 575.7 666.7 58.7 92.0(29.0–88.4)‡92.0(54.7–129.0)White menNo. 1 7 8 3 19 — —Population 6,020 2,296 1,305 443 30,349 — —Prevalence rate 16.6 304.9 613.0 667.0 62.6 54.7(34.5–90.7)—(28.4–81.0)White womenNo. 14 12 34 12 73 — —Population 7,036 2,446 1,710 636 38,275 — —Prevalence rate 199.0 490.6 1,074.7 1,886.8 167.3 86.0(147.0–243.0)—(131.0–114.0)Hispanic menNo. 1 7 6 1 15 — —Population 4,265 1,216 530 150 25,556 — —Prevalence rate 23.4 575.7 666.7 58.7 92.0 92.0(29.0–88.4)—(54.7–129.0)Hispanic womenNo. 1 7 6 1 15 — —Population 4,265 1,216 530 150 25,556 — —Prevalence rate 23.4 575.7 666.7 58.7 92.0 92.0(29.0–88.4)—(54.7–129.0)TotalNo. 1 7 6 1 15 — —Population 4,265 1,216 530 150 25,556 — —Prevalence rate 23.4 575.7 666.7 58.7 92.0 92.0(29.0–88.4)—(54.7–129.0)Source: From Mayeux et al. (1995), The frequency of idiopathic Parkinson’s disease by age, ethnic group and sex in northern Manhattan, 1988–1993, American Journal of Epidemiology, 142:820–27; with permission from Oxford Press.C005_011_r03.indd 379C005_011_r03.indd 379 11/18/2005 10:25:42 AM11/18/2005 10:25:42 AM
380
Ypopulation. This provides information on the distribution of the disease and possibly allocation of resources in its prevention and treatment. Although the use of prevalence and incidence was demonstrated for a chronic disease, Parkinson’s disease, it can also be used for occupational and environmental diseases and events. Application of preralence incidence are illustrated in Table 2 and 3. SICKNESS SURVEYS In some cases an estimate of the amount of sickness in the population has been made by market-research techniques, whereby people in the street are interrogated about their health in the last week (or month, but the shorter period is preferred for purposes of better accuracy). This method was used by the British government during World War II and was described as the “Survey of Sickness.” There are several obvious omissions that are likely to distort the fi ndings, such as the chronically ill who cannot get out into the street, or those who return straight to work after short illness and are not available to be questioned in the street. Nevertheless it is a cheap method that may have suffi cient consistency to validate time trends of indices based on it. For more severe illnesses, statistics of admissions to hospitals, diagnoses, treatment methods, length of stays, etc. may serve to supple-ment the measurement sickness in the population. Not all hospitals may be able to provide useful fi gures, however, nor may their catchment areas be suffi ciently clearly defi ned. However, with the advent of computers and development of databases for diseases, these issues of disease are better defi ned, especially in Westernized countries. Because of the wide range of sickness itself, the means of dealing with it, and variation in reporting, some form of sampling from the various sources is likely to yield the most useful results. However, even with attempts at standardization, ICD codes, there is often a wide variation in the incidence and preva-lence of disease, even in the same community. One solu-tion to this problem, in providing an accurate estimate of disease, is to employ the capture-recapture method (CRM). Since the problem in determining the occurrence of sickness and disease is at the heart of counting, the CRM has been suggested as the most accurate method for counting (Lange et al., 2003c). However, since this method was originally derived for counting wildlife, it is best known as an eco-logical- and population-biology method, and has not been widely adopted by epidemiologists. Its recent use in count-ing hazardous-waste sites (Lange et al., 2003a) demonstrates this method’s versatility for counting, including in the area of epidemiology. DISEASE REGISTERS For a number of diseases, attempts have been made to make and maintain lists or registers of those affected. Infectious diseases are among the most obvious to fall into this cat-egory, since isolation of those affected was for so long the only effective deterrent to their spread. The advent of spe-cifi c treatment methods, or more usefully of vaccines and immunization, has greatly reduced their impact, except per-haps for rarities such as Lhasa fever, or, in another category, AIDS. The pulmonary-tuberculosis register was an important one until treatment became readily available. Notifi cation of the local health authority of any of the range of diseases has often been a requirement of general practitioners, in order to obtain early warning of an impending epidemic, and to mon-itor the occurrence of those diseases. Some heart conditions have formed the subjects of registers, though limited usually by time or space. Furthermore, a number of diseases, usually rare and often genetic, have registers or societies of affected patients, which can be useful not only for the discussion and possible alleviation of common problems, but also for the purposes of research. Most recently, disease registries, or what could be included as registries, have emerged for spe-cifi c cohorts such as migrant agricultural workers (Zahm and Blair, 2001) as well as for specifi c occurrences of disease (Lange et al., 2003d). CANCER REGISTERS Cancer registers, or more commonly registries, form a very distinct and important group of disease lists. They fall into three categories: (1) special registries concerned only with certain sites of the disease (e.g., bone cancer or gastrointes-tinal cancers); (2) hospital-based registries, which record all those cases seen at a particular hospital or groups of hospitals; and (3) population-based registries, which endeavor to collect records of every case of cancer within a specifi c population. The last group is the most important as a source of morbidity data about cancer. Cancers form a special group of diseases of exceptional importance, at least historically, which attract a great deal of interest and research, and for which epide-miological methods are of outstanding relevance. The date of diagnosis of cancer can be used as the basis of morbidity rates analogously to the mortality rates, so that from a population-based registry, rates of morbidity by sex, age, and site can be constructed, using the sex and age structure of the population for appropriate denominators. Cancer registries exist now in many parts of the world, though more in developed than in the underdeveloped countries, and their incidence rates by sex, age, and site have been collectively published in the succes-sive volumes of Cancer Incidence in Five Continents , begin-ning in 1966 and subsequently at intervals of approximately 5 years. They have formed a valuable source of comparative data about the different patterns of cancer found geographi-cally, and in combination with other data sources can lead to the generalization hypotheses of etiology. To their use in a variety of other ways, such as in the evaluation of occupa-tional and environmental carcinogenic hazards, in the conduct of comparative clinical trails (especially in those patients not included), and among the sequelae of certain types of chronic disease, we shall refer later. The pattern of cancer displayed in relation to sex, age, and site, whether in terms of mortality or morbidity, can C005_011_r03.indd 380C005_011_r03.indd 380 11/18/2005 10:25:42 AM11/18/2005 10:25:42 AM
Y 381provide important information on carcinogenic hazards in the area to which it refers. The different proportions by site throughout the world, where data are available, affect climatic, geographical, and lifestyle variations but are not always simple to analyze. Furthermore, some sources of data may consist of numerator information only (e.g., deaths or diagnosed cases of disease) without the corresponding pop-ulation fi gures by sex and age, which enable the construc-tion of rates of mortality and morbidity. Rather than have to ignore such partial information, it is possible to present it in the form of proportionate mortality or morbidity rates. In its simplest form this method expresses the omitting age, since it may not be available; then it may facilitate comparison with another source of data that may have affi nities, perhaps in the likely age structure or in climate, to one under study. PROPORTIONATE MORTALITY RATE A situation somewhat similar to what has just been described can occur when a factory may be able to provide details (of cause, sex, and age) of the deaths of former employees over a period of time, but without adequate additional information to permit further analysis (see below). The pattern of their mor-tality, by cause and sex, can then be compared with the general patterns of the area where the factory is situated. Usually the deaths will be categorized into broad groups (e.g., cardiovas-cular, neoplasms, respiratory) (Lange et al., 2003b), but if there is a reason to examine certain sites of cancer individu-ally, they can be included. Each observed death is allotted an age group in the general population; the proportions of deaths (as fractions of 1) occurring in each of the chosen cause cat-egories are entered and summed after all the observed deaths have been included. The accumulated fractions in each group will then constitute the expected number of deaths to compare with the number observed. Accumulated by age into numbers of expected and observed deaths by sex and cause, the com-parison can be evaluated statistically for its signifi cance (see below). If the observed deaths are spread over a number of years, the expected deaths should be strictly obtained from the corresponding calendar years, though they can usually be taken in quinquennial groups without serious loss of accu-racy. It will be evident that an assumption implicit in the method is that the factory population has been suffi ciently similar to the general population to justify the comparison. Thus, proportionate mortality rates (PMRs) are commonly used for occupational cohorts. ANALYTICAL
Y It is conventional to divide epidemiology into two distinct branches: descriptive and analytical. Up to this point we have been concerned mainly with the description of the health status of a population by means of rates of mortality and morbidity, by sex, age, and cause; for geographical and other subgroups; and in calendar time. Some of the methods of comparison we have discussed, necessitating standardization of the calculation of expected fi gures, have touched on the analytic division, though the defi nitions are not always clear-cut. Other methods that will be discussed are experimental in their design, such as clinical trials where the treatments of a disease by two different regimes forms the basis of a compar-ison of their relative effi ciency, the numbers of patients being decided by consideration of the statistical power required or attainable. SCATTERGRAMS A method that has been frequently used in searching for fac-tors related, possibly in an etiological way, to the incidence of disease is to display in graphical form a correlation diagram—a scatter diagram or “scattergram” where the incidence (or mortality rate) of the disease is measured on one scale and the factor of interest on the other. Figure 7 gives an example of the method, whereby each point represents a country whose (standardized) rate of colon cancer is set against the per-capita consumption of fat in that country. It is clear that there is a relationship between these two measures, such that as one increases so does the other. This apparent movement together may suggest a possible causative relationship, such that the higher the average consumption of fats, the greater the risk of colon cancer. But note fi rst that it is the aver-age per-capita factor, which is obtained from the total fat consumed in a country divided by population. Clearly, indi-viduals in the population will vary in their mean levels of consumption; some average more while others less than the average. If there is a causative relationship, we would expect 80100120 140 16018051015202530TOTAL FAT (g/day)1977–79AGE-ADJUSTED DEATH RATE/100,000 (1978–79)GREECEFINLANDHONGKONGSINGAPOREJAPANISRAELAUSTRALIAGERMANYIRELANDDENMARKAUSTRIA BELGIUMSWEDENUS WHITEFRANCEE+WSWITZERLANDNEW ZEALANDITALYNORWAYCANADANETHERLANDr=0.53t=2.80p=0.01FIGURE 7 Cancer of the colon and fat consumption (scattergram).C005_011_r03.indd 381C005_011_r03.indd 381 11/18/2005 10:25:42 AM11/18/2005 10:25:42 AM
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Yto fi nd higher rates of colon cancer among those consum-ing more than the average. But this information we do not posses, though it is precisely what is required to demonstrate the relationship conclusively. LATENCY PERIOD Another consideration, which is of particular relevance in the fi eld of cancer and other areas of epidemiology, is that there is a latency period, often of at least 20 years, between expo-sure to a substance (like a carcinogen) and the development of a clinically observable disease (again, like cancer). Thus the per-capita fat consumption should refer to fi gures of 20 or more years ago. If the cancer incidence is not showing rapid secular change, this consideration may not be important. It has also been shown that there is a similar relationship between the consumption of protein and colon cancer. It may well be that both fat consumption and a diet high in protein are among the causative factors of colon cancer, but it may also be that some other factor or group of factors, correlated with these two in particular, is more directly relevant. Lifestyle factors or social status may each be included, and both subsume at the same time a wide variety of other measures, some of which may be more legitimately described as directly etiological. In sum, therefore, a correlation diagram can lead to the generation of hypotheses of causation but cannot of itself prove the rela-tionship. The gross correlation between national averages and disease incidence needs to be investigated on individual cases of the disease, for each of which measures of consumption of putatively carcinogenic items of diet can be obtained, prefer-ably over a large period of time in retrospect. Data of this kind, if suffi cient in quantity and reliability in substance, can form the basis of an informative etiological study, probably using multivariate analytical techniques. REGRESSION AND CORRELATION ANALYSIS The relationship between the incidence of lung cancer and the number of cigarettes smoked is now well known, and has been verifi ed many times in a variety of situations. For most of these studies it is possible to obtain a graph of the mortality (or morbidity) rate against the number of cigarettes smoked per day, yielding a straight-line relation of the form y ⫽ a ⫹ bx between them, where y is the morbidity rate and x the cigarettes smoked per day, a and b being appropriate constants. The values of a and b can of course be readily obtained from the data, being the parameter of the simple linear regression between the two quantities. Many books on statistics prescribe the technique of fi tting regression lines. INTERACTION A relationship of a similar kind has been shown between the incidence of esophageal cancer and the number of cigarettes smoked. The same disease is also related in the same way to quantity of alcohol consumed. We could combine these two fi ndings to obtain a regression equation using two quantities as infl uencing a third (the morbidity rate), of the form z ⫽ a ⫹ bx ⫹ cy where z is the morbidity rate, x is the number of cigarettes smoked, y is the quantity of alcohol consumed, and a, b, and c are appropriate constants. The form of this equation assumes independence between the actions of each quantity on the morbidity rate. It has been found in actual study that the combined effect of both quan-tities in the same individuals results in an enhanced rate of morbidity, above the additive effect of the two separately. This enhancement, amounting to a multiplicative rather than an additive effect, is known as “synergism” (Figure 8). A similar example of a synergistic effect is found in the occupational fi eld by the combination of the effects of exposure to asbes-tos and cigarette smoking on the development of lung cancer. Figure 9 shows the separate effects of each agent in terms of a rate set at 1 for those exposed to neither and also the rate for both together, which corresponds to multiplying rather than adding the separate rates. The establishment of a genuinely synergistic effect requires both extensive and reliable data. ANALYSIS OF OCCUPATIONAL DISEASE In studies of occupational disease, the basic question to be answered is whether there is an excess of cases of the disease 0–40 41–8081+0–910–1920+TOBACCO(g/day)107.318.03.48.419.95.112.344.4FIGURE 8 Cancer of the esophagus in relation to alcohol and smoking.C005_011_r03.indd 382C005_011_r03.indd 382 11/18/2005 10:25:43 AM11/18/2005 10:25:43 AM
Y 383among the workers exposed to the putative causative factor, whether that is a substance or a process that is used in certain parts of a factory. In its most elementary form, the results of an investigation can be put in the form of a 2 ⫻ 2 table, as in Figure 10. The fi rst two cells of this table, horizontally, include the numbers of those who were exposed (⫹) to the presumed hazard, the fi rst cell containing the number of those who devel-oped the disease in question (a), the second those who did not (b). In the lower line are those who were not exposed (⫺), the fi rst cell again including all those for this group who developed the disease © and the second those who did not (d). Clearly if the ratio of the left to the right is the same in both rows, there is no evidence of an effect. This is an example of the 2 ⫻ 2 or fourfold table to which the X 2 test can easily be applied, with one degree of freedom, to assess whether any difference in the proportion, horizontally or vertically, attains statistical signifi cance, at whatever level may be chosen. The conventional levels of signifi cance are 0.05 (5%), 0.01 (1%), and 0.001 (0.1%), each referring to the probabilities that the observed result could have occurred by chance alone (the levels are sometimes quoted in the form of percentages, multiplying their probabilities by 100). For each cell of the table of Figure 10 an “expected” fi gure can be calculated from the marginal and grand totals, by divid-ing, for instance, each row total in the proportions of the column totals: thus the expectation for the top left cell is the product of the fi rst row’s total divided by the grand total. The difference between the observed number in each cell is squared and divided by the expectation for that cell, and the sum of these four quantities constitute X 2 . Tables pro-vided in almost all books on statistics will enable the level of signifi cance to be obtained for the value of X 2 and for one degree of freedom. Two caveats should be noted: fi rst, that no expectation should be less than 5—if it is, a larger size of sample is required—and second, that when numbers are small (yet satisfy the proceeding conditions), Yates’s cor-rection should be made, which reduces the absolute size of the difference between observed and expected by the quan-tity ½. It will have been noted that this difference is the same magnitude in each of the four cells, though it changes sign, but that is irrelevant since it is squared. It is the abso-lute magnitude of this common difference that should be reduced by ½. ODDS RATIO AND RELATIVE RISK In the circumstances set out above and in Figure 10, the ratio c /( c ⫹ d ) is the risk of disease in the unexposed group, which we can call P 0 , and P 1 / P 0 is known as the “relative risk,” RR or r . In many cases the disease in question will be rare, even among the exposed, so that a and c will be small relative to b and d . If Q 0 ⫹ 1 ⫺ P 0 and Q 1 ⫹ 1 ⫺ P 1 express the risk of not contracting the disease, then they will both be close to 1, since P 0 and P 1 are supposed to be small. The quantity ( P 1 / Q 1 )/( P 0 / Q 0 ) is known as the “odds ratio,” since it is the ratio of the odds of occurrence of the disease in the exposed to the unexposed groups. Since we are presuming the Q ’s to be close to 1, the odds ratio can be put as P 1 / P 0 , which is the same as the relative risk, r . We shall see later that this fact permits the estimation of the ratio of the incidence of disease in the exposed and unexposed groups from a case-control type of investigation, though their absolute incidences are not obtainable. ETIOLOGICAL STUDIES A situation that is formally very similar to what we have just been considering arises if we suspect a certain factor may be one that is involved in the etiology of the disease. We shall again be comparing persons with and without the disease and those affected in the form of a 2 ⫻ 2 table like Figure 10, where we replace “Factor” for “Exposure.” If the factor is indeed an etiological one, it will be found more frequently SmokingAsbestosRelative risk01234567891011121314151617181920––––++++FIGURE 9 Cancer of the lung in relation to asbestos and smoking.DiseaseExposure––++abcd FIGURE 10 C005_011_r03.indd 383C005_011_r03.indd 383 11/18/2005 10:25:43 AM11/18/2005 10:25:43 AM
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Yin association with the presence of the disease, and less so with its absence. A case-control investigation led naturally to this end point, though it may take a variety of different forms. Take one of the earliest studies of smoking and lung cancer, Doll and Hill (1950), which was followed by a cohort of English physicians using a questionnaire (Doll and Hill, 1954) and then continued as a prospective study up to the present day (Doll et al., 2004). For this study 709 patients with lung cancer, in 20 hospitals, were matched with the same number of patients from the same hospital, but not having cancer or a respiratory disease. The matching was for the same hospi-tal, of the same sex, and within the same 5-year age group. All the patients were interviewed according to a standard questionnaire. The simplest form of the results is shown in Figure 11. The expectations in the two lower cells of the square are each 40, and in the upper cells each 699. The difference therefore in each cell is 19, with the result that the X 2 value, whether or not Yates’s correction is used (it is not necessary here), is very large, and the probability that the association between smoking and lung cancer might be a chance one is extremely unlikely. In the study itself the result of smoking (in numbers of cigarettes smoked per day) was quantifi ed, and the results given separately by sex. For the purpose of this illustration the study is summarized in Figure 11, but clearly the additional evidence afforded by the quantifi cation data, which for each sex showed a steadily increasing risk of lung cancer at each successive level of smoking, reinforces the basic etiological relationship of smoking to lung cancer. CASE-CONTROL STUDIES In any case-control study (“case-referent study” is a synony-mous term) the choice of appropriate controls is of special importance. In the study discussed above, the controls were matched for sex and age group—the two most commonly used characteristics for matching—and also for hospital, lest there should be some factor associated with that. There were two exclusions: cancer and a respiratory condition, which could confuse the contrast between cases and controls. When there are few cases available, and in some other circum-stances, it may be advisable to use more than one control per case. Beyond four controls per case little further advantage can be gained, but two, three, or four controls for every case may be useful, though expensive. In general the more closely the controls resemble the cases in terms of characteristics, the more effi cient the contrast, except that one or more of those characteristics may be of genuine etiological signifi cance, but because it is possessed by both case and control, it is impos-sible to distinguish. CLINICAL TRIALS The underlying philosophy is that of the experimentalists of the scientifi c renaissance, who began in physics or in chem-istry to look at the effects of a single factor alone, varying its contribution to the ultimate effect while endeavoring to keep other factors constant. The method could then be repeated for other factors, and thus the independent effects assessed, as well as those where separation proved impos-sible because of close correlations. The aim of the clinical therapeutic trial, for instance, is to obtain two groups of patients so similar in all known relevant respects that any difference in their responses can be reasonably attributed to their different treatments. Not only sex and age but the type and severity of the disease and its history, together possibly with socioeconomic or lifestyle factors, if relevant, need to be taken into account in ensuring the parallelism of the two treatment groups. It is important that the full treatment regi-men in both groups (experiment and control) be decided in advance and adhered to precisely. There must be of course a provision for emergencies, and therefore escape clauses or alternative regimens should form part of the design of the trial. A pilot trial, perhaps amounting to around 5% of the full trial, can greatly help to reveal aspects previously overlooked, and if the modifi cations it suggests are not too great, it may be possible to include it as the start of the main trial. For the reason that those directly concerned with the conduct of the trial, or with its assessment, may form prema-ture opinions about its outcome and hence introduce a bias if they know the actual treatment that patients receive, it is cus-tomary to run many clinical trials “blind”—that is, in such a way that the clinicians are unaware of the treatment given. If the active treatment consists of tablets, the control could be a placebo presented in the same form; if it is an injection, the control can receive an injection of normal saline; etc. The trial may also be “double-blind,” when neither clinician nor patient knows the identify of the “apparent” treatments. Of course, a singly blind trial may imply that the patient is unaware of his treatment but the clinician does know. There are also occasions when the two treatments have differences that cannot be distinguished, such as surgery for one and radiotherapy for another. STRATIFICATION We have stressed already the importance of the close similarity—almost identity—of the two groups of patients, referring to obvious characteristics such as sex and age. Other relevant features should also, if feasible, be similarly balanced between the groups, and each of them may be described as a 709709Lung CancerSmoking13888014186886502159++–– FIGURE 11 C005_011_r03.indd 384C005_011_r03.indd 384 11/18/2005 10:25:43 AM11/18/2005 10:25:43 AM