Estimation of relative risk from individually matched series.
TL;DR: The resulting maximum likelihood estimate is expressed in a closed form up to the case of two-to-one matching, while with 3 or more controls for each case a simple iterative procedure of obtaining the estimate is presented.
Abstract: Point and interval estimation of relative risk is investigated for the purpose of casecontrol studies of disease etiology with individual matching of cases and controls. It is assumed that the disease is rare and that the relative risk bears no relatioln to the matching factors. The resulting maximum likelihood estimate is expressed in a closed form up to the case of two-to-one matching, while with 3 or more controls for each case a simple iterative procedure of obtaining the estimate is presented. Results for exact and approximate interval estimation are also derived.
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TL;DR: Criteria appropriate to the evaluation of various proposed methods for interval estimate methods for proportions include: closeness of the achieved coverage probability to its nominal value; whether intervals are located too close to or too distant from the middle of the scale; expected interval width; avoidance of aberrations such as limits outside [0,1] or zero width intervals; and ease of use.
Abstract: Simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals. Criteria appropriate to the evaluation of various proposed methods include: closeness of the achieved coverage probability to its nominal value; whether intervals are located too close to or too distant from the middle of the scale; expected interval width; avoidance of aberrations such as limits outside [0,1] or zero width intervals; and ease of use, whether by tables, software or formulae. Seven methods for the single proportion are evaluated on 96,000 parameter space points. Intervals based on tail areas and the simpler score methods are recommended for use. In each case, methods are available that aim to align either the minimum or the mean coverage with the nominal 1 -alpha.
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TL;DR: It is shown that both parameters depend—in different ways—on the frequency of the marker among cases of the disease, and on the "standardized morbidity ratio" for those with the marker.
Abstract: Miettinen, O. S. (Harvard School of Public Health, Boston. Mass. 02115). Proportion of disease caused or prevented by a given exposure, trait or intervention. Am J Epidemiol 99: 325-332, 1974.—The structures of two epidemiologic parameters are explored. One, the \"etiologic fraction.\" relates to markers of increased risk, and it is the proportion of disease attributable to the marker and/or to factors associated with it. The other, the \"prevented fraction,\" is the equivalent of this for a marker of reduced risk. It is shown that both parameters depend—in different ways—on the frequency of the marker among cases of the disease, and on the \"standardized morbidity ratio\" for those with the marker. Point estimation of these parameters is often straight-forward, particularly in case-control studies.
940 citations
Cites methods from "Estimation of relative risk from in..."
...Thus, the computation of SMR estimates is not feasible in casecontrol studies with individual matching, and the practical alternative is simply to assume uniformity of the risk ratio and to use an appropriate estimate of that parameter (9) as a substitute for the SMR estimate....
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TL;DR: The incidence and clinical and economic consequences of primary hyperparathyroidism in residents of Rochester, Minn, from 1965 through 1976 were examined, with a sharp increase in the annual incidence in persons 40 or more years of age.
Abstract: We examined the incidence and clinical and economic consequences of primary hyperparathyroidism in residents of Rochester, Minn, from 1965 through 1976; 90 cases were found. From January 1, 1965, to June 31, 1974, the average annual incidence was 7.8 +/- 1.2 (mean +/- S.D.) cases per 100,000 population. However, after the introduction of routine measurement of serum calcium, the average annual incidence rose to 51.1 +/- 9.6 cases per 100,000. Even after availability of routine measurement of serum calcium, the annual incidence of primary hyperparathyroidism among persons 39 years of age or younger remained below 10 cases per 100,000. However, the annual incidence increased sharply in persons 40 or more years of age, reaching 188 cases per 100,000 among women 60 years of age and over and 92 cases per 100,000 among men 60 and over. For the last 1.5 years of the study, the average annual age-adjusted incidence of primary hyperparathyroidism was 27.7 +/- 5.8 per 100,000. The frequency of urolithiasis fell from 51 to 4 per cent (P less than 0.001), and the proportion of cases without symptoms or complications of primary hyperparathyroidism rose from 18 to 51 per cent (P less than 0.005). The median charge in 1977 for diagnosis and treatment of primary hyperparathyroidism was $1700. (N Engl J Med 302:189-193, 1980).
925 citations
TL;DR: The possibility that the use of conjugated estrogens increases the risk of endometrial carcinoma was investigated in patients and a twofold age-matched control series from the same population, and data suggest that conjugate estrogens have an etiologic role in endometrian carcinoma.
Abstract: The possibility that the use of conjugated estrogens increases the risk of endometrial carcinoma was investigated in patients and a twofold age-matched control series from the same population. Conjugated estrogens (principally sodium estrone sulfate) use was recorded for 57 per cent of 94 patients with endometrial carcinoma, and for 15 per cent of controls. The corresponding point estimate of the (instantaneous) risk ratio was 7.6 with a one-sided 95 per cent lower confidence limit of 4.7. The risk-ratio estimate increased with duration of exposure: from 5.6 for 1 to 4.9 years exposure to 13.9 for seven or more years. The estimated proportion of cases related to conjugated estrogens, the etiologic fraction, was 50 per cent with a one-sided 95 per cent lower confidence limit of 41 per cent. These data suggest that conjugated estrogens have an etiologic role in endometrial carcinoma.
909 citations
TL;DR: In this article, a retrospective study was done comparing the occurrence of fractures in 245 long-term estrogen users and 245 case-matched controls, followed for an average of 17.6 years.
Abstract: Although several case-control studies have shown an inverse association between postmenopausal estrogen use and fractures, quantitation of fracture incidence has been lacking. To quantify the degree to which estrogen replacement therapy prevents postmenopausal osteoporosis, a retrospective study was done comparing the occurrence of fractures in 245 long-term estrogen users and 245 case-matched controls, followed for an average of 17.6 years. Quantitative bone mineral assessments were obtained from 18 women using estrogen replacement therapy and their controls (average age, 73 years). Osteoporotic fracture incidence in estrogen users was 50% as great as in the controls (p less than 0.01). Estrogen users showed significantly greater bone mineral: 54.2% greater spinal mineral (p less than 0.0002), 19.4% greater forearm mineral (p less than 0.0005), and 15.6% greater metacarpal cortical thickness (p less than 0.005). Long-term estrogen replacement therapy confers significant protection against bone loss and fracture.
712 citations
References
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TL;DR: In this paper, the role and limitations of retrospective investigations of factors possibly associated with the occurrence of a disease are discussed and their relationship to forward-type studies emphasized, and examples of situations in which misleading associations could arise through the use of inappropriate control groups are presented.
Abstract: The role and limitations of retrospective investigations of factors possibly associated with the occurrence of a disease are discussed and their relationship to forward-type studies emphasized. Examples of situations in which misleading associations could arise through the use of inappropriate control groups are presented. The possibility of misleading associations may be minimized by controlling or matching on factors which could produce such associations; the statistical analysis will then be modified. Statistical methodology is presented for analyzing retrospective study data, including chi-square measures of statistical significance of the observed association between the disease and the factor under study, and measures for interpreting the association in terms of an increased relative risk of disease. An extension of the chi-square test to the situation where data are subclassified by factors controlled in the analysis is given. A summary relative risk formula, R, is presented and discussed in connection with the problem of weighting the individual subcategory relative risks according to their importance or their precision. Alternative relative-risk formulas, R I , R2, Ra, and R4/ which require the calculation of subcategory-adjusted proportions ot the study factor among diseased persons and controls for the computation of relative risks, are discussed. While these latter formulas may be useful in many instances, they may be biased or inconsistent and are not, in fact, overages of the relative risks observed in the separate subcategories. Only the relative-risk formula, R, of those presented, can be viewed as such an average. The relationship of the matched-sample method to the subclassification approach is indicated. The statistical methodolo~y presented is illustrated with examples from a study of women with epidermoid and undifferentiated pulmonary ccrclnomc.e-J. Nat. Cancer Inst, 22: 719748, 1959.
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"Estimation of relative risk from in..." refers background in this paper
...Ever since its introduction in a classical paper by Cornfield [1951], relative risk has been the focal point of the statistical analysis of data from casecontrol (retrospective) studies of disease etiology, and considerable attention has been given to problems encountered in its estimation (Cornfield [1951; 1956], Woolf [1955], Haldane [1956], Cox [1958], Mantel and Haenszel [1959], Cornfield and Haenszel [1960], Berger [1961], Gart [1962a, b], Goodman [1963; 1964], etc)....
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...For 95%0 and 99%0 confidence, the exact limits for H may be obtained conveniently from the charts by Clopper and Pearson [1934] or from their reproductions in Pearson and Hartley ([1954] pp....
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TL;DR: The use of x is recommended instead of d as a criterion of differential incidence of disease in relation to blood group, and in all statistical computations it is best to transform x into its logarithm.
Abstract: Following the demonstration of a significant excess of blood group A in patients with cancer of the stomach (Aird, Bentall & Roberts, 1953) and of group 0 in sufferers from peptic ulcer (Aird, Bentall, Mehigan & Roberts, 1954) and from toxaemia of pregnancy (Pike & Dickins, 1954) i t seems certain that many more studies will be made on the relation between blood groups and disease. It is therefore important that the best possible statistical methods should be used. The procedure recommended by Aird et al. (1954) is very efficient, but it is open to criticism on one rather important point. These workers take as criterion the difference in proportion of a given blood group in the disease and the control series. Denote the two blood types a and p. Suppose the disease series contains h patients of type a and k of type 8, where h + k = n, and the control series hw H of type a and K of type ,3, where H + K = N . Aird and associates calculate d = h/n H / N . This is tested for significance against its sampling variance, combined with estimates from other bodies of data to give a weighted mean estimate, and compared with these other estimates in tests for heterogeneity. Unfortunately, d will differ from one community to another even when the specific attack rate within any given blood group stays constant. This can be shown by a simple example. Consider a community of 10,000 people in which H and K are each 5000. Then if h= 100 and k = 50, d = 100/150 0.5, or 0.1667. Now consider another community in which His 9000 and K is 1000. In this case h= 180 and k10, so d = 180/190-0.9, or 0.0474. Even when the essential biological conditions are identical, differences in blood-group frequencies in the population will introduce spurious heterogeneity. This kind of artefact is avoided if one works with incidence rates in the various blood groups. The data usually do not permit calculation of absolute rates, nor are they needed. What is wanted and readily obtained is an estimate of the ratio of one rate to another. The incidence in group a will be h/H x some constant, and that in group /? will be k/K x the same constant. If the ratio is taken aa x to 1, an estimate of x will be hK/Hk, and it may readily be shown that this is the maximum-likelihood estimate. The use of x is recommended instead of d as a criterion of differential incidence of disease in relation to blood group. In all statistical computations it is best to transform x into its logarithm. This avoids difficulties due to asymmetry. If comparison of a with B gives x = 2 say, comparison of /3 with a will give x= 4; but log x will retain its numerical value, merely changing in sign. Moreover, the sampling variance of log x is a very simple expression free of ‘nuisance parameters’. This is especially true if one transforms into y=log, x. If V is the sampling variance of y, then v = l / h + l / k + 1/H+ 1/K,
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