In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample by the previous occurrence of some other event (called a loss). Losses may be either accidental or controlled, the latter resulting from a decision to terminate certain observations. In either case it is usually assumed in this paper that the lifetime (age at death) is independent of the potential loss time; in practice this assumption deserves careful scrutiny. Despite the resulting incompleteness of the data, it is desired to estimate the proportion P(t) of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t). The observation for each item of a suitable initial event, marking the beginning of its lifetime, is presupposed. For random samples of size N the product-limit (PL) estimate can be defined as follows: L...

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Nonparametric Estimation from Incomplete Observations

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.

Statistical Aspects of the Analysis of Data From Retrospective Studies of Disease

The secretion of glucocorticoids (GCs) is a classic endocrine response to stress. Despite that, it remains controversial as to what purpose GCs serve at such times. One view, stretching back to the time of Hans Selye, posits that GCs help mediate the ongoing or pending stress response, either via basal levels of GCs permitting other facets of the stress response to emerge efficaciously, and/or by stress levels of GCs actively stimulating the stress response. In contrast, a revisionist viewpoint posits that GCs suppress the stress response, preventing it from being pathologically overactivated. In this review, we consider recent findings regarding GC action and, based on them, generate criteria for determining whether a particular GC action permits, stimulates, or suppresses an ongoing stressresponse or, as an additional category, is preparative for a subsequent stressor. We apply these GC actions to the realms of cardiovascular function, fluid volume and hemorrhage, immunity and inflammation, metabolism, neurobiology, and reproductive physiology. We find that GC actions fall into markedly different categories, depending on the physiological endpoint in question, with evidence for mediating effects in some cases, and suppressive or preparative in others. We then attempt to assimilate these heterogeneous GC actions into a physiological whole. (Endocrine Reviews 21: 55‐ 89, 2000)

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How do glucocorticoids influence stress responses? Integrating permissive, suppressive, stimulatory, and preparative actions.

The prevalence of comorbid alcohol, other drug, and mental disorders in the US total community and institutional population was determined from 20 291 persons interviewed in the National Institute of Mental Health Epidemiologic Catchment Area Program. Estimated US population lifetime prevalence rates were 22.5% for any non—substance abuse mental disorder, 13.5% for alcohol dependence-abuse, and 6.1% for other drug dependence-abuse. Among those with a mental disorder, the odds ratio of having some addictive disorder was 2.7, with a lifetime prevalence of about 29% (including an overlapping 22% with an alcohol and 15% with another drug disorder). For those with either an alcohol or other drug disorder, the odds of having the other addictive disorder were seven times greater than in the rest of the population. Among those with an alcohol disorder, 37% had a comorbid mental disorder. The highest mental-addictive disorder comorbidity rate was found for those with drug (other than alcohol) disorders, among whom more than half (53%) were found to have a mental disorder with an odds ratio of 4.5. Individuals treated in specialty mental health and addictive disorder clinical settings have significantly higher odds of having comorbid disorders. Among the institutional settings, comorbidity of addictive and severe mental disorders was highest in the prison population, most notably with antisocial personality, schizophrenia, and bipolar disorders. (JAMA. 1990;264:2511-2518)

https://jamanetwork.com/HttpHandlers/ArticlePdfHandler.ashx?journal=JAMA&articleId=383975&pdfFileName=jama_264_19_026.pdf

Comorbidity of Mental Disorders With Alcohol and Other Drug Abuse. Results From the Epidemiologic Catchment Area (ECA) Study

When more than one statistical test is performed in analysing the data from a clinical study, some statisticians and journal editors demand that a more stringent criterion be used for “statistical significance” than the conventional P<0051 Many well meaning researchers, eager for methodological rigour, comply without fully grasping what is at stake Recently, adjustments for multiple tests (or Bonferroni adjustments) have found their way into introductory texts on medical statistics, which has increased their apparent legitimacy This paper advances the view, widely held by epidemiologists, that Bonferroni adjustments are, at best, unnecessary and, at worst, deleterious to sound statistical inference

#### Summary points

Adjusting statistical significance for the number of tests that have been performed on study data—the Bonferroni method—creates more problems than it solves

The Bonferroni method is concerned with the general null hypothesis (that all null hypotheses are true simultaneously), which is rarely of interest or use to researchers

The main weakness is that the interpretation of a finding depends on the number of other tests performed

The likelihood of type II errors is also increased, so that truly important differences are deemed non-significant

Simply describing what tests of significance have been performed, and why, is generally the best way of dealing with multiple comparisons

Bonferroni adjustments are based on the following reasoning1-3 If a null hypothesis is true (for instance, two treatment groups in a randomised trial do not differ in terms of cure rates), a significant difference (P<005) will be observed by chance once in 20 trials This is the type I error, or α When 20 independent tests are performed (for example, study groups are compared with regard to 20 unrelated variables) and the null hypothesis holds for all 20 comparisons, the chance of at least one test being significant is no longer 005, but 064 …

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What's wrong with Bonferroni adjustments

In the biologic laboratory we have a method of procedure for determining the effect of an agent or process that may be considered typical. It consists in dividing a group of animals into two cohorts, one considered the “experimental group,” the other the “control.” On the experimental group some variable is brought to play; the control is left alone. The results are set up as in table 1-a. If the results show that the ratio a:a þb is different from the ratio c:c þd, it is considered demonstrated that the process brought to bear on the experimental group has had a significant effect. A similar method is prevalent in statistical practice, which I venture to think has come into authority because of its apparent equivalence to the experimental procedure. In Biometrika it is referred to as the fourfold table and it is used as a paradigm of statistical analysis. The usual arrangement is that given in table 1-b. The entries, a, b, c and d are manipulated arithmetically to determine whether there is any correlation between A and B. A considerable number of indices have been elaborated to measure this correlation. Pearson has given the formula for calculating the product-moment correlation coefficient from a fourfold table on the assumption that the distribution of both variates is normal; Yule has an index of association for the fourfold table; there are the chi-square test and others. In essence, however, all these indices measure in different ways whether and how much, in comparison with the variation of random sampling, the ratio a:a þb differs from the ratio c:c þd. If the difference departs significantly from zero, there is said to be correlation, and the correlation is the greater the greater the difference. Now there is a distinction between the method as used in the laboratory and as applied in practical statistics. In the experimental situation, the groups, B and not B, are selected before the subgroupings, A and not A, are effected; that is, we start with a total group of unaffected animals. In the statistical application, the groupings, B and not B, are made after the subgroupings, A and not A, are already determined; that is, all the effects are already produced before the investigation starts. In the end, the tables of the results which are drawn up look alike for the two cases, but they have been arrived at differently. Correlative to this difference, a different interpretation may apply to the results, and this paper deals with a specific case of a kind that arises frequently in a medical clinic or a hospital. I take an example.

Limitations of the application of fourfold table analysis to hospital data.

(1944). Application of the Logistic Function to Bio-Assay. Journal of the American Statistical Association: Vol. 39, No. 227, pp. 357-365.

Application of the Logistic Function to Bio-Assay

On the basis of experience with calculated survivorships of patients following treatment for cancer, a simple function, in terms of two physically meaningful parameters, has been evolved, which fits such survivorship data very well. These two parameters can be used to compare succinctly the mortality of two groups, different in respect of treatment, type of cancer, or other characteristics. The parameters are c (“cured”), which represents the proportion of the population which is subject only to “normal” death rates, and β, which is the death rate from the cancer, to which the rest of the population [not “cured,” (1–c)] is subject. Thus if one treatment is characterized by c 1 = 0.30, β 1 = 0.25, another by c 2 = 0.20, β 2 = 0.15, this could be interpreted as meaning that while the first treatment “cured” a larger proportion of the population than did the second treatment, it did not ameliorate the deaths attributable to cancer in the patients not cured as much as did the second treatment. If l T...

Survival Curve for Cancer Patients Following Treatment

Probit Analysis: A Statistical Treatment of the Sigmoid Response Curve.

(1953). A Statistically Precise and Relatively Simple Method of Estimating the Bio-Assay with Quantal Response, Based on the Logistic Function. Journal of the American Statistical Association: Vol. 48, No. 263, pp. 565-599.

Joseph Berkson

Papers

Limitations of the application of fourfold table analysis to hospital data.

Application of the Logistic Function to Bio-Assay

Survival Curve for Cancer Patients Following Treatment

Probit Analysis: A Statistical Treatment of the Sigmoid Response Curve.

A Statistically Precise and Relatively Simple Method of Estimating the Bio-Assay with Quantal Response, Based on the Logistic Function