Hazard rate ratio and prospective epidemiological studies.

Analysis of prospective follow-up data usually includes a Cox regression model. When a hazard rate ratio, obtained as the exponential of an estimated regression coefficient from the Cox model, is greater than 1.0, it consistently exceeds relative risk, and is exceeded by the odds ratio. The divergence of these distinct epidemiologic measures increases with the product of three factors: (1) the length of follow-up, (2) the average rate of the end point occurence over the follow-up period, and (3) the magnitude of risk, either above or below 1. Cornfield's rare disease assumption is basically the product of the first two of these factors. However, risks in excess of 2.5 have a powerful effect on the divergence of these measures, and this point has received less emphasis. Conversely, and as seen frequently in applications, relative risk, hazard rate ratio, and odds ratio numerically approximate one another with shorter follow-up, rarer end points, and risks closer to 1. Although the hazard rate ratio is not always distinguished from relative risk, it is commonly close to, and is always between, relative risk and the odds ratio. Consistent and accurate terminology would have us use hazard rate ratio with Cox regression and odds ratio with logistic regression. The term "relative risk" seems to be a default choice, regardless of the model being used. However, when relative risk is the object of the model chosen, as in a Poisson regression approximation of two binomial proportions or an equivalent weighted least squares, then for us, relative risk is the accurate terminology.

Factors contributing to the poorer survival of black Americans diagnosed with oral cancer (United States).

OBJECTIVE: The purpose of this study was to identify factors that contribute to the poorer survival of blacks in the United States diagnosed with oral cancer. METHODS: Data for 6,338 whites and 1,165 blacks diagnosed from 1988 to 1993 with squamous cell carcinoma of the oral cavity and pharynx were obtained from the National Cancer Institute's Surveillance, Epidemiology and End Results (SEER) program 1973-1993 Public-Use Database. The covariables were sex, age, geographic area, marital status, socioeconomic status (five census-tract measures), stage, anatomic site, grade, lymph node involvement, tumor size, and treatment. Hazard ratios were estimated with Cox regression. RESULTS: Adjusted for age and geographic area, the hazard of death from oral cancer was 1.7 (95% confidence interval: 1.5-1.9) times greater among blacks than whites. The addition of the socioeconomic status (SES) variables to the model reduced the hazard ratio for race to 1.3 (1.0-1.7). Further adjustment by stage and treatment reduced the hazard ratio for race to 1.1 (0.9-1.4). In a model containing all covariables (except lymph node involvement and tumor size), the hazard ratio for race remained 1.1 (0.9-1.4). Analyses with the outcome death from any cause gave similar results. CONCLUSIONS: Lower SES, more advanced stage, and differences in treatment accounted for 86% of the excess hazard of death from oral cancer among blacks.

A method for implementing dynamic photon beam intensity modulation using independent jaws and a multileaf collimator.

A mathematical model is derived for digitally controlled linear accelerators to deliver a desired photon intensity distribution by combining collimator motion and machine dose rate variations. It shows that, at any instant, the quotient of the machine dose rate and the speed of collimator motion is proportional to the gradient of the desired in-air photon fluence distribution. The model is applicable for both independently controlled collimator jaws and multileaf collimators and can be implemented by controlling different parameters to accommodate linear accelerators from different manufactures. For independent jaws, each pair of jaws creates photon fluence variations along the direction of the jaw movement. For multileaf collimators, where each leaf is independently controlled, any two-dimensional (2D) photon fluence distribution can be delivered. The model has been implemented for wedged isodose distributions using independent jaws, and 2D intensity modulation using a multileaf collimator. One-dimensional (1D) wedged isodose distributions are created by moving an independent jaw at constant speed while varying machine dose rate. 2D intensity modulation has been implemented using a 'dynamic stepping' scheme, which controls the leaf progression during irradiation at constant machine dose rate. With this automated delivery scheme, the beam delivery time for dynamic intensity modulation, which depends on the complexity of the desired intensity distribution, approaches that of conventional beam modifiers. This paper shows the derivation of the model, its application, and our delivery scheme. Examples of 1D dynamic wedges and 2D intensity modulations will be given to illustrate the versatility of the model, the simplicity of its application, and the efficiency of beam delivery. These features make this approach practical for delivering conformal therapy treatments.

Mediators of depression among low-income, adolescent mothers of infants: A longitudinal perspective.

The purpose of this study was to identify, using a life events perspective, Stressors and resources that mediate depression for adolescent mothers at the time of the birth of their child and at one year postpartum. The data for this study consisted of interviews with 157 low-income adolescent mothers age 12-18 at the birth of their child. They were selected from a larger prospective study of mothers of infants and stress. Multiple regression analyses revealed two key results that were consistent for the data obtained at birth and at one year postpartum. Predictors of depressive symptomatology and of a clinical syndrome of depression were similar. Also, Stressors generally were more important as mediators of depression than resources.

Statistical and research quality of the medical and pharmacy literature.

The statistical and research quality of reports published in two U.S. medical journals and two U.S. pharmacy journals over a 12-month period was determined. A 50% random sample of issues of New England Journal of Medicine, Annals of Internal Medicine, American Journal of Hospital Pharmacy, and Drug Intelligence and Clinical Pharmacy published in 1979 was reviewed, and all citable items were classified as one of nine types of communications. Items classified as original evaluative research reports were evaluated for experimental design and research goals and rated for appropriateness of statistical testing and overall research quality according to a set of objective criteria. Reports that were not immediately classifiable were reviewed by one additional person, and classifications or ratings were assigned by mutual consent. Of a total of 1506 citable items, 120 met the criteria for original evaluative research reports. The two medical journals had the highest percentages of reports for which statistical methods were rated as correct but also had the most reports for which statistical methods could not be rated as a result of incomplete documentation or publication errors. Reports in the medical journals had conclusions based on a logical progression of hypothesis, methods, and analysis of results more frequently than did reports in pharmacy journals. Reports in the medical and pharmacy journals differed greatly according to research design and research goals. Improvement is needed in the statistical quality and research quality of original research reports published in the pharmacy literature.

Reconstruction of silica exposure in the North Carolina dusty trades.

The current occupational standard for quartz exposure is largely drawn from studies of the granite workers at Barre, Vermont. Since 1935, the North Carolina Dusty Trades program has accumulated data on work-place environmental conditions, occupational history and health status for persons exposed to silica in a broad range of mineral industries, including granite dimension stone. The environmental data have been collected with Greenburg-Smith and midget impingers and the respirable mass dust sampler. A procedure is presented to combine the results of these sampling methods and estimate exposure at the various jobs at each dusty trades plant. From an individual's occupational history, the environmental exposure estimates are used to formulate personal lifetime exposure summaries. The results of this procedure in the North Carolina granite industry compared well with historical data from Vermont granite sheds.

The relative roles of neurological examination, functional abilities, and computed tomography in the definition of treatment failure in patients with anaplastic gliomas.

Forty-one patients with anaplastic gliomas undergoing postoperative treatment and evaluation underwent bimonthly evaluation of the following indices of treatment failure: neurological examination; Karnofsky functional rating; and computed tomography (CT) brain scanning. Treatment failure was declared when neurological examination or Karnofsky rating showed increased impairment or when CT scan revealed an increase in tumor sizes. Most often, all three indices simultaneously indicated treatment failure. In only 6 of 41 cases the CT scan alone was the first indication of treatment failure. During the first 6 months of follow-up, tumor enlargement on CT scan as a sole index of treatment failure occurred in only 3 of 26 cases that showed evidence of treatment failure during that time. For patients with glioblastoma, about 6% of treatment failures within 6 months are predicted to be missed by Karnofsky rating plus neurological examination, whereas CT scan alone is predicted to miss about 30%. It would seem reasonable to rely on the neurological examination and Karnofsky rating for follow-up during the first 6 months after surgery, without routine serial CT scanning during that time.

Sample size and duration for cohort studies of survival time with covariables.

The determination of sample size and duration for cohort studies with covariables is considered. An exponential model, using the form due to Feigl and Zelen (1965, Biometrics 21, 826-838) for the hazard with covariates and asymptotic normality of the maximum likelihood estimators of the parameters, is assumed. Emphasis is on applications involving two parameters, namely an underlying hazard and the coefficient of a single concomitant variable. The results of George and Desu (1974, Journal of Chronic Diseases 27, 15-24) are reproduced and extended to take account of censoring. An example with more than two dose groups is presented. For situations where the sample size is fixed and Type I error is specified, extension of the follow-up time is considered for the purpose of achieving the desired Type II error, given a null hypothesis and specific alternative hypothesis. Generalizations to situations with other forms for the hazard rate and multiple covariables are indicated.

Clustering of rare events.

The clustering of cases of a rare disease is considered. The number of events observed for each unit is assumed to have a Poisson distribution, the mean of which depends upon the population size and the cluster membership of that unit. Here a cluster consists of those units that are homogeneous in their rate of occurrence of the rare events under study. A sample of units is modeled by a mixture of Poisson distributions, one for each cluster, the mixing parameters being the proportions of all units represented by the components of the mixture. Maximum likelihood and Bayes approaches are employed to determine criteria for separating a sample into groups of units with homogeneous rates. A likelihood ratio test for the significance of a two-component mixture is presented as an example. The performance of the criteria is illustrated with data on the spatial occurrence of sudden infant deaths (SIDs) in North Carolina counties over a four-year period. The results suggest that the practice of dividing the counties into high- and low-risk categories on the basis of the ordered rates alone should be questioned. Tests based upon combinatorial methods are also presented to examine the significance of the number of contiguous counties among those with high rates.

Exposures and mortality among chrysotile asbestos workers. Part I: exposure estimates.

A detailed study of plant processes and dust control methods over the period 1930-1975 was conducted in an asbestos textile plant processing chrysotile. Linear statistical models for reconstructing historic dust exposure levels, taking into account textile processes, dust control measures, and job assignments, were developed. Parameters of these statistical models were estimated using 5,952 industrial hygiene sampling measurements covering the period 1930-1975. For most textile operations, exposure levels were significantly reduced by about 1940, when most engineering dust control measures were in place. Results of the exposure estimates indicated "precontrol" exposure levels to range from 3 to 78 fibers/cc with typical levels well above 10 fibers/cc. After textile operations were provided with dust control measures, estimated exposure levels ranged from 3 to 17 fibers/cc and were usually in the range of 5 to 10 fibers/cc. These exposure estimates were combined with an assessment of mortality among workers at this plant to investigate exposure-response relationships. Exposure-response results are presented in the companion manuscript in this volume.

Exposures and mortality among chrysotile asbestos workers. Part II: mortality.

A retrospective cohort mortality study was conducted among a cohort of 1,261 white males employed one or more months in chrysotile asbestos textile operations and followed between 1940 and 1975. Statistically significant excess mortality was observed for all causes combined (standardized mortality ratio [SMR] = 150), lung cancer (SMR = 135), diseases of the circulatory system (SMR = 125), nonmalignant respiratory diseases (SMR = 294), and accidents (SMR = 134). Using estimated fiber exposure levels in conjunction with detailed worker job histories, exposure-response relationships were investigated. Strong exposure-response relationships for lung cancer and asbestos related non-malignant respiratory diseases were observed. Compared with data for chrysotile miners and millers, chrysotile textile workers were found to experience significantly greater lung cancer mortality at lower lifetime cumulative exposure levels. Factors such as differences in airborne fiber characteristics may partially account for the large differences in exposure response between textile workers and miners and millers.

A comparison of the logistic risk function and the proportional hazards model in prospective epidemiologic studies.

The logistic regression and proportional hazards models are each currently being used in the analysis of prospective epidemiologic studies examining risk factors in chronic disease applications. The advantages and disadvantages of each are yet to be fully described. However, a theoretical relationship between the two models has been documented. In this paper the conditions under which results from the two models approximate one another are described. It is shown that where the follow-up period is short and the disease is generally rare, the regression coefficients of the logistic model approximate those of the proportional hazards model with a constant underlying hazard rate. Since under the same conditions the likelihood functions approximate one another, the regression coefficients have similar estimated standard errors. Further, estimation of relative risk with these models is contrasted. These results are illustrated utilizing a previously published data set on metastatic cancer of the breast. With increasing follow-up time, the logistic regression coefficients become uncertain and less reliable.

Brain and central nervous system cancer mortality in U. S. rubber workers.

Since 1963 the observed mortality experience of BCNS cancers among rubber workers appears to be very comparable to that expected. A possible exception to this statement is the experience of one plant in Akron, Ohio, reported by Monson and Nakano. Excesses in earlier years may also be localized to one or two companies. The results of a case-control study did not support a hypothesized association of elevated BCNS cancer risk with exposures in the tire building/tire assembly segments of the rubber tire manufacturing process. The direction of future epidemiologic studies would benefit by the assembly of as large a number of cases as possible and should focus on calendar periods of exposure, make allowance for a latent period, and include retrospective industrial hygiene assessments of the specific exposures.

Practical considerations for approximating relative risk by the standardized mortality ratio.

The standardized mortality ratio is a widely used and often criticized summary statistic for studies of occupational mortality. In this paper the authors discuss practical conditions under which relative risk can reasonably be approximated by the standardized mortality ratio. When the true relative risk is greater than 100%, the standardized mortality ratio overestimates relative risk no matter how small the mortality rates or how short the age bands utilized in the analysis. However, when the excessive mortality is consistent across the age bands, the standardized mortality ratio can usefully approximate relative risk for some applications, such as those involving site-specific cancers, providing the age bands employed are not too large.

A method for monitoring the fertility of workers. 2. Validation of the method among workers exposed to dibromochloropropane.

A method has been developed for monitoring industrial workers and others exposed to environmental agents which may impair fertility. National birth probabilities specific for maternal birth cohort, age, parity, and race are used to derive expected fertility. Observed fertility is obtained by questionnaire. Standardized fertility ratios are computed for exposure and non-exposure periods and compared. The analytic techniques have been validated by applying the method to a group of 36 male factory employees working in an agricultural chemical division (ACD) where pesticides including the nematocide dibromochloropropane were formulated. Twelve of these employees in mid-1977 had been discovered to have severely depressed sperm counts related to occupational exposure. The standardized fertility ratio (SFR) computed from data available in mid-1977 for the period at risk from employment in the ACD (SFR = 0.75) was significantly lower than those derived for the entire not-at-risk period (SFR = 1.88) and the portion related to employment in other areas of the factory (SFR = 2.16). Similar differences also were evident from data available several years earlier, demonstrating that the surveillance technique would have been capable of detecting occupationally induced infertility among these workers in advance of the actual discovery date.