Beverly Rockhill

Validity and efficiency of approximation methods for tied survival times in Cox regression

Survival-time studies sometimes do not yield distinct failure times. Several methods have been proposed to handle the resulting ties. The goal of this paper is to compare these methods. Simulations were conducted, in which failure times were generated for a two-sample problem with an exponential hazard, a constant hazard ratio, and no censoring. Failure times were grouped to produce heavy, moderate, and light ties, corresponding to a mean of 10.0, 5.0, and 2.5 failures per interval. Cox proportional hazards models were fit using each of three approximations for handling ties with each interval size for sample sizes of n = 25, 50, 250, and 500 in each group. The Breslow (1974, Biometrics 30, 89-99) approximation tends to underestimate the true beta, while the Kalbfleisch-Prentice (1973, Biometrika 60, 267-279) approximation tends to overestimate beta. As the ties become heavier, the bias of these approximations increases. The Efron (1977, Journal of the American Statistical Association 72, 557-565) approximation performs far better than the other two, particularly with moderate or heavy ties; even with n = 25 in each group, the bias is under 2%, and for sample sizes larger than 50 per group, it is less than 1%. Except for the heaviest ties in the smallest sample, confidence interval coverage for all three estimators fell in the range of 94-96%. However, the tail probabilities were asymmetric with the Breslow and Kalbfleisch-Prentice formulas; using the Efron approximation, they were closer to the nominal 2.5%. Although the Breslow approximation is the default in many standard software packages, the Efron method for handling ties is to be preferred, particularly when the sample size is small either from the outset or due to heavy censoring.

The medical origins of homelessness

In 1989 through 1990, we conducted a cross-sectional survey of 1437 homeless adults in northern California (98% response rate). Prevalences of alcohol abuse, illegal drug use, and psychiatric hospitalization when adults first became homeless were 15% to 33% lower than prevalences following homelessness. The largest differences between the homeless and a comparison group of 3122 nonhomeless adults were for psychiatric hospitalization (odds ratios [ORs] of 4.6 for men and 5.9 for women) and alcohol abuse (ORs of 2.3 for men and 4.0 for women). However, when prehomeless prevalences of addictive and psychiatric disorders were compared with prevalences among the nonhomeless, absolute differences were no greater than 12%.

Trends in cardiovascular disease risk factors by educational level: The Stanford five-city project☆

BACKGROUND Trends in blood pressure, smoking, and cholesterol were examined from 1979-1980 through 1985-1986 in four cities in California by level of education (< high school, high school graduate, some college, college or postgraduate). METHODS Four biennial cross-sectional surveys (n = 6,580) were conducted in two treatment and two control cities to evaluate a 6-year community health education intervention, conducted as part of the Stanford Five-City Project. RESULTS Over the 8-year study period, men and women ages 25-74 from each educational group in the treatment cities showed significant declines in smoking prevalence and levels of blood pressure and cholesterol (with the exception of cholesterol in women). In general, declines in the least educated group (< high school) were stronger than declines in the most educated group (college or postgraduate). Similar declines occurred in each educational group in control cities. CONCLUSIONS These results illustrate that persons from all educational levels can modify their risk for CVD and are of particular importance because of the higher prevalence of CVD risk factors among those with less education. The similarity of time trends in treatment as well as control cities suggests that the broad-based, multisource health education efforts in the United States are succeeding across the educational spectrum.

Effects of life-style on body mass index change.

The objective of this study was to determine the effects of age and life-style factors on body mass index (BMI) in a longitudinal, community-based sample. A total of 568 men and 668 women (20–60 years of age) were randomly chosen from four Northern California communities and followed for up to 7 years. Age, sex, marital status, smoking status, hours of television watched, frequency of consumption of several food items physical activity were used to predict rate of change of body mass index (BMI-slope). BMI increased the most for both sexes through at least age 54. The BMI-slope was higher for women compared with men for smokers who stopped compared with those who never smoked or continued to smoke during the study. The BMI-slopes were lower for individuals who increased activity. Other life-style variables had weak or inconsistent effects on the BMI-slope. We conclude that the BMI-slope increases over age for both sexes and that increased physical activity may reduce the BMI-slope. (Epidemiology 1994;5:599–603)

Comparability of Self-Reported Hispanic Ethnicity and Spanish Surname Coding:

Few empirical analyses have assessed the concordance between self-reported Hispanic ethnicity and ethnicity obtained from Spanish surname coding programs. Using data from 4,918 Hispanic and non-Hispanic individuals, aged 12-74, who participated in cross-sectional surveys conducted in Northern California during 1979-1980 and 1989-1990, The authors e-xamined agreement between self-reported and surname-coded ethnicity. Of self-reportedHispanics, 84. 1% were coded as Spanish surnamed and 77.9% ofthose identified by the surnameprogram were self-reportedHispanics. Misclassification was higher for English-speaking groups than for Spanish-speaking groups, and higher for females than for males. English-speaking married and previously married women showed the highest discordance between self-reported ethnicity and surname coding. Results suggest that Spanish surname programs can be a valuable tool for analyzing data sets with inadequate ethnic identifiers, especially in samples having a high proportion of Spanish-speaking respondents.

RACE, POVERTY, AFFLUENCE, AND BREAST CANCER

Nancy Krieger rightly argues that labeling breast cancer a disease of the affluent is simplistic and may lead to correspondingly oversimplified views on screening and prevention.1 We would like to extend her analysis of racial differences in US patterns of breast cancer incidence and mortality to consider the issue of heterogeneity of socioeconomic status within racial categories and the potential relevance of this issue for breast cancer incidence. According to cancer statistics collected by Surveillance, Epidemiology, and End Results (SEER) in the metropolitan Atlanta area, age-specific breast cancer incidence rates in Black women were higher than the corresponding rates in White women in all age groups younger than 55 years in the period 1992 through 1999.2 At older ages, rates in Black and White women were similar. By 1993, the overall age-adjusted incidence rate of breast cancer in Black women in Atlanta had modestly surpassed that of White women, suggesting that the “catch-up” phenomenon described by Krieger is at least a decade old in metropolitan Atlanta. In contrast, in metropolitan Detroit over the same time period, age-specific breast cancer incidence rates for Black and White women conformed to the pattern commonly noted by epidemiologists: Blacks’ rates were modestly higher than Whites’ rates up to the age of 40 years, while Whites’ rates were considerably higher than Blacks’ rates at older ages. Further, Black women in Detroit had lower incidence rates than Black women in Atlanta at all ages.2 Aggregate-level data indicate that Black women in metropolitan Atlanta are of higher socioeconomic status than Black women in other parts of the United States, including Detroit.3 Black women in Atlanta are more likely to be college educated and living above the poverty level than Black women in Detroit, and the total fertility rate (as estimated by the number of children ever born per 1000 women aged 35–44 years) of Black women in Atlanta is lower than that of Black women in Detroit. In some counties in the Atlanta metro area, Black women have a lower total fertility rate than White women, while in Detroit-area counties, Black women have a consistently higher total fertility rate than White women.4,5 This evidence suggests a reality that Krieger has pointed out: broad categorizations of “race” and “socioeconomic status” (SES) hide important heterogeneity within groups that is critical to a deeper understanding of the etiology of breast cancer.6 In many respects, the international data cited by Krieger1 and the data presented here suggest a similar explanation: as reproductive behaviors in different racial and ethnic groups converge to a pattern of later onset of childbearing and fewer births, breast cancer incidence rates similarly converge to the higher rates that have been well described in higher-SES White populations in industrial societies. However, this explanation does not address the higher breast cancer incidence in young Black women compared with young White women that has been observed since 1973, a gap that may be narrowing.2 The labels of “affluence” or “poverty,” when removed from the context of reproductive patterns, likely have little relevance for describing and predicting breast cancer incidence. However, given that there are few known or hypothesized risk factors that serve as accurate screeners of an individual woman’s risk of breast cancer, and given the current lack of broadly acceptable and effective primary prevention strategies against the disease, ensuring access to breast cancer screening and treatment services to all women, regardless of race or SES or reproductive profile, remains an important public health goal.

Physical Activity and Cancer Prevention

The diseases linked to sedentariness are major causes of morbidity and mortality in industrialized societies; thus the impact of sedentariness on public health is large. Significant health benefits are achievable with moderate amounts of physical activity. To substantially reduce the public health burden of disease due to sedentariness, the population distribution of physical activity must be shifted upwards. A “high-risk” strategy that focuses only on the most inactive tail of the distribution will not have a large public health impact. Physical activity has proved difficult to modify on a large scale by using individually-focused approaches to behavior change. Environmental and policy approaches to increasing physical activity across the population include efforts in increase physical activity within schools and workplaces, offering incentives for physically-active commuting, providing safe paths/routes for bicyclists and walkers and giving priority to such persons over auto drivers, and opening community venues such as malls, school, etc. for physical activity programs.