A comment on: statistical evaluation of biomarkers as surrogate endpoints: a literature review by C. J. Weir and R. J. Walley, Statistics in Medicine 2006; 25:183-203.
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Biomedical subjects
Publications and source records attributed to Niels Keiding.
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Examples are given of problems in event history analysis, where several time origins (generating calendar time, age, disease duration, time on study, etc.) are considered simultaneously. The focus is on complex sampling patterns generated around a cross-section. A basic tool is the Lexis diagram.
The purpose was to describe four-year change in functional ability among older persons and the relationship to sex, age, and other background factors. The baseline study, performed in 1986, is based on a random sample of older persons (n=1261). Follow-up data were collected four-years later (n=912). The analyses of change in functional ability were based on the assumption that the categories reflected an underlying latent continuous dimension. The change in functional ability, DeltaFA, was calculated by a logistic model for paired observations and applied in parallel analyses with and without inclusion of the dead to deal with the attrition problem. Fifty percent had no change in functional ability, 37% had declined and 13% improved. Models including the dead showed more functional decline with increasing age but this was not the case when the dead were excluded. Functional change was not related to sex, functional ability at baseline, relative wealth, social network, self-rated health, and life-satisfaction. Inclusion of the dead in statistical models for the study of change in functional ability reduced the attrition problem. A logistic model for paired observations of functional ability at two points in time reduced the problem related to the floor/ceiling problem.
AIMS: The authors examined causes of death contributing to the relatively high mortality of Danish women born 1915-45, and evaluated the impact of smoking related causes of death. METHODS: Age-period-cohort analysis of mortality of Danish women aged 40-89 in 1960-98. Estimate of the negative curvature in parabola patterns for 50 causes of death. RESULTS: A total of 34 causes of death contributed to the relatively high mortality for women born 1915-45. The main contribution came from smoking-related causes of death. CONCLUSION: The results indicate a high smoking prevalence to be the main explanation behind the relatively low life expectancy of Danish women born 1915-45.
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Approaches for monitoring time trends in couples' fecundity and for studying its sensitivity to environmental factors are needed. Two approaches rely on the inclusion of a cross-sectional sample of couples currently "at risk" of pregnancy either with follow up (prevalent cohort) or without follow up (current-duration design). To illustrate the feasibility of the current-duration design, we contacted a random sample of 1204 French women age 18 to 44 years in 2004 and recruited those who were currently having unprotected sexual intercourse. The current duration since the beginning of unprotected intercourse was defined for 69 women (5.7%). An additional 15 women (1.2%) were planning to start trying to become pregnant within the next 6 months. Parametric methods allowed, based on current duration of unprotected intercourse, estimation of fecundity as if the couples had been followed prospectively. The estimated proportion of couples not pregnant after 12 months of unprotected intercourse was 34% (95% confidence interval [CI] = 15-54%). The accelerated-failure time model allows study of the influence of environmental factors on fecundity. As an illustration, tobacco smoking by the woman was associated with a doubling in the median duration of unprotected intercourse before pregnancy (adjusted time ratio = 2.4; 95% CI = 1.1-5.2). We quantified the influence of time trends in the prevalence of smoking on this estimate. We suggest ways to quantify or avoid other potential bias. In conclusion, it is possible to recruit a sample of couples currently having unprotected intercourse. The current-duration design appears feasible with approximately 5 times as many women eligible for study as for an incident cohort design.
Time-to-pregnancy(TTP), the duration that a couple waits from initiating attempts to conceive until conception occurs, is regarded as one of the direct measures of natural fecundity. Statistical tools for designing and analysing TTP studies belong to the general area of survival analysis, but several special features have been developed: it is customary to work in discrete time, and random heterogeneity between couples has always played a prominent role. This review works on this background with focus on how to perform valid analyses, under various prospective, retrospective and cross-sectional sampling frames. We illustrate using examples from our own experience.
Biologic fertility can be measured using time to pregnancy (TTP). Retrospective designs, although lacking detailed timed information about behavior and exposure, are useful since they have a well-defined target population, often have good response rates, and are simpler and less expensive to conduct than prospective studies. This paper reviews retrospective TTP studies from a methodological viewpoint and shows how methodological problems can be avoided or minimized by appropriate study design, conduct, and analysis. Sensitivity analyses using data from four European retrospective TTP studies are presented to explore the issues. Although the identified biases tend to have small impacts, the effects are not systematic across studies, and sensitivity analyses are recommended routinely. Planning bias can be checked by comparing propensity to report contraceptive failures in different exposure groups. Medical intervention bias can be avoided by censoring and inclusion of unsuccessful pregnancy attempts. Truncation bias can be a serious problem if unrecognized, but it is avoidable with appropriate study design and/or analysis. Behavior change bias can be minimized by assessing the covariates at the beginning of unprotected intercourse. More complete inference is possible if the study design covers the whole population, not just those who achieve a pregnancy.
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It is often of interest to assess how much of the effect of an exposure on a response is mediated through an intermediate variable. However, systematic approaches are lacking, other than assessment of a surrogate marker for the endpoint of a clinical trial. We review a measure of "proportion explained" in the context of observational epidemiologic studies. The measure has been much debated; we show how several of the drawbacks are alleviated when exposures, mediators, and responses are continuous and are embedded in a structural equation framework. These conditions also allow for consideration of several intermediate variables. Binary or categorical variables can be included directly through threshold models. We call this measure the mediation proportion, that is, the part of an exposure effect on outcome explained by a third, intermediate variable. Two examples illustrate the approach. The first example is a randomized clinical trial of the effects of interferon-alpha on visual acuity in patients with age-related macular degeneration. In this example, the exposure, mediator and response are all binary. The second example is a common problem in social epidemiology-to find the proportion of a social class effect on a health outcome that is mediated by psychologic variables. Both the mediator and the response are composed of several ordered categorical variables, with confounders present. Finally, we extend the example to more than one mediator.
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Epidemiologic studies have shown an increased risk of breast cancer following hormone replacement therapy (HRT). The aim of this study was to investigate whether different treatment regimens or the androgenecity of progestins influence the risk of breast cancer differently. The Danish Nurse Cohort was established in 1993, where all female nurses aged 45 years and above received a mailed questionnaire (n = 23,178). A total of 19,898 women returned the questionnaire (86%). The questionnaire included information on HRT types and regimens, reproductive history and lifestyle-related factors. Breast cancer cases were ascertained using nationwide registries. The follow-up ended on 31 December 1999. Women with former cancer diagnoses, women with missing information on HRT, surgical menopause, premenopausal, as well as hysterectomized women were excluded, leaving 10,874 for analyses. Statistical analyses were performed using Cox proportional hazards model. A total of 244 women developed breast cancer during follow-up. After adjustment for confounding factors, an increased risk of breast cancer was found for the current use of estrogen only (RR = 1.96; 95% CI = 1.16-3.35), for the combined use of estrogen and progestin (RR = 2.70; 95% CI = 1.96-3.73) and for current users of tibolone (RR = 4.27; 95% CI = 1.74-10.51) compared to the never use of HRT. In current users of combined HRT with testosterone-like progestins, the continuous combined regimens were associated with a statistically significant higher risk of breast cancer than the cyclical combined regimens (RR = 4.16, 95% CI = 2.56-6.75, and RR = 1.94, 95% CI = 1.26-3.00, respectively). An increased risk of breast cancer was noted with longer durations of use for the continuous combined regimens (p for trend = 0.048). The European traditional HRT regimens were associated with an increased risk of breast cancer. The highest risk was found for the use of continuous combined estrogen and progestin.
Between 1996 and 1999, the authors invited all young men from five European countries who were undergoing compulsory medical examination for possible military service to participate in a study on male reproductive health. The participation rate was 19% in two cities in Denmark (n = 889), 17% in Oslo, Norway (n = 221), 13% in Turku, Finland (n = 313), 14% in Kaunas, Lithuania (n = 157), and 19% in Tartu, Estonia (n = 190). Each man provided a semen sample, was examined by a physician, and, in collaboration with his mother, completed a questionnaire about general and reproductive health, current smoking habits, and exposure to smoking in utero. After adjustment for confounding factors, men exposed to smoking in utero had a reduction in sperm concentration of 20.1% (95% confidence interval (CI): 6.8, 33.5) and a reduction in total sperm count of 24.5% (95% CI: 9.5, 39.5) in comparison with unexposed men. Percentages of motile and morphologically normal sperm cells were 1.85 (95% CI: 0.46, 3.23) and 0.64 (95% CI: -0.02, 1.30) percentage points lower, respectively, among men exposed in utero, and exposed men had a 1.15-ml (95% CI: 0.66, 1.64) smaller testis size. The associations were present when data from the study centers were analyzed separately (though not in Lithuania, where only 1% of mothers smoked during pregnancy), although the strength of the association varied. Maternal smoking may have long-term implications for the reproductive health of the offspring. This is another good reason to advise pregnant women to avoid smoking.
When studying a regression model measures of explained variation are used to assess the degree to which the covariates determine the outcome of interest. Measures of predictive accuracy are used to assess the accuracy of the predictions based on the covariates and the regression model. We give a detailed and general introduction to the two measures and the estimation procedures. The framework we set up allows for a study of the effect of misspecification on the quantities estimated. We also introduce a generalization to survival analysis.
Mercury concentrations were measured in paired hair and blood samples from a cohort of about 1000 children examined at birth and at 7 and 14 years of age. The ratio between concentrations in maternal hair (in microg/g) and in cord blood (microg/L) was approximately 200, but samples from the children at age 14 years showed a ratio of about 250. These findings are in accordance with previous data from smaller studies. However, an even higher ratio of about 360 was seen at 7 years of age, suggesting that hair strands at this age retain more mercury. The 95th percentile of the hair-to-blood ratio was between five-fold and nine-fold greater than the 5th percentile. The results were examined in structural equation models to estimate the total imprecision of the individual biomarker results and the possibility that the ratio may not be constant. The hair-to-blood ratio was found to increase at lower mercury concentrations, a tendency that could not be explained by potential confounders, such as alcohol intake or number of amalgam fillings. The total imprecision (coefficient of variation) for the blood determinations averaged about 30%, thereby substantially exceeding normal laboratory imprecision. Yet hair-mercury results had an even greater imprecision, which suggested that preanalytical factors, such as variable sample characteristics, impacted the results. These findings are in accordance with other evidence that the cord blood concentration is a better predictor of neurobehavioral toxicity than is the maternal hair concentration. Although practical for field studies and monitoring purposes, hair-mercury concentration results, therefore, need to be calibrated and interpreted in regard to each specific study setting.