Standardization and Control for Confounding in Observational Studies: A Historical Perspective

Control for confounders in observational studies was generally handled through stratification and standardization until the 1960s. Standardization typically reweights the stratum-specific rates so that exposure categories become comparable. With the development first of loglinear models, soon also of nonlinear regression techniques (logistic regression, failure time regression) that the emerging computers could handle, regression modelling became the preferred approach, just as was already the case with multiple regression analysis for continuous outcomes. Since the mid 1990s it has become increasingly obvious that weighting methods are still often useful, sometimes even necessary. On this background we aim at describing the emergence of the modelling approach and the refinement of the weighting approach for confounder control.Comment: Published in at http://dx.doi.org/10.1214/13-STS453 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Product-limit estimators of the gap time distribution of a renewal process under different sampling patterns

Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes several such situations where simple product limit estimators, though inefficient, may still be useful

Biological and sociological interpretations of age-adjustment in studies of higher order birth rates

Several studies of the effect of education on second or third birth rates (e.g. Hoem et al. (2001)) have used the concept of relative age at previous birth (B.Hoem (1996)). B.Hoem's idea was to focus on the social meaning of age at previous birth. We broaden the discussion by considering other interpretations of the explanatory power of the age at previous birth, particularly via known trends in biological fecundity. A mathematical analysis of the approach reveals side effects that have not been taken sufficiently into account. Our recommendation is not to use the relative age approach without supplementing it with the more traditional approach which includes the actual age at previous birth.education, fertility, higher order birth rates, relative age

Graphical Models for Inference Under Outcome-Dependent Sampling

We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the conditional independencies among the variables. By including a node for the sampling indicator, assumptions about sampling processes can be made explicit. We demonstrate how to read off such graphs whether consistent estimation of the association between exposure and outcome is possible. Moreover, we give sufficient graphical conditions for testing and estimating the causal effect of exposure on outcome. The practical use is illustrated with a number of examples.Comment: Published in at http://dx.doi.org/10.1214/10-STS340 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modelling regional variation of first-time births in Denmark 1980-1994 by an age-period-cohort model

Despite the small size of Denmark, there have traditionally been rather consistent regional differences in fertility rates. We apply the statistical age-period-cohort model to include the effect of these three time-related factors thereby concisely illuminating the regional differences of first-time births in Denmark. From the Fertility of Women and Couples Dataset we obtain data on number of births by nulliparous women by year (1980-1994), age (15-45) and county of residence. We show that the APC-model describes the fertility rates of nulliparous women satisfactorily. To catch the regional variation an interaction parameter between age and county is necessary, which provides a surprisingly good description suggesting that the county-specific age-distributions of first-time fertility rates differ. Our results are in general agreement with the 'moral geography' concepts of Tonboe (2001).age-period-cohort models, Denmark, fertility, fertility rate, nulliparous women, regional variation

Education and second birth rates in Denmark 1981-1994

A high educational attainment is shown to have a positive effect on second birth rates for Danish one-child mothers during the period 1981-94. We examine whether a time-squeeze is a possible explanation: due to the longer enrolment in the educational system, highly educated women have less time at their disposal in order to get the desired number of children. Also, we examine to what extent the partner's education can explain some of the positive effect. We find no evidence that the positive effect of education is due to either a time-squeeze nor to a partner effect.birth rate, Denmark, education, fertility, partner effect, time-squeeze

Rates of induced abortion in Denmark according to age, previous births and previous abortions

Background: Whereas the effects of various socio-demographic determinants on a woman’s risk of having an abortion are relatively well-documented, less attention has been given to the effect of previous abortions and births. Objective: To study the effect of previous abortions and births on Danish women’s risk of an abortion, in addition to a number of demographic and personal characteristics. Data and methods: From the Fertility of Women and Couples Dataset we obtained data on the number of live births and induced abortions by year (1981-2001), age (16-39), county of residence and marital status. Logistic regression analysis was used to estimate the influence of the explanatory variables on the probability of having an abortion in a relevant year. Main findings and conclusion: A woman’s risk of having an abortion increases with the number of previous births and previous abortions. Some interactions were was found in the way a woman’s risk of abortion varies with calendar year, age and parity. The risk of an abortion for women with no children decreases while the risk of an abortion for women with children increases over time. Furthermore, the risk of an abortion decreases with age, but relatively more so for women with children compared to childless women. Trends for teenagers are discussed in a separate section.abortion parity, abortion rates, family situation, fertility parity, urbanization

Cause-specific measures of life years lost

Background: A new measure of the number of life years lost due to specific causes of death is introduced. Methods: This measure is based on the cumulative incidence of death, it does not require "independence" of causes, and it satisfies simple balance equations: "total number of life years lost = sum of cause-specific life years lost", and "total number of life years lost before age x + temporary life expectancy between birth and age x = x". Results: The measure is contrasted to alternatives suggested in the demographic literature and allmethods are illustrated using Danish and Russian multiple decrement life-tables