An introduction to event history analysis via multi-state models is given. Examples include the two-state model for survival analysis, the competing risks and illness-death models, and models for bone marrow transplantation. Statistical model specification via transition intensities and likelihood inference is introduced. Consequences of observational patterns are discussed, and a real example concerning mortality and bleeding episodes in a liver cirrhosis trial is discussed.

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Multi-state models for event history analysis

The methods of calculation of survival corrected for independent cause of death are discussed, and a maximum likelihood method is proposed and illustrated by survival of colon cancer patients in Geneva. The methods which are at present favoured for doing such calculations are subject to various biases when estimating net survival if the populations are heterogeneous for life expectancy. The proposed maximum likelihood approach would eliminate these biases by enabling relevant adjustment for covariates which influence survival. The routine use of such methods would permit better comparison of survival within and between populations.

Relative survival and the estimation of net survival: elements for further discussion.

Background Few studies have examined the effects of paternal and maternal history of myocardial infarction (MI), including age at MI, on cardiovascular disease (CVD) risk, particularly among women. Methods and Results We prospectively studied 22 071 men from the Physicians’ Health Study and 39 876 women from the Women’s Health Study with data on parental history and age at MI. Among men, 2654 CVD cases developed over 13.0 years; among women, 563 CVD cases occurred over 6.2 years. Compared with men with no parental history, only maternal, only paternal, and both maternal and paternal history of MI conferred relative risks (RRs) of CVD of 1.71, 1.40, and 1.85; among women, the respective RRs were 1.46, 1.15, and 2.05. For men, maternal age at MI of <50, 50 to 59, 60 to 69, 70 to 79, and ≥80 years had RRs of 1.00, 1.88, 1.88, 1.67, and 1.17; for women, the RRs for maternal age at MI of <50, 50 to 59, and ≥60 years were 2.57, 1.33, and 1.52. Paternal age at MI of <50, 50 to 59, 60 to 69, 70 to 79, and ≥80 yea...

Maternal and Paternal History of Myocardial Infarction and Risk of Cardiovascular Disease in Men and Women

Recent work has extended the methods for the analysis of nested case-control studies to accommodate a broad variety of risk set sampling designs. These results have implications for the design of sam- pled epidemiologic cohort studies. We describe a model which is a natural extension of the Cox proportional hazards model and may be used to es- timate parameters from sampled risk set data. We illustrate how these techniques may be used to solve three diverse design and analysis prob- lems from epidemiologic research. craft manufacturing firm in San Diego County, Cal- ifornia, by the families of a group of employees who had died of esophagus cancer. Their claim was that occupational exposures to carcinogenic agents were to blame for the disease. In order to objectively as- sess whether there truly was an unusually high rate of cancer among employees and whether any partic- ular substances used at the firm were related to the risk of esophagus cancer, a cohort mortality study and a case-control study were undertaken. Inves- tigators compiled basic information such as birth dates, sex, race and dates of employment for the cohort of 14,067 employees from company records. Other data sources were required to determine vital status and, if dead, the cause of death. For the mortality study, the number of deaths in the cohort from various causes were then com- pared to those expected based on United States cause-specific mortality rates. There were 14 cases of esophagus cancer observed compared to 12.27 ex- pected (standardized mortality ratio (SMR) = O/E = 1.14, 95% confidence interval 0.62-1.92; Garabrant, Held, Langholz and Bernstein, 1988). Although this excess is certainly not significantly different from 1, cancer mortality was generally lower in the cohort

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Risk set sampling in epidemiologic cohort studies

Methods are provided for regression parameter and cumulative baseline hazard estimation in the Cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law. The key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes, leading to estimation methods parallel to those for full cohort data. These techniques are illustrated for a number of sampling designs, including three novel designs : counter-matching with additional randomly sampled controls ; quota sampling of controls ; and nested case-control sampling with number of controls dependent on the failure's exposure status. General asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs.

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Methods for the Analysis of Sampled Cohort Data in the Cox Proportional Hazards Model

A Cox-type regression model for the ratio between the mortality in a cohort and that in a reference population is introduced. By means of the model it is possible to include in the survival analysis both individual (possibly time-dependent) characteristics for the study cohort and changing trends in the mortality in the reference population. This is particularly relevant in long-term follow-up studies where there may be considerable changes in the mortality in the reference population. Estimation procedures in the model are discussed and large-sample properties of the estimators are outlined. The model is applied to the analysis of two sets of data concerning the survival among insulin-dependent diabetics in Denmark.

A cox regression model for the relative mortality and its application to diabetes mellitus survival data

This paper presents a study of the mortality of insulin-dependent diabetics diagnosed before age 31. The analysis includes the effect of various covariates on the mortality and on the risk of developing diabetic nephropathy, a serious renal complication associated with diabetes. The results show that it is the risk of developing nephropathy combined with very high mortality rates of patients with nephropathy which are the main reasons for the excess mortality usually experienced among insulin-dependent diabetics. The results are used to provide examples of the cost of individual life and group life insurance for diabetics who, at the time of issue of insurance, show no sign of diabetic nephropathy.

Life insurance for insulin-dependent diabetics

STUDY OBJECTIVES: To identify possible modifiable mediators of familial predisposition to myocardial infarction (MI) by assessing the risk factor profile in individuals without MI in relation to parental occurrence of MI. DESIGN AND METHODS: Cross sectional survey of the general population. The odds of an adverse cardiovascular risk factor profile in subjects reporting parental occurrence of MI versus subjects not reporting parental occurrence were estimated by logistic regression models. SETTING: The Copenhagen Centre for Prospective Population Studies, where subjects investigated in three Danish prospective population studies are integrated. PARTICIPANTS: Subjects were 9306 females and 11,091 males aged 20-75 years with no history of MI. A total of 1370 subjects reported maternal MI and 2583 reported paternal MI. MAIN RESULTS: Increased systolic and diastolic blood pressure, increased cholesterol level, low ratio between high density lipoprotein (HDL) and total cholesterol (TC), and heavy smoking, were more frequent in subjects with parental occurrence of MI than in controls irrespective of sex and age of the subjects. Maternal MI was more predictive for increased cholesterol and decreased HDL/ TC ratio than paternal MI, and the risk of an increased cholesterol level was higher in subjects aged 20-39 years than in older subjects. No differences in body mass index, triglycerides, and physical inactivity were observed. CONCLUSIONS: Subjects free of previous MI who reported a parental occurrence of MI had an adverse cardiovascular risk factor profile regarding systolic and diastolic blood pressure, total cholesterol, the ratio between HDL and total cholesterol, and smoking. Thus, these modifiable risk factors may be mediators of the familial predisposition to MI.

https://jech.bmj.com/content/jech/51/3/266.full.pdf

Knut Borch-Johnsen

Papers

A cox regression model for the relative mortality and its application to diabetes mellitus survival data

Life insurance for insulin-dependent diabetics

Cardiovascular risk factor profile in subjects with familial predisposition to myocardial infarction in Denmark