Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms.

Directed acyclic graphs (DAGs) play a large role in the modern approach to causal inference. DAGs describe the relationship between measurements taken at various discrete times including the effect of interventions. The causal mechanisms, on the other hand, would naturally be assumed to be a continuous process operating over time in a cause-effect fashion. How does such immediate causation, that is causation occurring over very short time intervals, relate to DAGs constructed from discrete observations? We introduce a time-continuous model and simulate discrete observations in order to judge the relationship between the DAG and the immediate causal model. We find that there is no clear relationship; indeed the Bayesian network described by the DAG may not relate to the causal model. Typically, discrete observations of a process will obscure the conditional dependencies that are represented in the underlying mechanistic model of the process. It is therefore doubtful whether DAGs are always suited to describe causal relationships unless time is explicitly considered in the model. We relate the issues to mechanistic modeling by using the concept of local (in)dependence. An example using data from the Swiss HIV Cohort Study is presented.

Estimating influenza-related excess mortality and reproduction numbers for seasonal influenza in Norway, 1975-2004.

Influenza can be a serious, sometimes deadly, disease, especially for people in high-risk groups such as the elderly and patients with underlying, severe disease. In this paper we estimated the influenza-related excess mortality in Norway for 1975-2004, comparing it with dominant virus types and estimates of the reproduction number. Analysis was done using Poisson regression, explaining the weekly all-cause mortality by rates of reported influenza-like illness, together with markers for seasonal and year-to-year variation. The estimated excess mortality was the difference between the observed and predicted mortality, removing the influenza contribution from the prediction. We estimated the overall influenza-related excess mortality as 910 deaths per season, or 2.08% of the overall deaths. Age-grouped analyses indicated that the major part of the excess mortality occurred in the > or =65 years age group, but that there was also a significant contribution to mortality in the 0-4 years age group. Estimates of the reproduction number R, ranged from about 1 to 1.69.

Definition and estimation of an actual reproduction number describing past infectious disease transmission: application to HIV epidemics among homosexual men in Denmark, Norway and Sweden.

Prevalence and incidence measures are the common way to describe epidemics. The reproduction number supplies information on the potential for growth or decline of an epidemic. We define an actual reproduction number for infectious disease transmission that has taken place. An estimator is suggested, based on the number of new infections observed in a given time-interval, the number of those infected at the start of the interval, and the length of the infectious period. That estimator is applied to HIV among men having sex with other men over the period, 1977-1995, in Scandinavia. The actual reproduction number was estimated with acceptable certainty from the period, 1981-1982, yielding a value of 15 secondary cases. A value of less than one secondary case was assessed for the period, 1988-1995, in Denmark and Sweden. The actual reproduction number gives us some additional understanding of the dynamics of epidemics, compared with prevalence and incidence curves.

Covariate adjustment of event histories estimated from Markov chains: the additive approach.

Markov chain models are frequently used for studying event histories that include transitions between several states. An empirical transition matrix for nonhomogeneous Markov chains has previously been developed, including a detailed statistical theory based on counting processes and martingales. In this article, we show how to estimate transition probabilities dependent on covariates. This technique may, e.g., be used for making estimates of individual prognosis in epidemiological or clinical studies. The covariates are included through nonparametric additive models on the transition intensities of the Markov chain. The additive model allows for estimation of covariate-dependent transition intensities, and again a detailed theory exists based on counting processes. The martingale setting now allows for a very natural combination of the empirical transition matrix and the additive model, resulting in estimates that can be expressed as stochastic integrals, and hence their properties are easily evaluated. Two medical examples will be given. In the first example, we study how the lung cancer mortality of uranium miners depends on smoking and radon exposure. In the second example, we study how the probability of being in response depends on patient group and prophylactic treatment for leukemia patients who have had a bone marrow transplantation. A program in R and S-PLUS that can carry out the analyses described here has been developed and is freely available on the Internet.

Back-calculation based on HIV and AIDS registers in Denmark, Norway and Sweden 1977-95 among homosexual men: estimation of absolute rates, incidence rates and prevalence of HIV.

BACKGROUND: The Scandinavian countries, Denmark, Norway and Sweden, have established both HIV and AIDS registers to monitor the HIV epidemic. Information in such registers can be used to estimate the number of new HIV infections over time, incidence rates and prevalence. Information from the HIV registers made it possible to study what kind of effects such information had in the estimation process, compared with using information about new AIDS cases only. METHODS: A Markov model back-calculation approach was used. One model incorporated data on cases of both HIV and AIDS. Another model incorporated data on cases of AIDS only. Death or emigration prior to the onset of AIDS and effects of treatment were included in both models. RESULTS: Estimates of absolute rates of HIV for men who have sex with men (MSM) showed a distinct development in each country. Significant differences in incidence rates and prevalence of HIV among MSM were found between Scandinavian countries when information on diagnosed HIV was incorporated. Precision was improved when using both HIV and AIDS diagnosed cases compared with using AIDS cases only. The epidemic in Denmark was more extensive than in the two other countries for the whole study period. DISCUSSION: The results were fairly robust against reasonable variation in the model parameters. The more extensive epidemic in Denmark may have been caused by the homosexual culture denying that HIV was a disease more relevant to them than to others, until the HIV test was publicly available in 1985.

Medical statistics--no time for complacency.

Statistical science plays an important role in medical research. Whether this will continue to be so, depends to a large extent on the future of fields like clinical trials and epidemiology. Will these continue to play the important role they do today in the development of medicine? Traditional, frequentist, methodology still dominates in medical statistics. Statisticians should have an open and pragmatic attitude towards new approaches. Survival analysis is a field of biostatistics that has been through considerable recent development. The need for further methodological development in this field is stressed. There is also need for connecting statistical work more intimately to biological knowledge than is the case today.

[Resuscitation of newborn infants with room air or oxygen]. / Gjenoppliving av nyfødte med romluft eller oksygen.

In this article we present results from the Resair 2 study in which we tested whether room air is more efficient than 100% oxygen in newborn resuscitation. Eleven participating centres in Egypt, Estonia, India, Norway, Philippines, and Spain recruited 609 infants who needed resuscitation at birth; of these, 288 were resuscitated with room air and 321 with 100% oxygen. There were no differences between the two groups with regard to outcome. One minute Apgar scores were significantly lower in the oxygen group than in the room air group. Median time to first breath was significantly delayed with 24 seconds in the oxygen group compared with the room air group. It seems that 100% oxygen depresses ventilation in newborn infants. Room air is as safe and efficient as 100% oxygen at least in most cases of newborn resuscitation. Further studies confirming these results are needed before new resuscitation routines are implemented.

Analyzing incidence of testis cancer by means of a frailty model.

There are two striking epidemiological features of testicular cancer. First, the incidence has increased strongly over the past few decades. Secondly, the incidence is greatest among younger men, and then declines from a certain age. We have constructed a statistical model to fit these observations. The idea of the model is that a subgroup of men is particularly susceptible to testicular cancer. In statistical terminology this is called a frailty model, since it focuses on varying frailty of the individuals. The frailty, or susceptibility, is considered as being established by birth, and due to a mixture of genetic and environmental effects. The strong increase in incidence over calendar time points to strong environmental effects, which are thought to operate in fetal life, causing damage to the fetus. Based on data from the Norwegian Cancer Registry we fit a frailty model to incidence data collected during 1953-93. The model gives a good fit and we discuss the interpretations of our findings.

Spatial smoothing of cancer survival: a Bayesian approach.

A major aim of this paper is to propose and evaluate a method for describing the geographical variation in cancer survival. A fully hierarchical Bayesian approach (FB) which incorporates spatial autocorrelation of the hazard ratios is presented. The method was tried out on data sets of breast cancer and malignant melanoma patients from a population-based cancer registry. The performance of FB was compared with an ordinary Cox proportional hazard method. For both cancers both methods localized some areas of increased and some areas of decreased cancer-specific survival. The estimates provided by the Cox and the FB approach resembled each other, but the FB approach gave more geographical details. In particular, the boundaries of the clusters of high or low survival provided by the FB are more realistic.

New therapy explains the fall in AIDS incidence with a substantial rise in number of persons on treatment expected.

BACKGROUND: A marked decline in the number of reported AIDS cases has been observed in the United Kingdom, as in many industrialized countries, in 1996 and 1997. In England and Wales, a large reduction in AIDS cases has been recorded among homosexual and bisexual men. OBJECTIVES: To investigate, using data from the homosexuals and bisexuals in England and Wales as an example, possible explanations for the above decline such as the effects of new anti-retroviral therapies, or a decrease in the incidence of HIV in recent years. METHODS: A multistage model of HIV infection, HIV diagnosis, treatment and of AIDS diagnosis has been used to represent the pattern of HIV and AIDS incidence in homosexual and bisexual men in England and Wales up to the end of 1995. Scenarios for the post-1995 period were examined under different assumptions about changes in HIV incidence in recent years and treatment uptake and efficacy. RESULTS: The fall in the incidence of AIDS is unlikely to be the result of a reduction in HIV transmission during the 1990s. The most plausible explanation for this fall is the effect of new, more effective, anti-retroviral therapies. As a consequence, the number of individuals on treatment is likely to increase by 50 to 100% compared with the pre-1996 levels by the year 2001. Also, if the effect of the new therapies has a limited duration, or the use of such therapies is not well tolerated, the incidence of AIDS will rise again in the near future. CONCLUSIONS: These findings indicate that a substantial workload increase is under way for the healthcare system, and reiterate the need for measures to reduce HIV transmission as a means of bringing about a sustainable change in the incidence of AIDS.

Adjusting and comparing survival curves by means of an additive risk model.

Survival curves may be adjusted for covariates using Aalen's additive risk model. Survival curves may be compared by taking the ratio of two adjusted survival curves; the ratio is denoted the generalized relative survival rate. Adjusting both survival curves for all but one of a common set of covariates gives the partial relative survival rate, which measures the covariate-specific contribution to the generalized relative survival rate. The generalized and partial relative survival rates have interpretations similar to the traditional relative survival rates frequently used in cancer epidemiology. In fact, the traditional relative survival rate can be generalized to a regression context using the additive risk model. This population-adjusted relative survival rate is an alternative and useful method for removing confounding effects of age, cohorts, and sex. The authors use a data set of malignant melanoma patients diagnosed from 1965 to 1974 in Norway. The 25-year survival of 1967 individuals is studied.

A Markov model for HIV disease progression including the effect of HIV diagnosis and treatment: application to AIDS prediction in England and Wales.

Back-calculation is a widely used method to estimate HIV incidence rates, and is commonly based on times of AIDS diagnosis. Following up earlier work, we extend this method to also incorporate knowledge of times of HIV diagnosis (first positive test). This is achieved through the use of a Markov model which describes the progress of an HIV infected person through various stages, and which allows causal connections between events to be explicitly modelled. Estimation is based on maximum likelihood, the likelihood being calculated within a discretized version of the Markov model. The effect of sampling uncertainty and model uncertainty (sensitivity) is evaluated simultaneously by means of a combined bootstrap and simulation procedure. At each replication we resample both the data and the model (from a set of possible models described by randomizing one or more parameters). For instance, uncertain knowledge about the incubation distribution affects the estimates of some parameters, but not others. The Markov approach is applied to the prediction of AIDS incidence for homosexuals in England and Wales up to the year 2000.

Analysis of dependent survival data applied to lifetimes of amalgam fillings.

When studying lifetimes of amalgam fillings, one is faced with the fact that each patient may contribute multiple survival data. This creates a dependence problem, and some methods for solving it are presented here. Analysis for individual patients with simple approaches for combining data is discussed first. Then a parametric frailty model is applied to analyse variation within and between patients. The results are presented in the form of an empirical Bayes estimate for each patient.

Bronchial responsiveness decreases in relocated aluminum potroom workers compared with workers who continue their potroom exposure.

We have compared the bronchial responsiveness (BR) of 12 aluminum potroom workers (index group) who were relocated due to work-related asthmatic symptoms (WASTH) and 26 subjects (reference group) with WASTH who continued to work in potrooms. The subjects were examined at regular intervals during a 2-year follow-up period. BR was expressed as the log-transformed dose-response slope [Ln(DRS 5)]. The monthly change in BR (delta BR) in the index group was -4.87 x 10(-2) compared with -1.58 x 10(-2) in the reference group. After adjustment for potential confounders, the difference between the index group and the reference group was -2.39 x 10(-2) (95% CI: -4.07 x 10(-2) to -0.71 x 10(-2)), i.e. 49% of the decrease in BR in the index group could be explained by the removal from exposure. No improvement in lung function was found in the index group compared with the reference group. The results indicate that the removal of potroom workers from exposure causes a decrease in BR.

Effects of frailty in survival analysis.

Unobserved individual heterogeneity, also called frailty, is a major concern in the application of survival analysis. Hazard rates do not give direct information on the change over time in the individual risk, but are strongly influenced by selection effects operating in the population. The individuals surviving up to a certain time will on average be less frail than the original population. Models are reviewed that account for this phenomenon, and some medical examples are discussed. It is emphasized that the frailty phenomenon may be modelled in many different ways, and a stochastic process approach is discussed as an alternative to the common proportional frailty model.

Further results on the non-parametric linear regression model in survival analysis.

This paper gives further developments of a non-parametric linear regression model in survival analysis. Three subjects are studied. First, martingale residuals, originally developed for the Cox model, are introduced for our linear model. Their theory is developed and they are shown to be useful for judging goodness of fit. The second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation. In particular, this is applied to judging whether the effect of a covariate disappears over time, a problem for which no formal test exists. The third subject is density type, or kernel, estimation of the regression functions themselves. This might give more direct information than the cumulative plots. The approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx, and by survival times of grafts in renal patients.