Odd O. Aalen

Survival and Event History Analysis

An introduction to survival and event history analysis.- Stochastic processes in event history analysis.- Nonparametric analysis of survival and event history data.- Regression models.- Parametric counting process models.- Unobserved heterogeneity: The odd effects of frailty.- Multivariate frailty models.- Marginal and dynamic models for recurrent events and clustered survival data.- Causality.- First passage time models: Understanding the shape of the hazard rate.- Diffusion and L#x00E9 vy process models for dynamic frailty.

Resuscitation of asphyxiated newborn infants with room air or oxygen : an international controlled trial : The Resair 2 study

Objective. Birth asphyxia represents a serious problem worldwide, resulting in ∼1 million deaths and an equal number of serious sequelae annually. It is therefore important to develop new and better ways to treat asphyxia. Resuscitation after birth asphyxia traditionally has been carried out with 100% oxygen, and most guidelines and textbooks recommend this; however, the scientific background for this has never been established. On the contrary, theoretic considerations indicate that resuscitation with high oxygen concentrations could have detrimental effects. We have performed a series of animal studies as well as one pilot study indicating that resuscitation can be performed with room air just as efficiently as with 100% oxygen. To test this more thoroughly, we organized a multicenter study and hypothesized that room air is superior to 100% oxygen when asphyxiated newborn infants are resuscitated. Methodology. In a prospective, international, controlled multicenter study including 11 centers from six countries, asphyxiated newborn infants with birth weight >999 g were allocated to resuscitation with either room air or 100% oxygen. The study was not blinded, and the patients were allocated to one of the two treatment groups according to date of birth. Those born on even dates were resuscitated with room air and those born on odd dates with 100% oxygen. Informed consent was not obtained until after the initial resuscitation, an arrangement in agreement with the new proposal of the US Food and Drug Administrations rules governing investigational drugs and medical devices to permit clinical research on emergency care without the consent of subjects. The protocol was approved by the ethical committees at each participating center. Entry criterion was apnea or gasping with heart rate <80 beats per minute at birth necessitating resuscitation. Exclusion criteria were birth weight <1000 g, lethal anomalies, hydrops, cyanotic congenital heart defects, and stillbirths. Primary outcome measures were death within 1 week and/or presence of hypoxic–ischemic encephalopathy, grade II or III, according to a modification of Sarnat and Sarnat. Secondary outcome measures were Apgar score at 5 minutes, heart rate at 90 seconds, time to first breath, time to first cry, duration of resuscitation, arterial blood gases and acid base status at 10 and 30 minutes of age, and abnormal neurologic examination at 4 weeks. The existing routines for resuscitation in each participating unit were followed, and the ventilation techniques described by the American Heart Association were used as guidelines aiming at a frequency of manual ventilation of 40 to 60 breaths per minute. Results. Forms for 703 enrolled infants from 11 centers were received by the steering committee. All 94 patients from one of the centers were excluded because of violation of the inclusion criteria in 86 of these. Therefore, the final number of infants enrolled in the study was 609 (from 10 centers), with 288 in the room air group and 321 in the oxygen group. Median (5 to 95 percentile) gestational ages were 38 (32.0 to 42.0) and 38 (31.1 to 41.5) weeks (NS), and birth weights were 2600 (1320 to 4078) g and 2560 (1303 to 3900) g (NS) in the room air and oxygen groups, respectively. There were 46% girls in the room air and 41% in the oxygen group (NS). Mortality in the first 7 days of life was 12.2% and 15.0% in the room air and oxygen groups, respectively; adjusted odds ratio (OR) = 0.82 with 95% confidence intervals (CI) = 0.50–1.35. Neonatal mortality was 13.9% and 19.0%; adjusted OR = 0.72 with 95% CI = 0.45–1.15. Death within 7 days of life and/or moderate or severe hypoxic–ischemic encephalopathy (primary outcome measure) was seen in 21.2% in the room air group and in 23.7% in the oxygen group; OR = 0.94 with 95% CI = 0.63–1.40. Heart rates did not differ between the two groups at any time point and were (mean ± SD) 90 ± 31 versus 93 ± 33 beats per minute at 1 minute and 110 ± 27 versus 113 ± 30 beats per minute at 90 seconds in the room air and oxygen groups, respectively. Apgar scores at 1 minute (median and 5 to 95 percentiles) were significantly higher in the room air group (5 [1 to 6.7]) than in the oxygen group (4 [1 to 7]); however, at 5 minutes there were no significant differences, with 8 (4 to 9) versus 7 (3 to 9). There were significantly more infants with very low 1-minute Apgar scores (<4) in the oxygen group (44.4%) than in the room air group (32.3%). There also were significantly more infants with 5-minute Apgar score <7 in the oxygen group (31.8%) than in the room air group (24.8%). There were no differences in acid base status or Sao 2during the observation period between the two groups. Mean (SD) Pao 2 was 31 (17) versus 30 (22) mm Hg in cord blood in the room air and oxygen groups, respectively (NS). At 10 minutes Pao 2 was 76 (32) versus 87 (49) mm Hg (NS), and at 30 minutes, the values were 74 (29) versus 89 (42) mm Hg in the room air and oxygen groups, respectively. Median (95% CI) time to first breath was 1.1 (1.0–1.2) minutes in the room air group versus 1.5 (1.4 to 1.6) minutes in the oxygen group. Time to the first cry also was in mean 0.4 minute shorter in the room air group compared with the oxygen group. In the room air group, there were 25.7% so-called resuscitation failures (bradycardia and/or central cyanosis after 90 seconds) that were switched to 100% oxygen after 90 seconds. The percentage of resuscitation failures in the oxygen group was 29.8%. Conclusions. This study with patients enrolled primarily from developing countries indicates that asphyxiated newborn infants can be resuscitated with room air as efficiently as with pure oxygen. In fact, time to first breath and first cry was significantly shorter in room air- versus oxygen-resuscitated infants. Resuscitation with 100% oxygen may depress ventilation and therefore delay the first breath. More studies are needed confirming these results before resuscitation guidelines are changed.

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 phenom enon may be modelled in many different ways, and a stochastic process approach is discussed as an alternative to the common proportional frailty model.

Breast cancer tumor growth estimated through mammography screening data

IntroductionKnowledge of tumor growth is important in the planning and evaluation of screening programs, clinical trials, and epidemiological studies. Studies of tumor growth rates in humans are usually based on small and selected samples. In the present study based on the Norwegian Breast Cancer Screening Program, tumor growth was estimated from a large population using a new estimating procedure/model.MethodsA likelihood-based estimating procedure was used, where both tumor growth and the screen test sensitivity were modeled as continuously increasing functions of tumor size. The method was applied to cancer incidence and tumor measurement data from 395,188 women aged 50 to 69 years.ResultsTumor growth varied considerably between subjects, with 5% of tumors taking less than 1.2 months to grow from 10 mm to 20 mm in diameter, and another 5% taking more than 6.3 years. The mean time a tumor needed to grow from 10 mm to 20 mm in diameter was estimated as 1.7 years, increasing with age. The screen test sensitivity was estimated to increase sharply with tumor size, rising from 26% at 5 mm to 91% at 10 mm. Compared with previously used Markov models for tumor progression, the applied model gave considerably higher model fit (85% increased predictive power) and provided estimates directly linked to tumor size.ConclusionScreening data with tumor measurements can provide population-based estimates of tumor growth and screen test sensitivity directly linked to tumor size. There is a large variation in breast cancer tumor growth, with faster growth among younger women.

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.

Digital ambulatory manometry of the small intestine in healthy adults. Estimates of variation within and between individuals and statistical management of incomplete MMC periods.

A new technique for ambulatory manometry of the small intestine with digital storage of signals is presented. Postprandial motility after a 1700-kJ meal and nighttime fasting motility were recorded in 19 healthy young adults. A comprehensive statistical approach was worked out to illuminate the statistical properties of fasting motility data from long-term studies. Separate quantifications of the variation within and between individuals are presented for the migrating motor complex (MMC). The overall mean for the MMC period was 107 min, with incomplete periods included as censored data. Standard deviation within individuals was 49 min, and standard deviation between individuals 16 min. Presented in the same manner, phase III in the proximal jejunum lasted 5.3 min, with standard deviations of 1.5 and 1.1 min, respectively. The propagation velocity of phase III in the distal duodenum was 10.8 cm/min, with standard deviations of 3.7 and 4.1 cm/min, respectively. Fed-state lasted 324±110 min (mean±sd), and adjusted fed-state, an alternative definition proposed in this study, 290±80 min. This variance component model, extended to handle censored data, provides a useful statistical approach for the analyses of the MMC. The MMC period proved to be less suitable for quantitative comparisons because of dominating intraindividual variance. Comparisons presented indicate that discrepancies in reference values depend, to a great extent, on the statistical methods applied.

Age-Incidence Curves of Nasopharyngeal Carcinoma Worldwide: Bimodality in Low-Risk Populations and Aetiologic Implications

The distinct geographic variation in the global incidence of nasopharyngeal carcinoma reflects a complex etiology involving viral, environmental, and genetic components. The high to intermediate rates observed in endemic areas contrast markedly with the uniformly low rates seen in much of the world. An interesting epidemiologic observation is the early peak in age-incidence curves observed in certain geographically disparate populations, suggestive of distinct causal entities and the possible exhaustion of susceptible individuals from the population at a certain age. The aim of this study was to systematically evaluate the age-incidence profiles of NPC worldwide on partitioning populations according to level of risk, in an effort to provide clues about the importance of early-in-life factors and genetic susceptibility. Using data from 23 high-quality population-based cancer registries for the period 1983-1997, a key finding was the consistent pattern of bimodality that emerged across low-risk populations, irrespective of geographic location. Continual increases in NPC risk by age up to a first peak in late adolescence/early adulthood (ages 15-24 years) were observed, followed by a second peak later in life (ages 65-79 years). No such early peak in NPC incidence by age group was evident among the high-risk populations studied. These findings are discussed according to existing lines of biological and epidemiologic evidence related to level of population risk, age at diagnosis, and histologic subtype. A modified model for NPC tumor development is proposed on the basis of these observations. (Cancer Epidemiol Biomarkers Prev 2008;17(9):2356–65)

Dynamic modelling and causality

Abstract In 1965 Erling Sverdrup published a paper on the use of Markov chains in modelling disability. This paper has been a source of inspiration for further development of statistical theory for Markov processes and the closely related counting processes. The main importance of introducing Markov chains does not lie so much in the Markov property, but more in the fact that a dynamic stochastic process is used as model. For statistical purposes one may dispense with the Markov assumption and may use much more general dynamic models than the Markovian ones. The key concept in this extension is the Doob-Meyer decomposition which is a part of modern martingale theory. With this as a starting point I define a general dynamic statistical model and discuss several examples. Intuitively, a dynamic model will be one where the future development is “explained” in terms of the past. Not surprisingly this is closely related to a causal understanding of the phenomenon. Tore Schweder in 1970 wrote a paper where he r...

Causality, mediation and time: a dynamic viewpoint.

Summary. Time dynamics are often ignored in causal modelling. Clearly, causality must operate in time and we show how this corresponds to a mechanistic, or system, understanding of causality. The established counterfactual definitions of direct and indirect effects depend on an ability to manipulate the mediator which may not hold in practice, and we argue that a mechanistic view may be better. Graphical representations based on local independence graphs and dynamic path analysis are used to facilitate communication as well as providing an overview of the dynamic relations ‘at a glance’. The relationship between causality as understood in a mechanistic and in an interventionist sense is discussed. An example using data from the Swiss HIV Cohort Study is presented.

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.