Statistical methods in cancer research

Statistical Analysis with Missing Data

Standard survival data measure the time span from some time origin until the occurrence of one type of event. If several types of events occur, a model describing progression to each of these competing risks is needed. Multi-state models generalize competing risks models by also describing transitions to intermediate events. Methods to analyze such models have been developed over the last two decades. Fortunately, most of the analyzes can be performed within the standard statistical packages, but may require some extra effort with respect to data preparation and programming. This tutorial aims to review statistical methods for the analysis of competing risks and multi-state models. Although some conceptual issues are covered, the emphasis is on practical issues like data preparation, estimation of the effect of covariates, and estimation of cumulative incidence functions and state and transition probabilities. Examples of analysis with standard software are shown.

/pdf/tutorial-in-biostatistics-competing-risks-and-multi-state-tg28odevkn.pdf

Tutorial in biostatistics: competing risks and multi-state models.

Remaining useful life estimation - A review on the statistical data driven approaches

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

The Web of Human Sexual Contacts

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.

https://www.springer.com/productFlyer_978-0-387-20287-7.pdf?SGWID=0-0-1297-52088484-0

Survival and Event History Analysis: A Process Point of View

A linear model is suggested for the influence of covariates on the intensity function. This approach is less vulnerable than the Cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed. A method of non-parametric estimation of regression functions is presented. This results in plots that may give information on the change over time in the influence of covariates. A test method and two goodness of fit plots are also given. The approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx.

A linear regression model for the analysis of life times.

Objective. Birth asphyxia represents a serious problem worldwide, resulting in ;1 million deaths and an equal number of serious sequelae annu- ally. 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; how- ever, the scientific background for this has never been established. On the contrary, theoretic considerations in- dicate that resuscitation with high oxygen concentrations could have detrimental effects. We have performed a series of animal studies as well as one pilot study indi- cating 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 hy- pothesized that room air is superior to 100% oxygen when asphyxiated newborn infants are resuscitated. Methodology. In a prospective, international, con- trolled 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 arrange- ment in agreement with the new proposal of the US Food and Drug Administration's rules governing investiga- tional drugs and medical devices to permit clinical re- search on emergency care without the consent of sub- jects. 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 cri- teria were birth weight <1000 g, lethal anomalies, hy- drops, 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 partici- pating unit were followed, and the ventilation tech- niques 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 cen- ters were received by the steering committee. All 94 pa- tients from one of the centers were excluded because of violation of the inclusion criteria in 86 of these. There- fore, 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) 5 0.82 with 95% confidence intervals (CI) 5 0.50 -1.35. Neonatal mortality was 13.9% and 19.0%; adjusted OR 5 0.72 with 95% CI 5 0.45-1.15. Death within 7 days of life and/or moderate or severe hypoxic-ischemic encephalopathy (primary out- come measure) was seen in 21.2% in the room air group and in 23.7% in the oxygen group; OR 5 0.94 with 95% CI 5 0.63-1.40.

https://pediatrics.aappublications.org/content/pediatrics/102/1/e1.full.pdf

Resuscitation of Asphyxiated Newborn Infants With Room Air or Oxygen: An International Controlled Trial: The Resair 2 Study

I discuss the impact of individual heterogeneity in survival analysis. It is well known that this phenomenon may distort what is observed. A general class of mixing (or frailty) distributions is applied, extending a model of Hougaard. The extension allows part of the population to be non-susceptible, and contains the traditional gamma distribution as a special case. I consider the mixing of both a constant and a Weibull individual rate, and also discuss the comparison of rates from two populations. A number of practical examples are mentioned. Finally, I analyse two data sets, the main one containing data from the Norwegian Cancer Registry on the survival of breast cancer patients. The statistical analysis is of necessity speculative, but may still provide some insight.

Heterogeneity in survival analysis

When making probabilistic models for survival times, one should consider the fact that individuals are heterogeneous. The observed changes in population intensities (or hazard rates) over time are a mixed result of two influences: on the one hand, the actual changes in the individual hazards, and, on the other hand, the selection due to high-risk individuals leaving the risk group early. I will consider the common multiplicative model for heterogeneity, but with the new feature that the random proportionality factor has a compound Poisson distribution. This distribution is studied in some detail. It is pointed out how its application to the survival situation extends a model of Hougaard, inheriting several nice properties. One important feature of the model is that it yields a subgroup of zero susceptibility, which "survives forever." This is a relevant model in medicine and demography. Two examples are given where the model is fitted to data concerning marriage rates and fertility.

/pdf/modelling-heterogeneity-in-survival-analysis-by-the-compound-ru9wufe2il.pdf

Odd O. Aalen

Papers

Survival and Event History Analysis: A Process Point of View

A linear regression model for the analysis of life times.

Resuscitation of Asphyxiated Newborn Infants With Room Air or Oxygen: An International Controlled Trial: The Resair 2 Study

Heterogeneity in survival analysis

Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution