On null hypotheses in survival analysis

The conventional nonparametric tests in survival analysis, such as the log-rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby we can test hypotheses based on survival parameters that solve differential equations driven by cumulative hazards, and it is easy to implement the tests on a computer. We present simulations, suggesting that our tests perform well for several hypotheses in a range of scenarios. Finally, we use our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomised controlled trial

The surprising implications of familial association in disease risk

Background: A wide range of diseases show some degree of clustering in families; family history is therefore an important aspect for clinicians when making risk predictions. Familial aggregation is often quantified in terms of a familial relative risk (FRR), and although at first glance this measure may seem simple and intuitive as an average risk prediction, its implications are not straightforward. Methods: We use two statistical models for the distribution of disease risk in a population: a dichotomous risk model that gives an intuitive understanding of the implication of a given FRR, and a continuous risk model that facilitates a more detailed computation of the inequalities in disease risk. Published estimates of FRRs are used to produce Lorenz curves and Gini indices that quantifies the inequalities in risk for a range of diseases. Results: We demonstrate that even a moderate familial association in disease risk implies a very large difference in risk between individuals in the population. We give examples of diseases for which this is likely to be true, and we further demonstrate the relationship between the point estimates of FRRs and the distribution of risk in the population. Conclusions: The variation in risk for several severe diseases may be larger than the variation in income in many countries. The implications of familial risk estimates should be recognized by epidemiologists and clinicians.Comment: 17 pages, 5 figure

Transforming cumulative hazard estimates

Time to event outcomes are often evaluated on the hazard scale, but interpreting hazards may be difficult. Recently, there has been concern in the causal inference literature that hazards actually have a built in selection-effect that prevents simple causal interpretations. This is even a problem in randomized controlled trials, where hazard ratios have become a standard measure of treatment effects. Modeling on the hazard scale is nevertheless convenient, e.g. to adjust for covariates. Using hazards for intermediate calculations may therefore be desirable. Here, we provide a generic method for transforming hazard estimates consistently to other scales at which these built in selection effects are avoided. The method is based on differential equations, and generalize a well known relation between the Nelson-Aalen and Kaplan-Meier estimators. Using the martingale central limit theorem we also find that covariances can be estimated consistently for a large class of estimators, thus allowing for rapid calculations of confidence intervals. Hence, given cumulative hazard estimates based on e.g. Aalen's additive hazard model, we can obtain many other parameters without much more effort. We present several examples and associated estimators. Coverage and convergence speed is explored using simulations, suggesting that reliable estimates can be obtained in real-life scenarios.Comment: 22 pages, 4 figures. Added Lemma 1 stating sufficient conditions for P-UT for our considerations, and Proposition 1 showing the conditions are satisfied for estimated additive hazard coefficients and their martingale residual

Separable effects for adherence

Comparing different medications is complicated when adherence to these medications differs. We can overcome the adherence issue by assessing effectiveness under sustained use, as in the usual causal `per-protocol' estimand. However, when sustained use is challenging to satisfy in practice, the usefulness of this estimand can be limited. Here we propose a different class of estimands: separable effects for adherence. These estimands compare modified medications, holding fixed a component responsible for non-adherence. Under assumptions about treatment components' mechanisms of effect, the separable effects estimand can eliminate differences in adherence. These assumptions are amenable to interrogation by subject-matter experts and can be evaluated using causal graphs. We describe an algorithm for constructing causal graphs for separable effects, illustrate how these graphs can be used to reason about assumptions required for identification, and provide semi-parametric weighted estimators

[Mendelian randomisation - a genetic approach to an epidemiological method]

BACKGROUND Genetic information is becoming more easily available, and rapid progress is being made in developing methods of illuminating issues of interest. Mendelian randomisation makes it possible to study causes of disease using observational data. The name refers to the random distribution of gene variants in meiosis. The methodology makes use of genes that influence a risk factor for a disease, without influencing the disease itself. In this review article I explain the principles behind Mendelian randomisation and present the areas of application for this methodology.MATERIAL AND METHOD Methodology articles describing Mendelian randomisation were reviewed. The articles were found through a search in PubMed with the combination «mendelian randomization» OR «mendelian randomisation», and a search in McMaster Plus with the combination «mendelian randomization». A total of 15 methodology articles were read in full text. Methodology articles were supplemented by clinical studies found in the PubMed search.RESULTS In contrast to traditional observational studies, Mendelian randomisation studies are not affected by two important sources of error: conventional confounding variables and reverse causation. Mendelian randomisation is therefore a promising tool for studying causality. Mendelian randomisation studies have already provided valuable knowledge on the risk factors for a wide range of diseases. It is nevertheless important to be aware of the limitations of the methodology. As a result of the rapid developments in genetics research, Mendelian randomisation will probably be widely used in future years.INTERPRETATION If Mendelian randomisation studies are conducted correctly, they may help to reveal both modifiable and non-modifiable causes of disease

Inequality in genetic cancer risk suggests bad genes rather than bad luck

Heritability is often estimated by decomposing the variance of a trait into genetic and other factors. Interpreting such variance decompositions, however, is not straightforward. In particular, there is an ongoing debate on the importance of genetic factors in cancer development, even though heritability estimates exist. Here we show that heritability estimates contain information on the distribution of absolute risk due to genetic differences. The approach relies on the assumptions underlying the conventional heritability of liability model. We also suggest a model unrelated to heritability estimates. By applying these strategies, we describe the distribution of absolute genetic risk for 15 common cancers. We highlight the considerable inequality in genetic risk of cancer using different metrics, e.g., the Gini Index and quantile ratios which are frequently used in economics. For all these cancers, the estimated inequality in genetic risk is larger than the inequality in income in the USA