Cause‑specific Cox modelRegression on cause-specific hazards is an extension ofthe popular Cox proportional hazards model for CRs

The aims of this manuscript can be summarised as:(i) examination of extensions of PLANNCR method(PLANNCR extended) for the development and vali-dation of prognostic clinical prediction models withcompeting events, (ii) systematic evaluation of model-predictive performance for ML techniques (PLANNCRoriginal, PLANNCR extended, RSFCR) and SM (cause-specific Cox, Fine-Gray) regarding discrimination andcalibration, (iii) investigation of the potential role ofML in contrast to conventional regression methods forCRs in non-complex eSTS data (small/medium samplesize, low dimensional setting), (iv) practical utility of themethods for prediction

Nowadays, there is a growing interest in applyingmachine learning (ML) for prediction (diagnosis or prog-nosis) of clinical outcomes [12, 13] which has sparked adebate regarding the added value of ML techniques ver-sus SM in the medical field. Criticism is attributed toML prediction models. Despite no assumptions aboutthe data structure are made, and being able to naturallyincorporate interactions between predictive features,they are prone to overfitting of the training data andthey lack extensive assessment of predictive accuracy(i.e., absence of calibration curves) [14, 15]. On the otherhand, traditional regression methods are consideredstraightforward to use and harder to overfit. That beingsaid, they do make certain (usually strong) assumptionssuch as the proportional hazards over time for the Coxmodel, and require manual pre-specification of interac-tion terms.

Historical Context and Path Dependence

Path Dependence in Historical Sociology

… This article does not seek to reorient all such modes of analysis toward the study of path dependence. Nevertheless, the article does seek to establish that path-dependent analysis …

… of the so-called path dependence and historical context in contextual political analysis. It analyzes the different meanings and uses of the concept of path dependence in contemporary …

J Mahoney, D Schensul - … of contextual political analysis, 2006 - scholars.northwestern.edu

so that instead of predicting the time of event, we are predicting the probability that an event happens at a particular time .

In practice, we found that it is not appropriate to use Aalen’s additive hazardsmodel for all datasets, because when we estimate cumulativeregression functionsB(t),they are restricted to the time interval where X (X has been defined in Chapter 3) is offull rank, that meansX0Xis invertible. Sometimes we found that X is not of full rank,which was not a problem with the Cox model.

An overall conclusion is that the two models give different pieces of informationand should not be viewed as alternatives to each other, but ascomplementary methodsthat may be used together to give a fuller and more comprehensive understanding ofdata

The effect ofthe covariates on survival is to act multiplicatively on some unknown baseline hazardrate, which makes it difficult to model covariate effects that change over time. Secondly,if covariates are deleted from a model or measured with a different level of precision, theproportional hazards assumption is no longer valid. These weaknesses in the Cox modelhave generated interest in alternative models. One such alternative model is Aalen’s(1989) additive model. This model assumes that covariates act in an additive manneron an unknown baseline hazard rate. The unknown risk coefficients are allowed to befunctions of time, so that the effect of a covariate may vary over time.

Note that, three often used transformations can be specified using the argument fun: “log”: log transformation of the survivor function, “event”: plots cumulative events (f(y) = 1-y). It’s also known as the cumulative incidence, “cumhaz” plots the cumulative hazard function (f(y) = -log(y))

Note that, the confidence limits are wide at the tail of the curves, making meaningful interpretations difficult. This can be explained by the fact that, in practice, there are usually patients who are lost to follow-up or alive at the end of follow-up. Thus, it may be sensible to shorten plots before the end of follow-up on the x-axis (Pocock et al, 2002).

RF is now a standard to effectively analyze a large number of variables, of many different types, with no previous variable selection process. It is not parametric, and in particular for survival target it does not assume the proportional risks assumption.

Thesurvival function gives,for every time,the probability of surviving(or not experiencing the event) up to that time.The hazard function gives the potential that the event will occur, per time unit, given that an individual has survived up to the specified time.