arXiv subjects

Madan Gopal Kundu

Publications and source records attributed to Madan Gopal Kundu.

2 recordsLinked to original sources

arXiv2020

Survival trees for right-censored data based on score based parameter instability test

Survival analysis of right censored data arises often in many areas of research including medical research. Effect of covariates (and their interactions) on survival distribution can be studied through existing methods which requires to pre-specify the functional form of the covariates including their interactions. Survival trees offer relatively flexible approach when the form of covariates' effects is unknown. Most of the currently available survival tree construction techniques are not based on a formal test of significance; however, recently proposed ctree algorithm (Hothorn et al., 2006) uses permutation test for splitting decision that may be conservative at times. We consider parameter instability test of statistical significance of heterogeneity to guard against spurious findings of variation in covariates' effect without being overly conservative. We have proposed SurvCART algorithm to construct survival tree under conditional inference framework (Hothorn et al., 2006) that selects splitting variable via parameter instability test and subsequently finds the optimal split based on some maximally chosen statistic. Notably, unlike the existing algorithms which focuses only on heterogeneity in event time distribution, the proposed SurvCART algorithm can take splitting decision based in censoring distribution as well along with heterogeneity in event time distribution. The operating characteristics of parameter instability test and comparative assessment of SurvCART algorithm were carried out via simulation. Finally, SurvCART algorithm was applied to a real data setting. The proposed method is fully implemented in R package LongCART available on CRAN.

stat.ME↗

arXiv2014

Regression Trees for Longitudinal Data

While studying response trajectory, often the population of interest may be diverse enough to exist distinct subgroups within it and the longitudinal change in response may not be uniform in these subgroups. That is, the timeslope and/or influence of covariates in longitudinal profile may vary among these different subgroups. For example, Raudenbush (2001) used depression as an example to argue that it is incorrect to assume that all the people in a given population would be experiencing either increasing or decreasing levels of depression. In such cases, traditional linear mixed effects model (assuming common parametric form for covariates and time) is not directly applicable for the entire population as a group-averaged trajectory can mask important subgroup differences. Our aim is to identify and characterize longitudinally homogeneous subgroups based on the combination of baseline covariates in the most parsimonious way. This goal can be achieved via constructing regression tree for longitudinal data using baseline covariates as partitioning variables. We have proposed LongCART algorithm to construct regression tree for the longitudinal data. In each node, the proposed LongCART algorithm determines the need for further splitting (i.e. whether parameter(s) of longitudinal profile is influenced by any baseline attributes) via parameter instability tests and thus the decision of further splitting is type-I error controlled. We have obtained the asymptotic results for the proposed instability test and examined finite sample behavior of the whole algorithm through simulation studies. Finally, we have applied the LongCART algorithm to study the longitudinal changes in choline level among HIV patients.

stat.ME↗