The Kumaraswamy Lindley Regression Model with Application on the Egyptian Stock Exchange

We introduce and study the Kumaraswamy Lindely Distribution (KLD) model, which has increasing, decreasing, upside-down bathtub and bathtub shaped hazard functions.. We perform a Monte Carlo simulation study to assess the finite sample behavior of the maximum likelihood estimates of the parameters. We define a new regression model based on the new distribution. The new regression was applied to data from the Egyptian stock exchange in the period of (2015-2019). Finally, we study some properties of regression Residual analysis The martingale residual, Deviance component residual.

Adjustment for time-dependent unmeasured confounders in marginal structural Cox models using validation sample data

Large databases used in observational studies of drug safety often lack information on important confounders. The resulting unmeasured confounding bias may be avoided by using additional confounder information, frequently available in smaller clinical “validation samples”. Yet, no existing method that uses such validation samples is able to deal with unmeasured time-varying variables acting as both confounders and possible mediators of the treatment effect. We propose and compare alternative methods which control for confounders measured only in a validation sample within marginal structural Cox models. Each method corrects the time-varying inverse probability of treatment weights for all subject-by-time observations using either regression calibration of the propensity score, or multiple imputation of unmeasured confounders. Two proposed methods rely on martingale residuals from a Cox model that includes only confounders fully measured in the large database, to correct inverse probability of treatment weight for imputed values of unmeasured confounders. Simulation demonstrates that martingale residual-based methods systematically reduce confounding bias over naïve methods, with multiple imputation including the martingale residual yielding, on average, the best overall accuracy. We apply martingale residual-based imputation to re-assess the potential risk of drug-induced hypoglycemia in diabetic patients, where an important laboratory test is repeatedly measured only in a small sub-cohort.

A general goodness-of-fit test for survival analysis

Existing goodness-of-fit tests for survival data are either exclusively graphical in nature or only test specific model assumptions, such as the proportional hazards assumption. We describe a flexible, parameter-free goodness-of-fit test that provides a simple numerical assessment of a model’s suitability regardless of the structure of the underlying model. Intuitively, the goodness-of-fit test utilizes the fact that for a good model early event occurrence is predicted to be just as likely as late event occurrence, whereas a bad model has a bias towards early or late events. Formally, the goodness-of-fit test is based on a novel generalized Martingale residual which we call the martingale survival residual. The martingale survival residual has a uniform probability density function defined on the interval −0.5 to +0.5 if censoring is either absent or accounted for as one outcome in a competing hazards framework. For a good model, the set of calculated residuals is statistically indistinguishable from the uniform distribution, which is tested using the Kolmogorov-Smirnov statistic.

Comparison of Splitting Methods on Survival Tree

We compare splitting methods for constructing survival trees that are used as a model of survival time based on covariates. A number of splitting criteria on the classification and regression tree (CART) have been proposed by various authors, and we compare nine criteria through simulations. Comparative studies have been restricted to criteria that suppose the survival model for each terminal node in the final tree as a non-parametric model. As the main results, the criteria using the exponential log-likelihood loss, log-rank test statistics, the deviance residual under the proportional hazard model, or square error of martingale residual are recommended when it appears that the data have constant hazard with the passage of time. On the other hand, when the data are thought to have decreasing hazard with passage of time, the criterion using the two-sample test statistic, or square error of deviance residual would be optimal. Moreover, when the data are thought to have increasing hazard with the passage of time, the criterion using the exponential log-likelihood loss, or impurity that combines observed times and the proportion of censored observations would be the best. We also present the results of an actual medical research to show the utility of survival trees.

Prognostic significance of maximal tumor size (MTS) in young patients with good-prognosis diffuse large B-cell lymphoma (DLBCL) treated with CHOP-like chemotherapy with and without rituximab: Analysis of the MabThera International Trial Group (MInT) study

8053 Purpose: To determine the impact of MTS in young (18 to 60 years) patients with DLBCL and aaIPI=0,1. Patients and Methods: Outcome of patients treated with CHOP-like chemotherapy with (R-CHEMO) or without rituximab (CHEMO) was analyzed according to MTS. Results: A Martingale residual analysis revealed a linear negative prognostic impact of MTS on event-free (EFS) and overall (OS) survival. The hazard ratios for MTS per centimeter increase were significant for EFS (1.07; 95%-CI: 1.04–1.11; p<0.001) and OS (1.11; 95%-CI: 1.06–1.16; p<0.001). CHEMO 3-year EFS rates ranged between 78% for MTS <5cm and 41% for MTS >10cm. R-CHEMO 3-year EFS ranged from 83% (MTS <5cm) to 73% (MTS >=10cm). CHEMO 3-year OS rates decreased from 93% (MTS <5cm) to 74% (MTS >=10cm). R-CHEMO 3-year OS decreased from 98% (MTS <5cm) to 85% (MTS >=10cm). With CHEMO, any cut-off point between 5 and 10 cm separated a thus defined “non-bulky” from a “bulky” population with a 3-year EFS difference >20% (p<0.0001) and OS difference >12% (p<0.003), while with R-CHEMO only cut-off points >=10cm separated two populations with a significant EFS difference (9.1%; p=0.047), and cut-off points >=6cm discriminated two populations with a significant OS difference (7.6%-11.3%; p=0.037–0.0009). Conclusion: Due to the linear prognostic impact of MTS on outcome, cut-off points for “bulky” disease can be set rather arbitrarily between 5 and 10cm depending on clinical considerations. Rituximab reduces, but does not eliminate the negative prognostic impact of MTS in young patients with good-prognosis DLBCL. [Table: see text]