An Empirical Comparison between Partial Likelihood and Penalized Partial Likelihood Estimators for Semi-parametric Non-proportional Hazards Models with Frailty

This study compared partial likelihood (PL) and penalized partial likelihood (PPL) estimators in non-proportional hazards model with dichotomous time-varying covariates and subject–specific frailty. We considered Gamma and Inverse Gaussian as frailty distributions. The methods were illustrated with a dataset on diabetes. Extensive numerical studies were conducted using Monte Carlo simulations to compare the efficacy of the methods in terms of Relative Bias (RB) and Root Mean Square Error (RMSE). A sensitivity analysis was carried out to assess the power of the estimators under misspecification of frailty distributions. It was found, that PPL estimator generally outperformed PL estimator in all scenarios considered. Efficiency was found to increase with increase in sample size, and decrease with increase in censoring proportion. The sensitivity analysis conducted to assess the effect of frailty misspecification revealed that sample size, proportion of censored observations and the shape of the frailty distribution (log-skewed) severely affected the power of the estimators

Gamma and Inverse Gaussian Frailty Models with Time-varying co-variates Based on Some Parametric Baselin Hazards Function

. Ignoring the existence of frailty term in the analysis of survival time data, when heterogeneity is present will produce a less accurate  estimated parameters with higher standard errors. In survival analysis, Cox proportional hazards model is frequently used to measure the effects of covariates. The covariates may fail to fully account for the true differences in hazard. This may be due to an existence of another response variable that is disregarded in the model but can be explained by the term known as frailty. The incorporation of frailty in the model thereby avoid underestimation and overestimation of parameters and also correctly measure the effects of the covariates on the response variable. This paper presents a parametric non-proportional hazard models with Weibull, Loglogistic and Gompertz as baseline distributions and Gamma and Inverse Gaussian as frailty distribution. A maximum likelihood method is used and is illustrated with a numerical example in which the fit is compared using Akaike Information Criterion (AIC): Key words: time-varying co-variate; unobserved co-variates; non-proportional hazard model; inverse Cumulative Hazard; survival time; frailty models; Akaike Information Criterion   (French) Ignorer l’existence d’un terme de fragilite dans l’analyse des ´ donnees de temps de survie, lorsque l’h ´ et´ erog ´ en´ eit ´ e est pr ´ esente, peut aboutir a des ´ estimateurs de parametres moins pr ` ecis avec des erreurs standard ´ elev ´ ees. Dans ´ l’analyse de survie, le modele des risques proportionnels de Cox est fr ` equemment ´ utilise pour mesurer les effets des covariables. Les covariables peuvent ne  pas tenir ´ pleinement compte des vraies differences de risque. Cela peut ´ etre d ˆ uˆ a l’existence ` d’une autre variable de reponse qui n’est pas prise en compte dans le mod ´ ele mais ` peut etre expliqu ˆ ee par un terme connu sous le labeli fragile. L’incorporation de ´ la fragilite dans le mod ´ ele ` evite ainsi la sous-estimation et la surestimation des ´ parametres et mesure ` egalement correctement les effets des covariables sur la ´ variable de reponse. Cet article pr ´ esente des mod ´ eles de risques param ` etriques ´ non proportionnels avec Weibull, Loglogistic et Gompertz comme distributions de base et Gamma et Gaussian inverse comme distribution de fragilite. La m ´ ethode du ´maximum de vraisemblance est utilisee et la proc ´ edure est illustr ´ ee par un exem- ´ ple numerique et l’ajustement est compar ´ e´ a l’aide du crit ` ere d’information Akaike ` (AIC)

Time-varying covariates and coefficients in Cox regression models

Time-varying covariance occurs when a covariate changes over time during the follow-up period. Such variable can be analyzed with the Cox regression model to estimate its effect on survival time. For this it is essential to organize the data in a counting process style. In situations when the proportional hazards assumption of the Cox regression model does not hold, we say that the effect of the covariate is time-varying. The proportional hazards assumption can be tested by examining the residuals of the model. The rejection of the null hypothesis induces the use of time varying coefficient to describe the data. The time varying coefficient can be described with a step function or a parametric time function. This article aims to illustrate how to carry out statistical analyses in the presence of time-varying covariates or coefficients with R

Adaptation of the Wound Healing Questionnaire universal-reporter outcome measure for use in global surgery trials (TALON-1 study): mixed-methods study and Rasch analysis

BackgroundThe Bluebelle Wound Healing Questionnaire (WHQ) is a universal-reporter outcome measure developed in the UK for remote detection of surgical-site infection after abdominal surgery. This study aimed to explore cross-cultural equivalence, acceptability, and content validity of the WHQ for use across low- and middle-income countries, and to make recommendations for its adaptation.MethodsThis was a mixed-methods study within a trial (SWAT) embedded in an international randomized trial, conducted according to best practice guidelines, and co-produced with community and patient partners (TALON-1). Structured interviews and focus groups were used to gather data regarding cross-cultural, cross-contextual equivalence of the individual items and scale, and conduct a translatability assessment. Translation was completed into five languages in accordance with Mapi recommendations. Next, data from a prospective cohort (SWAT) were interpreted using Rasch analysis to explore scaling and measurement properties of the WHQ. Finally, qualitative and quantitative data were triangulated using a modified, exploratory, instrumental design model.ResultsIn the qualitative phase, 10 structured interviews and six focus groups took place with a total of 47 investigators across six countries. Themes related to comprehension, response mapping, retrieval, and judgement were identified with rich cross-cultural insights. In the quantitative phase, an exploratory Rasch model was fitted to data from 537 patients (369 excluding extremes). Owing to the number of extreme (floor) values, the overall level of power was low. The single WHQ scale satisfied tests of unidimensionality, indicating validity of the ordinal total WHQ score. There was significant overall model misfit of five items (5, 9, 14, 15, 16) and local dependency in 11 item pairs. The person separation index was estimated as 0.48 suggesting weak discrimination between classes, whereas Cronbach's α was high at 0.86. Triangulation of qualitative data with the Rasch analysis supported recommendations for cross-cultural adaptation of the WHQ items 1 (redness), 3 (clear fluid), 7 (deep wound opening), 10 (pain), 11 (fever), 15 (antibiotics), 16 (debridement), 18 (drainage), and 19 (reoperation). Changes to three item response categories (1, not at all; 2, a little; 3, a lot) were adopted for symptom items 1 to 10, and two categories (0, no; 1, yes) for item 11 (fever).ConclusionThis study made recommendations for cross-cultural adaptation of the WHQ for use in global surgical research and practice, using co-produced mixed-methods data from three continents. Translations are now available for implementation into remote wound assessment pathways