A bivariate survival model with compound Poisson frailty

On a reparameterization of a flexible family of cure models

The existence of items not susceptible to the event of interest is of both theoretical and practical importance. Although researchers may provide, for example, biological, medical, or sociological evidence for the presence of such items (cured), statistical models performing well under the existence or not of a cured proportion, frequently offer a necessary flexibility. This work introduces a new reparameterization of a flexible family of cure models, which not only includes among its special cases, the most studied cure models (such as the mixture, bounded cumulative hazard, and negative binomial cure model) but also classical survival models (ie, without cured items). One of the main properties of the proposed family, apart from its computationally tractable closed form, is that the case of zero cured proportion is not found at the boundary of the parameter space, as it typically happens to other families. A simulation study examines the (finite) performance of the suggested methodology, focusing to the estimation through EM algorithm and model discrimination, by the aid of the likelihood ratio test and Akaike information criterion; for illustrative purposes, analysis of two real life datasets (on recidivism and cutaneous melanoma) is also carried out.

Modeling the rate of HIV testing from repeated binary data amidst potential never-testers

Many longitudinal studies with a binary outcome measure involve a fraction of subjects with a homogeneous response profile. In our motivating data set, a study on the rate of human immunodeficiency virus (HIV) self-testing in a population of men who have sex with men (MSM), a substantial proportion of the subjects did not self-test during the follow-up study. The observed data in this context consist of a binary sequence for each subject indicating whether or not that subject experienced any events between consecutive observation time points, so subjects who never self-tested were observed to have a response vector consisting entirely of zeros. Conventional longitudinal analysis is not equipped to handle questions regarding the rate of events (as opposed to the odds, as in the classical logistic regression model). With the exception of discrete mixture models, such methods are also not equipped to handle settings in which there may exist a group of subjects for whom no events will ever occur, i.e. a so-called "never-responder" group. In this article, we model the observed data assuming that events occur according to some unobserved continuous-time stochastic process. In particular, we consider the underlying subject-specific processes to be Poisson conditional on some unobserved frailty, leading to a natural focus on modeling event rates. Specifically, we propose to use the power variance function (PVF) family of frailty distributions, which contains both the gamma and inverse Gaussian distributions as special cases and allows for the existence of a class of subjects having zero frailty. We generalize a computational algorithm developed for a log-gamma random intercept model (Conaway, 1990. A random effects model for binary data. Biometrics46, 317-328) to compute the exact marginal likelihood, which is then maximized to obtain estimates of model parameters. We conduct simulation studies, exploring the performance of the proposed method in comparison with competitors. Applying the PVF as well as a Gaussian random intercept model and a corresponding discrete mixture model to our motivating data set, we conclude that the group assigned to receive follow-up messages via SMS was self-testing at a significantly lower rate than the control group, but that there is no evidence to support the existence of a group of never-testers.

A retrospective survey of the causes of bracket- and tube-bonding failures

OBJECTIVE

To investigate the causes of bonding failures of orthodontic brackets and tubes and the effect of premedicating for saliva reduction.

MATERIALS AND METHODS

Premedication with atropine sulfate was administered randomly. Failure rate of brackets and tubes placed in a group of 158 consecutive patients was evaluated after a mean period of 67 weeks after bonding.

RESULTS

The failure rate in the group without atropine sulfate premedication was 2.4%. In the group with premedication, the failure rate was 2.7%. The Cox regression analysis of these groups showed that atropine application did not lead to a reduction in bond failures. Statistically significant differences in the hazard ratio were found for the bracket regions and for the dental assistants who prepared for the bonding procedure.

CONCLUSIONS

Premedication did not lead to fewer bracket failures. The roles of the dental assistant and patient in preventing failures was relevant. A significantly higher failure rate for orthodontic appliances was found in the posterior regions.

Modelling recurrent events: comparison of statistical models with continuous and discontinuous risk intervals on recurrent malaria episodes data

Background

Recurrent events data analysis is common in biomedicine. Literature review indicates that most statistical models used for such data are often based on time to the first event or consider events within a subject as independent. Even when taking into account the non-independence of recurrent events within subjects, data analyses are mostly done with continuous risk interval models, which may not be appropriate for treatments with sustained effects (e.g., drug treatments of malaria patients). Furthermore, results can be biased in cases of a confounding factor implying different risk exposure, e.g. in malaria transmission: if subjects are located at zones showing different environmental factors implying different risk exposures.

Methods

This work aimed to compare four different approaches by analysing recurrent malaria episodes from a clinical trial assessing the effectiveness of three malaria treatments [artesunate + amodiaquine (AS + AQ), artesunate + sulphadoxine-pyrimethamine (AS + SP) or artemether-lumefantrine (AL)], with continuous and discontinuous risk intervals: Andersen-Gill counting process (AG-CP), Prentice-Williams-Peterson counting process (PWP-CP), a shared gamma frailty model, and Generalized Estimating Equations model (GEE) using Poisson distribution. Simulations were also made to analyse the impact of the addition of a confounding factor on malaria recurrent episodes.

Results

Using the discontinuous interval analysis, AG-CP and Shared gamma frailty models provided similar estimations of treatment effect on malaria recurrent episodes when adjusted on age category. The patients had significant decreased risk of recurrent malaria episodes when treated with AS + AQ or AS + SP arms compared to AL arm; Relative Risks were: 0.75 (95% CI (Confidence Interval): 0.62-0.89), 0.74 (95% CI: 0.62-0.88) respectively for AG-CP model and 0.76 (95% CI: 0.64-0.89), 0.74 (95% CI: 0.62-0.87) for the Shared gamma frailty model.

With both discontinuous and continuous risk intervals analysis, GEE Poisson distribution models failed to detect the effect of AS + AQ arm compared to AL arm when adjusted for age category. The discontinuous risk interval analysis was found to be the more appropriate approach.

Conclusion

Repeated event in infectious diseases such as malaria can be analysed with appropriate existing models that account for the correlation between multiple events within subjects with common statistical software packages, after properly setting up the data structures.