On a new piecewise regression model with cure rate: Diagnostics and application to medical data

Reduced incidence of diabetes during the COVID-19 pandemic in Alberta: A time-segmented longitudinal study of Alberta's Tomorrow Project

AIM

To characterize the impact of the COVID-19 pandemic on diabetes diagnosis using data from Alberta's Tomorrow Project (ATP), a population-based cohort study of chronic diseases in Alberta, Canada.

MATERIALS AND METHODS

The ATP participants who were free of diabetes on 1 April 2018 were included in the study. A time-segmented regression model was used to compare incidence rates of diabetes before the COVID-19 pandemic, during the first two COVID-19 states of emergency, and in the period when the state of emergency was relaxed, after adjusting for seasonality, sociodemographic factors, socioeconomic status, and lifestyle behaviours.

RESULTS

Among 43 705 ATP participants free of diabetes (65.5% females, age 60.4 ± 9.5 years in 2018), the rate of diabetes was 4.75 per 1000 person-year (PY) during the COVID-19 pandemic (up to 31 March 2021), which was 32% lower (95% confidence interval [CI] 21%, 42%; p < 0.001) than pre-pandemic (6.98 per 1000 PY for the period 1 April 2018 to 16 March 2020). In multivariable regression analysis, the first COVID-19 state of emergency (first wave) was associated with an 87.3% (95% CI -98.6%, 13.9%; p = 0.07) reduction in diabetes diagnosis; this decreasing trend was sustained to the second COVID-19 state of emergency and no substantial rebound (increase) was observed when the COVID-19 state of emergency was relaxed.

CONCLUSIONS

The COVID-19 public health emergencies had a negative impact on diabetes diagnosis in Alberta. The reduction in diabetes diagnosis was likely due to province-wide health service disruptions during the COVID-19 pandemic. Systematic plans to close the post-COVID-19 diagnostic gap are required in diabetes to avoid substantial downstream sequelae of undiagnosed disease.

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

Ignoring the presence of dependent censoring in data analysis can lead to biased estimates, for example, not considering the effect of abandonment of the tuberculosis treatment may influence inferences about the cure probability. In order to assess the relationship between cure and abandonment outcomes, we propose a copula Bayesian approach. Therefore, the main objective of this work is to introduce a Bayesian survival regression model, capable of taking into account the dependent censoring in the adjustment. So, this proposed approach is based on Clayton's copula, to provide the relation between survival and dependent censoring times. In addition, the Weibull and the piecewise exponential marginal distributions are considered in order to fit the times. A simulation study is carried out to perform comparisons between different scenarios of dependence, different specifications of prior distributions, and comparisons with the maximum likelihood inference. Finally, we apply the proposed approach to a tuberculosis treatment adherence dataset of an HIV cohort from Alvorada-RS, Brazil. Results show that cure and abandonment outcomes are negatively correlated, that is, as long as the chance of abandoning the treatment increases, the chance of tuberculosis cure decreases.

Cure rate models for heterogeneous competing causes

Cure rate models have been widely studied to analyze time-to-event data with a cured fraction of patients. In this type of model, the number of concurrent causes is assumed to be a random variable. However, in practice, it is natural to admit that the distribution of the number of competing causes is different from individual to individual. Our proposal is to assume that the number of competing causes belongs to a class of a finite mixture of competing causes distributions. We assume the number of malignant cells follow a mixture of two power series distributions and suppose that the time to the event of interest follows a Weibull distribution. We consider the proportion of the cured number of competing causes depending on covariates, allowing direct modeling of the cure rate. The proposed model includes several well-known models as special cases and defines many new special models. An expectation-maximization algorithm is proposed for parameter estimation, where the expectation step involves the computation of the expected number of concurrent causes for each individual. A Monte Carlo simulation is performed to assess the behavior of the estimation method. In order to show the potential for the practice of our model, we apply it to the real medical data set from a population-based study of incident cases of cutaneous melanoma diagnosed in the state of São Paulo, Brazil, illustrating that the model proposed can outperform traditional models in terms of model fitting.

A general class of promotion time cure rate models with a new biological interpretation

Over the last decades, the challenges in survival models have been changing considerably and full probabilistic modeling is crucial in many medical applications. Motivated from a new biological interpretation of cancer metastasis, we introduce a general method for obtaining more flexible cure rate models. The proposal model extended the promotion time cure rate model. Furthermore, it includes several well-known models as special cases and defines many new special models. We derive several properties of the hazard function for the proposed model and establish mathematical relationships with the promotion time cure rate model. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. Simulation studies are conducted to evaluate its performance with a discussion of the obtained results. A real dataset from population-based study of incident cases of melanoma diagnosed in the state of São Paulo, Brazil, is discussed in detail.

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.

A two-way flexible generalized gamma transformation cure rate model

We propose a two-way flexible cure rate model. The first flexibility is provided by considering a family of Box-Cox transformation cure models that include the commonly used cure models as special cases. The second flexibility is provided by proposing the wider class of generalized gamma distributions to model the associated lifetime. The advantage of this two-way flexibility is that it allows us to carry out tests of hypotheses to select an adequate cure model (within the family of Box-Cox transformation cure models) and a suitable lifetime distribution (within the wider class of generalized gamma distributions) that jointly provides the best fit to a given data. First, we study the maximum likelihood estimation of the generalized gamma Box-Cox transformation (GGBCT) model parameters. Then, we use the flexibility of our proposed model to carry out power studies to demonstrate the power of likelihood ratio test in rejecting mis-specified models. Furthermore, we study the bias and efficiency of the estimators of the cure rates under model mis-specification. Our findings strongly suggest the importance of selecting a correct lifetime distribution and a correct cure rate model, which can be achieved through the proposed two-way flexible model. Finally, we illustrate the applicability of our proposed model using a data from a breast cancer study and show that our model provides a better fit than the existing semiparametric Box-Cox transformation cure model with piecewise exponential approximation to the lifetime distribution.