9 research outputs found
Flexible hazard-based models and quantile regression for right-censored data using two-piece asymmetric distributions
No full textIn many applications of statistical modelling, a vital complexity is that only partial information on the variables of interest is observed. Among such complex data settings are censored
data, particularly in time-to-event or survival analysis. In a right-censoring context, it is only
known for some studied objects that the survival time of interest exceeds the observed time.
This dissertation focuses on statistical inference for a large class of two-piece asymmetric
(TPA) distributions in the context of flexible quantile regression and hazard-based models for
right-censored survival data. One of the exciting features of these families is that the location
parameter coincides with a specific quantile of the distribution. In the particular case of a
symmetric distribution, the location parameter coincides with the mean. The first part of the
dissertation focuses on statistical inference for the unconditional setting of the TPA family of
distributions. We discuss the theoretical development (consistency and asymptotic normality
properties) for the maximum likelihood estimators for an entire class of TPA distributions by
considering some necessary regularity conditions on the probabilistic distributions involved.
We conduct a simulation study to examine the method’s properties in finite–sample cases. We
illustrate the applicability of the proposed methods on clinical and non-clinical data examples
and compare their performances with some existing survival models.
In classical regression analysis, we usually fit the model for the mean of the response
variable conditioning on the set of covariates. One may thus estimate the average (mean)
of the conditional distribution corresponding to the given set of covariates, and draw only a
single regression curve. However, one might be interested in getting the entire picture of the
conditional distribution. The second part of the dissertation focuses on the flexible regression
setting of TPA families with the aim of conditional quantile curves and survival estimation.
Covariates can affect not only the location but also, more generally, the scale and shape of the
distribution of the survival time in a multi-parametric regression framework. We exploit the
local likelihood estimation technique when covariates come into play in the model through
non-parametric (completely unspecified) functional forms. In addition, we propose a general
profile (local) likelihood method to estimate the parametric and non-parametric components
in the case of a partially linear regression model. We investigate the method’s performance
through an extensive simulation study. In addition, the application of the proposed method
is discussed with clinical data examples.
In time-to-event analysis, many commonly used statistical methods assume that the covariate effects on a monotone transformation of the survival time are linear, and the regression coefficients are constant over time. For instance, the accelerated failure time model
estimates the linear covariate effects on the logarithmic scale of the survival time. In contrast,
the proportional hazards model assumes linearity on the hazard ratio. These assumptions,
however, might be chosen for their mathematical convenience, and the actual associations
in practical applications may be more complex than the prespecified linear structure of the
covariate effects. The third part of the work deals with a hybrid hazard (HH) model where
we consider a parametric TPA baseline hazard distribution with flexible regression settings.
We examine the covariate effects at the time-scale and hazard-scale changes in parametric, semi-parametric and non-parametric functional forms. The general hybrid hazard-based
model includes the three most commonly used survival models as subclasses: proportional
hazards (PH), accelerated failure time (AFT), and accelerated hazards (AH) models. We discuss in detail the estimation procedures in the general profile (local) likelihood technique.
We investigate the validity of the flexible HH model formulation and proposed estimation
methodology through a comprehensive Monte Carlo simulation study and demonstrate its
practical use in real data examples.In veel toepassingen van statistisch modelleren worden variabelen waarin we ge¨ınteresseerd
zijn slechts deels geobserveerd. E´en van dergelijke complexe data situaties zijn gecensureerde
gegevens. Deze komen in het bijzonder voor in overlevingsanalyse. In een context van rechtse
censurering is voor sommige individuen enkel geweten dat hun overlevingstijd groter is dan
de geobserveerde tijd. Deze thesis focust op statistische besluitvorming in een brede familie van twee-stuks asymmetrische (TPA) verdelingen in de context van flexibele kwantielregressie en hazard-gebaseerde modellen voor rechts gecensureerde overlevingsgegevens. Een
belangrijke eigenschap van deze familie is dat de locatieparameter overeenkomt met een
specifiek kwantiel van de verdeling. In het bijzonder geval van een symmetrische verdeling valt de locatieparameter samen met het gemiddelde. In het eerste deel van de thesis
focussen we op statistische besluitvorming voor een niet-voorwaardelijke setting binnen de
TPA familie van verdelingen. We onderzoeken de theoretische eigenschappen (consistentie
en asymptotische normaliteit) van maximum likelihood schatters voor de hele klasse van
TPA verdelingen, onder enkele noodzakelijke regulariteitsvoorwaarden op de verdeling. In
een simulatiestudie worden de eindige steekproefkwaliteiten van de methoden onderzocht.
Verder illustreren we het gebruik van de voorgestelde methoden op klinische en niet-klinische
data en vergelijken we hun prestatie met enkele bestaande overlevingsmodellen.
In klassieke regressieanalyse modelleert men het gemiddelde van een respons op basis
van een aantal covariaten. Men modelleert dus enkel het gemiddelde van een voorwaardelijke verdeling aan de hand van covariaten. Daarnaast kan men ook ge¨ınteresseerd zijn in de
volledige voorwaardelijke verdeling. Het tweede deel behandelt een flexibele regressiesetting
met TPA verdelingen met als doel het schatten van de kwantielfunctie en de overlevingskans.
In een regressiesetting kunnen covariaten zowel de locatie als de schaal en vorm van de
verdeling van de overlevingstijd be¨ınvloeden. We verkennen lokale maximum likelihood
schatters wanneer ook covariaten op een niet-parametrische manier in het model worden
opgenomen. Bovendien stellen we een algemene profile likelihood methode voor om zowel
de parametrische als niet-parametrische componenten te schatten in het geval van een deels
lineair regressiemodel. We onderzoeken de werking van de methoden in een uitgebreide
simulatiestudie en op enkele klinische data.
Vaak gebruikte statistische methoden in overlevingsanalyse veronderstellen dat de covariaten een linear effect hebben op de overlevingstijd via a monotone transformation, en dat de regressieco¨effici¨enten constant zijn in de tijd. In bijvoorbeeld een accelerated failure
time model hebben de covariaten een linear effect op het logaritme van de overlevingstijd.
In een proportional hazards model daarentegen geldt dit linear effect op de hazard functie
(ratio). Deze veronderstellingen worden misschien gemaakt omwille van de wiskundige eenvoud. In de praktijk kunnen de eigenlijke verbanden echter complexer zijn. Het derde deel
van de thesis beschouwt een hybride hazard model waarbij we een parametrische TPA basis
hazard verdeling veronderstellen met een flexibele regressiesetting. We onderzoeken de effecten van de covariaten in de tijds- en hazardschaal in parametrische, semi-parametrische
en niet-parametrische situaties. De algemene hybride hazardgebaseerde modellen omvatten
de drie meest gebruikte overlevingsmodellen: proportional hazard (PH), accelerated failure
time (AFT) en accelerated hazards (AH) modellen. We bespreken de schattingsprocedures
gebaseerd op de lokale profile likelihood techniek. Op basis van een simulatiestudie onderzoeken we de toepasbaarheid van de methoden. Daarnaast illustreren we het praktische
gebruik van de methoden via data voorbeelde
Flexible two-piece distributions for right censored survival data
No full textAn important complexity in censored data is that only partial information on the variables of interest is observed. In recent years, a large family of asymmetric distributions and maximum likelihood estimation for the parameters in that family has been studied, in the complete data case. In this paper, we exploit the appealing family of quantile-based asymmetric distributions to obtain flexible distributions for modelling right censored survival data. The flexible distributions can be generated using a variety of symmetric distributions and monotonic link functions. The interesting feature of this family is that the location parameter coincides with an index-parameter quantile of the distribution. This family is also suitable to characterize different shapes of the hazard function (constant, increasing, decreasing, bathtub and upside-down bathtub or unimodal shapes). Statistical inference is done for the whole family of distributions. The parameter estimation is carried out by optimizing a non-differentiable likelihood function. The asymptotic properties of the estimators are established. The finite-sample performance of the proposed method and the impact of censorship are investigated via simulations. Finally, the methodology is illustrated on two real data examples (times to weaning in breast-fed data and German Breast Cancer data).sponsorship: The authors are grateful to the editor, and associate editor and reviewers for their valuable comments that led to an improvement of the manuscript. The second author gratefully acknowledge support from Research Grant FWO G0D6619N of the Flemish Science Foundation, and from the C16/20/002 project of the Research Fund KU Leuven. (Flemish Science Foundation|FWO G0D6619N, Research Fund KU Leuven|C16/20/002)status: Published onlin
Flexible hazard-based models and quantile regression for right-censored data using two-piece asymmetric distributions
No full textIn many applications of statistical modelling, a vital complexity is that only partial information on the variables of interest is observed. Among such complex data settings are censored
data, particularly in time-to-event or survival analysis. In a right-censoring context, it is only
known for some studied objects that the survival time of interest exceeds the observed time.
This dissertation focuses on statistical inference for a large class of two-piece asymmetric
(TPA) distributions in the context of flexible quantile regression and hazard-based models for
right-censored survival data. One of the exciting features of these families is that the location
parameter coincides with a specific quantile of the distribution. In the particular case of a
symmetric distribution, the location parameter coincides with the mean. The first part of the
dissertation focuses on statistical inference for the unconditional setting of the TPA family of
distributions. We discuss the theoretical development (consistency and asymptotic normality
properties) for the maximum likelihood estimators for an entire class of TPA distributions by
considering some necessary regularity conditions on the probabilistic distributions involved.
We conduct a simulation study to examine the method’s properties in finite–sample cases. We
illustrate the applicability of the proposed methods on clinical and non-clinical data examples
and compare their performances with some existing survival models.
In classical regression analysis, we usually fit the model for the mean of the response
variable conditioning on the set of covariates. One may thus estimate the average (mean)
of the conditional distribution corresponding to the given set of covariates, and draw only a
single regression curve. However, one might be interested in getting the entire picture of the
conditional distribution. The second part of the dissertation focuses on the flexible regression
setting of TPA families with the aim of conditional quantile curves and survival estimation.
Covariates can affect not only the location but also, more generally, the scale and shape of the
distribution of the survival time in a multi-parametric regression framework. We exploit the
local likelihood estimation technique when covariates come into play in the model through
non-parametric (completely unspecified) functional forms. In addition, we propose a general
profile (local) likelihood method to estimate the parametric and non-parametric components
in the case of a partially linear regression model. We investigate the method’s performance
through an extensive simulation study. In addition, the application of the proposed method
is discussed with clinical data examples.
In time-to-event analysis, many commonly used statistical methods assume that the covariate effects on a monotone transformation of the survival time are linear, and the regression coefficients are constant over time. For instance, the accelerated failure time model
estimates the linear covariate effects on the logarithmic scale of the survival time. In contrast,
the proportional hazards model assumes linearity on the hazard ratio. These assumptions,
however, might be chosen for their mathematical convenience, and the actual associations
in practical applications may be more complex than the prespecified linear structure of the
covariate effects. The third part of the work deals with a hybrid hazard (HH) model where
we consider a parametric TPA baseline hazard distribution with flexible regression settings.
We examine the covariate effects at the time-scale and hazard-scale changes in parametric, semi-parametric and non-parametric functional forms. The general hybrid hazard-based
model includes the three most commonly used survival models as subclasses: proportional
hazards (PH), accelerated failure time (AFT), and accelerated hazards (AH) models. We discuss in detail the estimation procedures in the general profile (local) likelihood technique.
We investigate the validity of the flexible HH model formulation and proposed estimation
methodology through a comprehensive Monte Carlo simulation study and demonstrate its
practical use in real data examples.In veel toepassingen van statistisch modelleren worden variabelen waarin we ge¨ınteresseerd
zijn slechts deels geobserveerd. E´en van dergelijke complexe data situaties zijn gecensureerde
gegevens. Deze komen in het bijzonder voor in overlevingsanalyse. In een context van rechtse
censurering is voor sommige individuen enkel geweten dat hun overlevingstijd groter is dan
de geobserveerde tijd. Deze thesis focust op statistische besluitvorming in een brede familie van twee-stuks asymmetrische (TPA) verdelingen in de context van flexibele kwantielregressie en hazard-gebaseerde modellen voor rechts gecensureerde overlevingsgegevens. Een
belangrijke eigenschap van deze familie is dat de locatieparameter overeenkomt met een
specifiek kwantiel van de verdeling. In het bijzonder geval van een symmetrische verdeling valt de locatieparameter samen met het gemiddelde. In het eerste deel van de thesis
focussen we op statistische besluitvorming voor een niet-voorwaardelijke setting binnen de
TPA familie van verdelingen. We onderzoeken de theoretische eigenschappen (consistentie
en asymptotische normaliteit) van maximum likelihood schatters voor de hele klasse van
TPA verdelingen, onder enkele noodzakelijke regulariteitsvoorwaarden op de verdeling. In
een simulatiestudie worden de eindige steekproefkwaliteiten van de methoden onderzocht.
Verder illustreren we het gebruik van de voorgestelde methoden op klinische en niet-klinische
data en vergelijken we hun prestatie met enkele bestaande overlevingsmodellen.
In klassieke regressieanalyse modelleert men het gemiddelde van een respons op basis
van een aantal covariaten. Men modelleert dus enkel het gemiddelde van een voorwaardelijke verdeling aan de hand van covariaten. Daarnaast kan men ook ge¨ınteresseerd zijn in de
volledige voorwaardelijke verdeling. Het tweede deel behandelt een flexibele regressiesetting
met TPA verdelingen met als doel het schatten van de kwantielfunctie en de overlevingskans.
In een regressiesetting kunnen covariaten zowel de locatie als de schaal en vorm van de
verdeling van de overlevingstijd be¨ınvloeden. We verkennen lokale maximum likelihood
schatters wanneer ook covariaten op een niet-parametrische manier in het model worden
opgenomen. Bovendien stellen we een algemene profile likelihood methode voor om zowel
de parametrische als niet-parametrische componenten te schatten in het geval van een deels
lineair regressiemodel. We onderzoeken de werking van de methoden in een uitgebreide
simulatiestudie en op enkele klinische data.
Vaak gebruikte statistische methoden in overlevingsanalyse veronderstellen dat de covariaten een linear effect hebben op de overlevingstijd via a monotone transformation, en dat de regressieco¨effici¨enten constant zijn in de tijd. In bijvoorbeeld een accelerated failure
time model hebben de covariaten een linear effect op het logaritme van de overlevingstijd.
In een proportional hazards model daarentegen geldt dit linear effect op de hazard functie
(ratio). Deze veronderstellingen worden misschien gemaakt omwille van de wiskundige eenvoud. In de praktijk kunnen de eigenlijke verbanden echter complexer zijn. Het derde deel
van de thesis beschouwt een hybride hazard model waarbij we een parametrische TPA basis
hazard verdeling veronderstellen met een flexibele regressiesetting. We onderzoeken de effecten van de covariaten in de tijds- en hazardschaal in parametrische, semi-parametrische
en niet-parametrische situaties. De algemene hybride hazardgebaseerde modellen omvatten
de drie meest gebruikte overlevingsmodellen: proportional hazard (PH), accelerated failure
time (AFT) en accelerated hazards (AH) modellen. We bespreken de schattingsprocedures
gebaseerd op de lokale profile likelihood techniek. Op basis van een simulatiestudie onderzoeken we de toepasbaarheid van de methoden. Daarnaast illustreren we het praktische
gebruik van de methoden via data voorbeelde
A hybrid hazard-based model using two-piece distributions
No full textCox proportional hazards model is widely used to study the relationship between the survival time of an event and covariates. Its primary objective is parameter estimation assuming a constant relative hazard throughout the entire follow-up time. The baseline hazard is thus treated as a nuisance parameter. However, if the interest is to predict possible outcomes like specific quantiles of the distribution (e.g. median survival time), survival and hazard functions, it may be more convenient to use a parametric baseline distribution. Such a parametric model should however be flexible enough to allow for various shapes of e.g. the hazard function. In this paper we propose flexible hazard-based models for right censored data using a large class of two-piece asymmetric baseline distributions. The effect of covariates is characterized through timescale changes on hazard progression and on the relative hazard ratio; and can take three possible functional forms: parametric, semi-parametric (partly linear) and non-parametric. In the first case, the usual full likelihood estimation method is applied. In the semi-parametric and non-parametric settings a general profile (local) likelihood estimation approach is proposed. An extensive simulation study investigates the finite-sample performances of the proposed method. Its use in data analysis is illustrated in real data examples.The authors thank the reviewers for their valuable comments that led to an improvement
of the manuscript. The second author gratefully acknowledges support from Research Grant C16/20/002
project of the Research Fund KU Leuven
Two-piece distribution based semi-parametric quantile regression for right censored data
No full textWidely used methods such as Cox proportional hazards, accelerated failure time, and Bennet proportional odds models do not model the quantiles directly, but rather allow to assess the influence of the covariates only on the location of the distribution. Quantile regression allows to assess the effects of covariates, not only on a location parameter (such as a mean or median) but also on specific percentiles of the conditional distribution. In recent years, a large family of flexible two-piece asymmetric distributions where the location parameter coincides with a specific quantile of the distribution has been studied. In a conditional (regression) setting the use of such a family of two-piece asymmetric distributions has only been investigated in the complete data case in the literature. In this paper, we propose a semi-parametric procedure to estimate the conditional quantile curves of two-piece asymmetric distributions based on right censored survival data. We use a local likelihood estimation technique in a multi-parameter functional form, via which the effect of a covariate on the location, scale, and index of the conditional survival distribution can be assessed. The finite sample performance of the estimators is investigated via simulations, and the methodology is illustrated on real data examples.The authors are grateful to an Associate Editor and two reviewers for their comments which led to an improvement of the manuscript. We thank the authors of Christou and Akritas (2019) to provide us with the R code to calculate their estimator in the SIQR model. The second author gratefully acknowledges support from Research Grant FWO G0D6619N of the Flemish Science Foundation, and from the C16/20/002 project of the Research Fund KU Leuven. The resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government
The spatio-temporal modeling of prostate cancer in Limburg
No full textThe main aim of this study was to assess the evolution of prostate cancer disease risk in Limburg, found in the north-east of Belgium. The data analyzed include yearly incidence counts from prostate cancer, which was subdivided according to 18 age groups in the male population as observed in each of these municipalities during the 1996-2005 period in Limburg. To address these main objectives, the data were analysed using several Bayesian hierarchical models, which accounts for the spatial and temporal effects as random effects, through prior distributions. In general, we examined four models for the spatial only data, and thirteen inseparable space-time interactions with two separable models, for the spatio-temporal dataset. The results of the Bayesian hierarchical models have typically been presented in the form of maps displaying the mean of the posterior distribution of the relative risk for each municipality. In this particular study, the results suggested that the time trends for every municipality do not rely on a parametric shape, but flexible to describe the variety of time trends that arise in the data. In conclusion, we have seen that sharing information among municipalities has been shown to improve the model more than sharing information among periods. This suggested in general that the spatial dependence is very important to describe the behavior of the risk in this specific data, indeed higher than the temporal one
The spatio-temporal modeling of prostate cancer in Limburg
No full textThe main aim of this study was to assess the evolution of prostate cancer disease risk in Limburg, found in the north-east of Belgium. The data analyzed include yearly incidence counts from prostate cancer, which was subdivided according to 18 age groups in the male population as observed in each of these municipalities during the 1996-2005 period in Limburg. To address these main objectives, the data were analysed using several Bayesian hierarchical models, which accounts for the spatial and temporal effects as random effects, through prior distributions. In general, we examined four models for the spatial only data, and thirteen inseparable space-time interactions with two separable models, for the spatio-temporal dataset. The results of the Bayesian hierarchical models have typically been presented in the form of maps displaying the mean of the posterior distribution of the relative risk for each municipality. In this particular study, the results suggested that the time trends for every municipality do not rely on a parametric shape, but flexible to describe the variety of time trends that arise in the data. In conclusion, we have seen that sharing information among municipalities has been shown to improve the model more than sharing information among periods. This suggested in general that the spatial dependence is very important to describe the behavior of the risk in this specific data, indeed higher than the temporal one
Estimated incidence of hospitalizations and deaths attributable to Respiratory Syncytial Virus infections among adults in Germany between 2015 and 2019
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© Pfizer Inc, CC-BY-NC 2024 </p
Estimated Incidence of Hospitalizations Attributable to RSV Infection Among Adults in Ontario, Canada, Between 2013 and 2019
No full textAbstract Introduction Adult respiratory syncytial virus (RSV) burden is underestimated due to non-specific symptoms, limited standard-of-care and delayed testing, reduced diagnostic test sensitivity—particularly when using single diagnostic specimen—when compared to children, and variable test sensitivity based on the upper airway specimen source. We estimated RSV-attributable hospitalization incidence among adults aged ≥ 18 years in Ontario, Canada, using a retrospective time-series model-based approach. Methods The Institute for Clinical Evaluative Sciences data repository provided weekly numbers of hospitalizations (from 2013 to 2019) for respiratory, cardiovascular, and cardiorespiratory disorders. The number of hospitalizations attributable to RSV was estimated using a quasi-Poisson regression model that considered probable overdispersion and was based on periodic and aperiodic time trends and viral activity. As proxies for viral activity, weekly counts of RSV and influenza hospitalizations in children under 2 years and adults aged 60 years and over, respectively, were employed. Models were stratified by age and risk group. Results In patients ≥ 60 years, RSV-attributable incidence rates were high for cardiorespiratory hospitalizations (range [mean] in 2013–2019: 186–246 [215] per 100,000 person-years, 3‒4% of all cardiorespiratory hospitalizations), and subgroups including respiratory hospitalizations (144–192 [167] per 100,000 person-years, 5‒7% of all respiratory hospitalizations) and cardiovascular hospitalizations (95–126 [110] per 100,000 person-years, 2‒3% of all cardiovascular hospitalizations). RSV-attributable cardiorespiratory hospitalization incidence increased with age, from 14–18 [17] hospitalizations per 100,000 person-years (18–49 years) to 317–411 [362] per 100,000 person-years (≥ 75 years). Conclusions Estimated RSV-attributable respiratory hospitalization incidence among people ≥ 60 years in Ontario, Canada, is comparable to other incidence estimates from high-income countries, including model-based and pooled prospective estimates. Recently introduced RSV vaccines could have a substantial public health impact
