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1.
PURPOSE: To compare adjusted effects of drug treatment for hypertension on the risk of stroke from propensity score (PS) methods with a multivariable Cox proportional hazards (Cox PH) regression in an observational study with censored data. METHODS: From two prospective population-based cohort studies in The Netherlands a selection of subjects was used who either received drug treatment for hypertension (n = 1293) or were untreated 'candidates' for treatment (n = 954). A multivariable Cox PH was performed on the risk of stroke using eight covariates along with three PS methods. RESULTS: In multivariable Cox PH regression the adjusted hazard ratio (HR) for treatment was 0.64 (CI(95%): 0.42, 0.98). After stratification on the PS the HR was 0.58 (CI(95%): 0.38, 0.89). Matching on the PS yielded a HR of 0.49 (CI(95%): 0.27, 0.88), whereas adjustment with a continuous PS gave similar results as Cox regression. When more covariates were added (not possible in multivariable Cox model) a similar reduction in HR was reached by all PS methods. The inclusion of a simulated balanced covariate gave largest changes in HR using the multivariable Cox model and matching on the PS. CONCLUSIONS: In PS methods in general a larger number of confounders can be used. In this data set matching on the PS is sensitive to small changes in the model, probably because of the small number of events. Stratification, and covariate adjustment, were less sensitive to the inclusion of a non-confounder than multivariable Cox PH regression. Attention should be paid to PS model building and balance checking.  相似文献   

2.
ABSTRACT

Background: Awareness of the economic burden of diabetes has led to a number of studies on economic issues. However, comparison among cost-of-illness studies is problematic because different methods are used to arrive at a final cost estimate.

Objective: The aim of the study is to show how estimates of hospitalisation costs for diabetic patients can vary significantly in relation to the statistical method adopted in the analysis.

Research design and methods: The study analyses diabetic patients’ costs as a function of demographic and clinical covariates, by applying the following statistical survival models: the parametric survival model assuming Weibull distribution, the Cox proportional hazard (PH) model and the Aalen additive regression for modelling costs. The Aalen approach is robust both for the non proportionality in hazard and for departures from normality. In addition it is able to easily model the effect of covariates on the extreme costs. This cost analysis is based on data collected for a retrospective observational study analysing repeated hospitalisations (N = 4816) in a cohort of 3892 diabetic patients.

Results: There is agreement in all models with the effects of the considered covariates (age, sex, duration of disease and presence of other pathologies). An effect of over- or under-estimation, according to the chosen model due to arguably inappropriate model fitting, was observed, being more evident for some specific profiles of the patients, and overall accounting for as much as 20% of the estimated effect. The Aalen model was able to cope with all the other models in furnishing unbiased estimates with the advantage of a greater flexibility in representing the covariates’ effect on the cost process.

Conclusions: An appropriate choice of the model is crucial in avoiding misinterpretation of cost determinants of type 2 diabetes care. For our data set the Aalen model proved itself to be a realistic and informative way to characterise the effect of covariates on costs.  相似文献   

3.
Sample size determination is essential during the planning phases of a study. When the study endpoint is the time to an event, Cox proportional hazard model is the traditional technique to analyze the effects of covariates on survival time. In contrast to the proportional hazard model, the additive hazard (AH) model specifies that the effect of covariates additively increases or decreases the hazard function. The popularity of this model is that it gives a more intuitive interpretation without the proportional hazard assumption. Because there is no literature estimating the required sample size based on the AH model, we provide a flexible formula for calculating the required sample size. The proposed formula incorporates time-independent and time-dependent effects of covariates without complicated mathematical calculations. The performance of the method was evaluated by extensive simulations. Finally, some pilot studies are shown to illustrate the applications.  相似文献   

4.
Identification and quantification of covariate relations is often an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modelling. The covariate model is regularly built in a stepwise manner. With such methods, selection bias may be a problem if only statistically significant covariates are accepted into the model. Competition between multiple covariates may further increase selection bias, especially when there is a moderate to high correlation between the covariates. This can also result in a loss of power to find the true covariates. The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and system-related quantities. Data sets with 20-1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation to the other four covariates, respectively. Data sets, in which each individual had two or three PK observations, were simulated using a one-compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter-individual variability in the structural model parameters were also introduced to the simulation model. A total of 7400 replicate data sets were simulated independently for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified P-value) the different covariates, along with the estimated covariate coefficient, was recorded. The results show that selection bias is very high for small data sets (< or = 50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to be more than twice its true value, making the covariate model useless for predictive purposes. Surprisingly, even though competition from false covariates caused substantial loss in the power of selecting the true covariate, the already high selection bias increased only marginally. This means that the bias due to competition is negligible if statistical significance is also required for covariate selection. Bias and predictive performance are direct functions of power, only indirectly affected by study design and system-related quantities. Mainly because of selection bias, low-powered covariates can be expected to harm the predictive performance when selected. For the same reason these low-powered covariates may falsely appear to be clinically relevant when selected. If the aim of an analysis is predictive modelling, we do not recommend stepwise selection or significance testing of covariates to be performed on small or moderately sized data sets (<50-100 subjects).  相似文献   

5.
Abstract

The treatment effect of a therapeutic product on a binary endpoint is often expressed as the difference in proportions of subjects with the outcome of interest between the treated and control groups of a clinical trial. Analysis of the proportional difference and construction of the associated confidence interval (CI) is often complicated due to the baseline covariate(s) being associated with the primary endpoint. Analysis adjusting for such baseline covariate(s) generally improves efficiency of hypothesis testing and precision of treatment effect estimation, and avoids possible bias caused by baseline covariate imbalances. Most existing literatures focus on constructing unadjusted or categorical covariate(s) adjusted only CI, which provides very limited advice on how different statistical methods perform and which method is optimal in terms of constructing both categorical and continuous baseline covariate(s) adjusted CI for proportional difference. We review and compare the performance of three commonly used model-based methods as well as the traditional nonparametric weighted-difference methods for the construction of covariate-adjusted CI for proportional difference via a real data application and simulations. The coverage of 95% CI, Type I error control, and power are examined. We also examine the factors leading to the model convergence failure in different scenarios via simulations.  相似文献   

6.
Automated Covariate Model Building Within NONMEM   总被引:6,自引:0,他引:6  
Purpose. One important task in population pharmacokinetic/pharmacodynamic model building is to identify the relationships between the parameters and demographic factors (covariates). The purpose of this study is to present an automated procedure that accomplishes this. The benefits of the proposed procedure over other commonly used methods are (i) the covariate model is built for all parameters simultaneously, (ii) the covariate model is built within the population modeling program (NONMEM) giving familiar meaning to the significance levels used, (iii) it can appropriately handle covariates that varies over time and (iv) it is not dependent on the quality of the posterior Bayes estimates of the individual parameter values. For situations in which the computer run-times are a limiting factor, a linearization of the non-linear mixed effects model is proposed and evaluated. Methods. The covariate model is built in a stepwise fashion in which both linear and non-linear relationships between the parameters and covariates are considered. The linearization is basically a linear mixed effects model in which the population predictions and their derivatives with respect to the parameters are fixed from a model without covariates. The stepwise procedure as well as the linearization was evaluated using simulations in which the covariates were taken from a real data set. Results. The covariate models identified agreed well with what could be expected based on the covariates that were actually supported in each of the simulated data sets. The predictive performance of the linearized model was close to that of the non-linearized model. Conclusions. The proposed procedure identifies covariate models that are close to the model supported by the data set as well as being useful in the prediction of new data. The linearized model performs nearly as well as the non-linearized model.  相似文献   

7.
To characterise the pharmacokinetics of dofetilide in patients and to identify clinically relevant parameter–covariate relationships. To investigate three different modelling strategies in covariate model building using dofetilide as an example: (1) using statistical criteria only or in combination with clinical irrelevance criteria for covariate selection, (2) applying covariate effects on total clearance or separately on non-renal and renal clearances and (3) using separate data sets for covariate selection and parameter estimation. Pooled concentration-time data (1,445 patients, 10,133 observations) from phase III clinical trials was used. A population pharmacokinetic model was developed using NONMEM. Stepwise covariate model building was applied to identify important covariates using the strategies described above. Inclusion and exclusion of covariates using clinical irrelevance was based on reduction in interindividual variability and changes in parameters at the extremes of the covariate distribution. Parametric separation of the elimination pathways was accomplished using creatinine clearance as an indicator of renal function. The pooled data was split in three parts which were used for covariate selection, parameter estimation and evaluation of predictive performance. Parameter estimations were done using the first-order (FO) and the first-order conditional estimation (FOCE) methods. A one-compartment model with first order absorption adequately described the data. Using clinical irrelevance criteria resulted in models containing less parameter–covariate relationships with a minor loss in predictive power. A larger number of covariates were found significant when the elimination was divided into a renal part and a non-renal part, but no gain in predictive power could be seen with this data set. The FO and FOCE estimation methods gave almost identical final covariate model structures with similar predictive performance. Clinical irrelevance criteria may be valuable for practical reasons since stricter inclusion/exclusion criteria shortens the run times of the covariate model building procedure and because only the covariates important for the predictive performance are included in the model. K. Tunblad and L. Lindbom contributed equally to the work.  相似文献   

8.
A frequent occurrence in medical research is that a patient is subject to different causes of failure, where each cause is known as a competing risk. The cumulative incidence curve is a proper summary curve, showing the cumulative failure rates over time due to a particular cause. A common question in medical research is to assess the covariate effects on a cumulative incidence function. The standard approach is to construct regression models for all cause-specific hazard rate functions and then model a covariate-adjusted cumulative incidence curve as a function of all cause-specific hazards for a given set of covariates. New methods have been proposed in recent years, emphasizing direct assessment of covariate effects on cumulative incidence function. Fine and Gray proposed modeling the effects of covariates on a subdistribution hazard function. A different approach is to directly model a covariate-adjusted cumulative incidence function, including a pseudovalue approach by Andersen and Klein and a direct binomial regression by Scheike, Zhang and Gerds. In this paper, we review the standard and new regression methods for modeling a cumulative incidence function, and give the sources of computer packages/programs that implement these regression models. A real bone marrow transplant data set is analyzed to illustrate various regression methods.  相似文献   

9.
Purpose. One of the main objectives of the nonlinear mixed effects modeling is to provide rational individualized dosing strategies by explaining the interindividual variability using intrinsic and/or extrinsic factors (covariates). The aim of the current study was to evaluate, using computer simulations and real data, methods for estimating the exact significance level for including or excluding a covariate during model building. Methods. Original data were simulated using a simple one-compartment pharmacokinetic model with (full model) or without (null model) covariates (one or two). The covariate values in the original data were resampled (using either permutations or parametric bootstrap methods) to generate data under the null hypothesis that there is no covariate effect. The original and permuted data were fitted to null and full models, using first-order and first-order condition estimation (with or without interaction) methods in NONMEM, to compare the asymptotic and conditional p-value. Target log-likelihood ratio cutoffs for assessing covariate effects were derived. Results. The simulations showed that for sparse as well as dense data, the first-order condition estimation methods yielded the best results while the first-order method performs somewhat better for sparse data. Depending on the modeling objective, the appropriate asymptotic p-value can be substituted for the conditional significance level. Target log-likelihood ratio cutoffs should be determined separately for each covariate when exact p-values are important. Conclusions. Resampling methods can be employed to estimate the exact significance level for including a covariate during nonlinear mixed effects model building. Some reasonable inferences can be drawn for potential application to design future population analyses.  相似文献   

10.
11.
The Cox model is the recognized industry standard when designing and analyzing randomized clinical trials with right-censored data. As the model is based on the proportional hazards (PH) assumption, if the hazard ratio changes over time, as often occurs during long-term studies, the interpretation of the Cox hazard ratio becomes problematic. Furthermore, the Cox model is not powerful in the event of crossing hazards. Here, we consider a range of tests to compare two treatment groups in randomized clinical trials where the PH assumption is in doubt. The proposed methods are evaluated on simulated data and compared using data from a cancer clinical trial.  相似文献   

12.
It is a common practice to analyze AIDS longitudinal data using nonlinear mixed-effects (NLME) models with normal distribution for HIV dynamics. Normality of model errors may unrealistically obscure important features of subject variations. To partially explain between- and within-subject variations, covariates are usually introduced in such models; some covariates, however, may be often measured with substantial errors. This article, motivated by an AIDS clinical study, discusses a Bayesian NLME joint modeling approach to viral dynamic models with skew-t distribution in the presence of covariate measurement error. In this model, we fully integrate viral load response, time-varying CD4 covariate with measurement error, and time-dependent drug efficacy, which is a function of multiple treatment factors, into the data analysis. Thus, the purpose of this article is to demonstrate our models and methods with application to an AIDS clinical trial study. The results suggest that modeling HIV dynamics and virologic responses with consideration of covariate measurement error and time-varying clinical factors may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to antiretroviral treatment and to help evaluation of clinical trial design in existing therapies.  相似文献   

13.
AIM: If appropriately accounted for in a pharmacokinetic (PK)-pharmacodynamic (PD) model, time-varying covariates can provide additional information to that obtained from time-constant covariates. The aim was to present and apply two models applicable to time-varying covariates that capture such additional information. METHODS: The first model estimates different covariate-parameter relationships for within- and between-individual variation in covariate values, by splitting the standard covariate model into a baseline covariate (BCOV) effect and a difference from baseline covariate (DCOV) effect. The second model allows the magnitude of the covariate effect to vary between individuals, by inclusion of interindividual variability in the covariate effect. The models were applied to four previously analysed data sets. RESULTS: The models were applied to 10 covariate-parameter relationships and for three of these the first extended model resulted in a significant improvement of the fit. Even when this model did not improve the fit significantly, it provided useful information because the standard covariate model, which assumes within- and between-patient covariate relationships of the same magnitude, was only supported by the data in four cases. The inclusion of BCOV was not supported in two cases and DCOV was unnecessary in three cases. In one case, significantly different, nonzero, relationships were found for DCOV and BCOV. The second extended model was found to be significant for four of the 10 covariate-parameter relationships. CONCLUSIONS: On the basis of the examples presented, traditionally made simplifications of covariate-parameter relationships are often inadequate. Extensions to the covariate-parameter relationships that include time-varying covariates have been developed, and their appropriateness and benefits have been described.  相似文献   

14.
ABSTRACT

In traditional survival analyses, hazard ratio (HR) is commonly used to evaluate treatment effects. However, HR may not be easy to interpret. Restricted mean survival time is a viable alternative to HR, particularly when the proportional hazards assumption is not satisfied. We developed a conditional restricted mean survival time (CRMST) estimator for a time interval of interest using counting process. The variance of CRMST was estimated using a perturbation re-sampling method for asymptotic normality. The utility of our CRMST seems promising based on comprehensive simulation studies and a real data case study.  相似文献   

15.
Abstract

Following the validation and replication of the Harvard Six Cities Study (Krewski et al., this issue), we conducted a wide range of sensitivity analyses to explore the observed associations between long-term exposure to fine particle or sulfate air pollution and mortality. We examined the impact of alternative risk models on estimates of risk, taking into account covariates not included in the original analyses. These risk models provided a basis for identifying covariates that may confound or modify the association between fine particle or sulfate air pollution and mortality, and for identifying sensitive population subgroups. The possibility of confounding due to occupational exposures was also investigated. Residence histories were coded for the study subjects and were used to examine temporal patterns of exposure and risk. Our sensitivity analyses showed the mortality risk estimates for fine particle and sulfate air pollution to be highly robust against alternative risk models of the Cox proportional hazards family, including models with additional covariates from the original questionnaires not included in the original published analyses. There was limited evidence of departures from the proportional hazards assumption. Flexible exposure-response models provided some evidence of departures from linearity at both low and high sulfate concentrations. Incorporating information on changes over time in cigarette smoking and body mass index had little effect on the association between fine particles and mortality. There was limited evidence of variation in risk with attained age, gender, smoking status, occupational exposure to dust and fumes, marital status, heart or lung diseases, or lung function. However, air pollution risk did appear to decreasing with increasing educational attainment. Extensive adjustment for occupation using aggregate indices of occupational “dirtiness” and occupational exposure to known lung carcinogens had little impact on the mortality risks associated with particulate air pollution. Our evaluation of population mobility indicated that relatively few subjects moved from their original city of residence. Attempts to identify critical exposure time windows were limited by the lack of marked interindividual variation in temporal exposure patterns throughout the study period. Overall, this extensive sensitivity analysis both supported the conclusions reached by the original investigators and demonstrated the robustness of these conclusions to alternative analytic approaches.  相似文献   

16.
Covariate models for population pharmacokinetics and pharmacodynamics are often built with a stepwise covariate modelling procedure (SCM). When analysing a small dataset this method may produce a covariate model that suffers from selection bias and poor predictive performance. The lasso is a method suggested to remedy these problems. It may also be faster than SCM and provide a validation of the covariate model. The aim of this study was to implement the lasso for covariate selection within NONMEM and to compare this method to SCM. In the lasso all covariates must be standardised to have zero mean and standard deviation one. Subsequently, the model containing all potential covariate–parameter relations is fitted with a restriction: the sum of the absolute covariate coefficients must be smaller than a value, t. The restriction will force some coefficients towards zero while the others are estimated with shrinkage. This means in practice that when fitting the model the covariate relations are tested for inclusion at the same time as the included relations are estimated. For a given SCM analysis, the model size depends on the P-value required for selection. In the lasso the model size instead depends on the value of t which can be estimated using cross-validation. The lasso was implemented as an automated tool using PsN. The method was compared to SCM in 16 scenarios with different dataset sizes, number of investigated covariates and starting models for the covariate analysis. Hundred replicate datasets were created by resampling from a PK-dataset consisting of 721 stroke patients. The two methods were compared primarily on the ability to predict external data, estimate their own predictive performance (external validation), and on the computer run-time. In all 16 scenarios the lasso predicted external data better than SCM with any of the studied P-values (5%, 1% and 0.1%), but the benefit was negligible for large datasets. The lasso cross-validation provided a precise and nearly unbiased estimate of the actual prediction error. On a single processor, the lasso was faster than SCM. Further, the lasso could run completely in parallel whereas SCM must run in steps. In conclusion, the lasso is superior to SCM in obtaining a predictive covariate model on a small dataset or on small subgroups (e.g. rare genotype). Run in parallel the lasso could be much faster than SCM. Using cross-validation, the lasso provides a validation of the covariate model and does not require the user to specify a P-value for selection.  相似文献   

17.
Latent covariates are covariates that are known to exist but are either observable but unavailable or unobservable at the time of the clinical study. Designs to account for latent covariates must incorporate both uncertainty in the prevalence of the covariate and the data-type of the covariate. The informativeness of the covariate will then depend on whether the covariate data is continuous, ordinal or nominal. In this work we consider designs for latent covariates that may either directly influence the parameter of interest, or indirectly via actions on an observable covariate which then influences the parameter of interest. We consider a motivating example based on the effect of a genetic polymorphism on the influence of a continuous covariate (age) on drug clearance (CL). The polymorphism could take the case of a haplotype with many variant alleles, or a copy number variation in genes with different phenotypic expressions which could be treated as continuous data, or as a bi- or tri-allelic single nucleotide polymorphism that could form either an ordinal or nominal covariate on drug CL. The aim of this study was to investigate designs for clinical studies for latent covariates that accommodate both unknown prevalence and unknown data-type. Initially, the informativeness of a covariate was explored using linear regression assuming the three data-types continuous, ordinal and nominal. The linear covariate model was then considered within a nonlinear mixed effects modelling framework. Two simulation scenarios were considered: (1) the influence of the latent covariate directly on the parameter of interest and (2) the influence of the latent covariate on an observable non-latent continuous covariate, which was assumed to follow a normal or stratified distribution, and the effect of this covariate on the parameter of interest. A power analysis for population PK modelling (1) where the latent covariate had direct influence on the parameter also showed similar behaviour to the linear regression solution. When the influence of the latent covariate was mediated via another observable non-latent continuous covariate, the power for the continuous model was highest but the power of the ordinal model was indistinguishable from that of the nominal model. Stratification of the observable non-latent continuous covariate did not appreciably change the power to identify the latent covariate from that when we assumed the observable covariate conformed to a normal distribution. It was found that parameter estimation is generally at least 1.5 to 7 fold more precise for continuous models than for categorical models.  相似文献   

18.
In many clinical trials, subjects are followed for two stages of outcomes, and it is of interest to compare the incidence of each outcome between two randomized groups. The outcome of the first stage may influence the outcome of the second stage. Moreover, the relative risks of the two outcomes may be linked, with the time-dependent profile of relative risk for the second outcome functionally dependent on that of the first. For example, during exposure to HIV, virologic and host factors simultaneously impact the probability of infection and the subsequent viral trajectories, and the efficacy of a tested vaccine to prevent infection and to prevent viral failure may work in concert. We address this problem by modeling the relationship between the stage two hazard function and covariates via Cox's proportional hazards model (Cox, 1972), with the stage one log-hazard ratio theta(*) at the first event time Tl, included as a covariate. With theta(*) estimated using three methods, 1) nonparametric kernel smoothing; 2) locally parametric penalized splines; and 3) fully parametric cubic linear splines, we subsequently develop inference procedures for the regression parameter in the stage two Cox model based on each of the estimator of theta(*). The inferential procedures are studied in simulations and are illustrated with application to data from the world's first preventive HIV vaccine efficacy trial.  相似文献   

19.
In the context of randomized clinical trials with time-to-event outcomes, estimates of covariate-adjusted log hazard ratios for comparing two treatments are obtained via nonparametric analysis of covariance by forcing the difference in means for covariables to zero. The method avoids the assumption of proportional hazards for each of the covariates, and it provides an adjusted analysis for the same population average treatment effect that the unadjusted analysis addresses. It is primarily useful in regulatory clinical trials that require analyses to be specified a priori. To illustrate, the method is applied to a study of lung disease with multivariate time-to-event outcomes.  相似文献   

20.
IntroductionSeveral studies have shown increased incidence, recurrence, and severity of Clostridium difficile infection (CDI) over the last decade. Patients with inflammatory bowel disease (IBD) who develop CDI are more prone to morbidity and mortality than CDI in patients without IBD. This study seeks to evaluate whether IBD patients who use vedolizumab are at increased risk of CDI compared to IBD patients using other therapies.MethodsThis was a retrospective cohort study, and 684 patients with confirmed IBD (228 on vedolizumab, 228 on anti-TNF, and 228 on 5- Aminosalicylates acid therapy) were enrolled from January 2009 to August 2019 at a tertiary referral IBD center at McMaster University Medical Centre (MUMC) in Hamilton, Ontario, Canada. The primary outcome was time to the development of CDI in IBD patients using different therapies. Secondary outcomes included rates of CDI and the association between baseline variables and risk of CDI. A Cox proportional hazards (PH) model was used to evaluate baseline factors and development of CDI.ResultThere was no difference in time to CDI between the three treatment groups (log rank p-value 0.37). CDI occurred in 16 patients (2.3%), specifically four patients (1.75%) in the vedolizumab group, four patients (1.75%) in the anti-TNF group, and eight patients (3.5%) in the 5-ASA group. The Cox PH model found current smoking, older age, and concomitant immunomodulator use as risk factors for CDI, after adjustment for other covariates. Vedolizumab was not associated with increased risk of CDI in the model.ConclusionBiologic therapy with vedolizumab or anti-TNF did not impact risk of CDI. Risk factors for CDI in IBD patients included smoking, older age at the onset of medication, and immunomodulator therapy. Clinicians should have high degree of suspicion for CDI in IBD patients presenting with diarrhea, particularly in those with risk factors identified in this study.  相似文献   

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