A comparison of two methods for the estimation of precision with incomplete longitudinal data, jointly modelled with a time-to-event outcome

Delineating the third age: joint models of older people's quality of life and attrition in Britain 2002-2010

OBJECTIVES

In the public mind, later life is being transformed by the emerging possibility of a flourishing third age with sustained quality of life. We draw trajectories of life quality measured using CASP-19 over eight years. We refine these trajectories by jointly modelling attrition, since older people tend to leave longitudinal studies (attrite) not at random.

METHODS

Growth curve models are applied to the English Longitudinal Study of Ageing waves 1 to 5. Then joint model is estimated where attrition is considered. Extensive predictors are entered including demographic attributes, social and economic status, health conditions, and behaviours.

RESULTS

Strong non-linear age trajectory of life quality is revealed by the growth curve models where the peak is achieved in the late 60s. Then the joint model uncovers the peak somewhat later in time, and also reveals secular improvement in life quality experienced by recent cohorts. Sharp estimates for many predictors of higher levels of life quality are also found.

CONCLUSION

For the first time, the trajectories of life quality in the third age are drawn and improvement across cohorts is demonstrated. The contributions are estimated for predictors amenable to intervention such as social capital. This can help in policy discussion on improving the lives of older people in the third age.

Risk factors for relapse of antineutrophil cytoplasmic antibody-associated vasculitis

OBJECTIVE

To determine the association between characteristics at diagnosis and the time to first relapse in a large cohort of patients with antineutrophil cytoplasmic antibody-associated vasculitis (AAV).

METHODS

We studied long-term followup data from 4 clinical trials that included newly diagnosed patients with a broad spectrum of AAV severity and manifestations. Patient and disease characteristics at baseline were used in competing risk regression models with relapse as the event of interest and death as the competing event.

RESULTS

We assessed 535 patients with 1,804 patient-years at risk of relapse. At diagnosis, the median age was 60.7 years (interquartile range [IQR] 48.8-69.1 years), 284 patients (53%) had granulomatosis with polyangiitis (Wegener's), and the median creatinine level was 203 μmoles/liter (IQR 97-498). A total of 201 patients (38%) experienced a relapse and 133 patients (25%) died, 96 of whom had not had prior relapse. Anti-proteinase 3 antibodies (subhazard ratio [sHR] 1.62 [95% confidence interval 1.39-1.89]) and cardiovascular involvement (sHR 1.59 [95% confidence interval 1.07-2.37]) were independently associated with a higher risk of relapse. Compared with patients with a creatinine level ≤100 μmoles/liter, patients with higher creatinine levels had a lower risk of relapse (sHR 0.81 [95% confidence interval 0.77-0.85] for a creatinine level of 101-200 μmoles/liter; sHR 0.39 [95% confidence interval 0.22-0.69] for a creatinine level >200 μmoles/liter).

CONCLUSION

Relapse of disease is common for patients with AAV. A creatinine level >200 μmoles/liter at the time of diagnosis is strongly associated with a reduced risk of relapse and may help guide monitoring and treatment of patients with AAV.

[Regression modeling strategies]

Multivariable regression models are widely used in health science research, mainly for two purposes: prediction and effect estimation. Various strategies have been recommended when building a regression model: a) use the right statistical method that matches the structure of the data; b) ensure an appropriate sample size by limiting the number of variables according to the number of events; c) prevent or correct for model overfitting; d) be aware of the problems associated with automatic variable selection procedures (such as stepwise), and e) always assess the performance of the final model in regard to calibration and discrimination measures. If resources allow, validate the prediction model on external data.

Joint modeling of multivariate longitudinal data and the dropout process in a competing risk setting: application to ICU data

BACKGROUND

Joint modeling of longitudinal and survival data has been increasingly considered in clinical trials, notably in cancer and AIDS. In critically ill patients admitted to an intensive care unit (ICU), such models also appear to be of interest in the investigation of the effect of treatment on severity scores due to the likely association between the longitudinal score and the dropout process, either caused by deaths or live discharges from the ICU. However, in this competing risk setting, only cause-specific hazard sub-models for the multiple failure types data have been used.

METHODS

We propose a joint model that consists of a linear mixed effects submodel for the longitudinal outcome, and a proportional subdistribution hazards submodel for the competing risks survival data, linked together by latent random effects. We use Markov chain Monte Carlo technique of Gibbs sampling to estimate the joint posterior distribution of the unknown parameters of the model. The proposed method is studied and compared to joint model with cause-specific hazards submodel in simulations and applied to a data set that consisted of repeated measurements of severity score and time of discharge and death for 1,401 ICU patients.

RESULTS

Time by treatment interaction was observed on the evolution of the mean SOFA score when ignoring potentially informative dropouts due to ICU deaths and live discharges from the ICU. In contrast, this was no longer significant when modeling the cause-specific hazards of informative dropouts. Such a time by treatment interaction persisted together with an evidence of treatment effect on the hazard of death when modeling dropout processes through the use of the Fine and Gray model for sub-distribution hazards.

CONCLUSIONS

In the joint modeling of competing risks with longitudinal response, differences in the handling of competing risk outcomes appear to translate into the estimated difference in treatment effect on the longitudinal outcome. Such a modeling strategy should be carefully defined prior to analysis.

Robustness of a parametric model for informatively censored bivariate longitudinal data under misspecification of its distributional assumptions: A simulation study

Repeated measurements of surrogate markers are frequently used to track disease progression, but these series are often prematurely terminated due to disease progression or death. Analysing such data through standard likelihood-based approaches can yield severely biased estimates if the censoring mechanism is non-ignorable. Motivated by this problem, we have proposed the bivariate joint multivariate random effects (JMRE) model, which has shown that when correctly specified it performs well in terms of bias reduction and precision. The bivariate JMRE model is fully parametric and belongs to the class of shared parameters joint models where a survival model for the dropouts and a mixed model for the markers' evolution are linked through a multivariate normal distribution of random effects. As in every parametric model, robustness under violations of its distributional assumptions is of great importance. In this study we generated 500 simulated data sets assuming that random effects jointly follow a heavy-tailed distribution, two skewed distributions or a mixture of two normal distributions. Moreover, we generated data where level-1 errors or residuals in the survival part of the model follow a skewed distribution. Further sensitivity analysis on the effects of reduced sample size, increased level-1 variances and altered fixed effects values was also performed. We found that fixed effects estimates are almost unaffected, but their standard errors (SEs) may be underestimated especially under heavily skewed distributions. The proposed model seems robust enough, but its performance on smaller data sets or under more extreme departures of its assumptions needs further investigation.

Spontaneous control of viral load and CD4 cell count progression among HIV-1 seroconverters

OBJECTIVES

To identify factors associated with sustained undetectable viraemia after HIV-1 seroconversion in treatment-naive patients, and to describe concomitant CD4 cell count progression.

METHODS

Seroconverters enrolled in CASCADE were assumed to control viraemia if at least two consecutive viral load measurements were < 400/500 copies/ml without treatment. Factors associated with undetectable viraemia were identified through a logistic regression. A joint model was used to describe simultaneously the CD4 cell count progression during and after that period and to identify factors associated with sustained undetectable viraemia.

RESULTS

Of 2176 seroconverters, 145 (6.7%) spontaneously controlled viraemia. Women were more likely than men to achieve undetectable viraemia [adjusted odds ratio (OR), 2.12; 95% confidence interval (CI), 1.49-3.12] unlike patients who reported a symptomatic primary infection (adjusted OR, 0.58; 95% CI, 0.36-0.94). AIDS and death rates were significantly lower in patients achieving undetectable viraemia than in the others. The median period of undetectable viraemia was 11.2 months; on average, CD4 cell counts remained stable during that period, and decreased with a mean rate of 5 cells/microl per month thereafter. High CD4 cell count at the beginning of undetectable viraemia and non-symptomatic primary infection favoured the preservation of undetectable viraemia.

CONCLUSION

A small proportion of seroconverters appeared to be able to control HIV viraemia spontaneously, mostly those without seroconversion illness and within a few years following seroconversion; this is associated with the benefits of slower CD4 cell count decline and improved long-term prognosis. Such persons should be targeted for in depth investigation.

Differences in HIV RNA levels before the initiation of antiretroviral therapy among 1864 individuals with known HIV-1 seroconversion dates

OBJECTIVE

To assess the effects of sex, risk group, age at and year of seroconversion (SC), and presentation during acute infection on HIV RNA trends before antiretroviral therapy (ART) initiation.

METHODS

Multiple HIV RNA measurements from 1864 individuals with reliably estimated dates of SC, aged >/= 15 years at SC were studied using random effects models. Models were adjusted for selective HIV RNA data truncation due to ART initiation or AIDS development and for HIV RNA quantification assay.

RESULTS

HIV RNA levels declined precipitously during the first 10 months after SC followed by a slow increase. Women infected heterosexually and through injecting drug use, had an average 34% [95% confidence interval (CI), 2.3-56%] and 46% (95% CI, 17-66%) lower HIV RNA load respectively, compared to men in the same risk group. Among men, those infected heterosexually and by injecting drug use had on average 56% (95% CI, 36-69%) lower HIV RNA levels than homosexual men. Older subjects tended to have higher viral levels. There was no evidence that differences by sex, risk or age group diminished over time, but follow-up was mostly before CD4 cell count had fallen below 200 x 10 cells/l.

CONCLUSIONS

HIV RNA levels at the same stage of HIV-1 infection differ significantly by sex, risk group and age at SC. Given the lack of evidence of a survival difference by sex or risk group prior to initiation of effective therapy, further research on differential effects of virus load on treatment-free disease progression is needed, before a conclusion about considering these factors for ART initiation is drawn.