Developing the follow-up schedules for women with breast cancer

Background: The follow-up care for women with breast cancer requires an understanding of disease recurrence patterns and the follow-up visit schedule should be determined according to the times when the recurrence are most likely to occur, so that preventive measure can be taken to avoid or minimize the recurrence. Objective: To model breast cancer recurrence through stochastic process with an aim to generate a hazard function for determining a follow-up schedule. Methods: We modeled the process of disease progression as the time transformed Weiner process and the first-hitting-time was used as an approximation of the true failure time. The women's "recurrence-free survival time" or a "not having the recurrence event" is modeled by the time it takes Weiner process to cross a threshold value which represents a woman experiences breast cancer recurrence event. We explored threshold regression model which takes account of covariates that contributed to the prognosis of breast cancer following development of the first-hitting time model. Using real data from SEER-Medicare, we proposed models of follow-up visits schedule on the basis of constant probability of disease recurrence between consecutive visits. Results: We demonstrated that the threshold regression based on first-hitting-time modeling approach can provide useful predictive information about breast cancer recurrence. Our results suggest the surveillance and follow-up schedule can be determined for women based on their prognostic factors such as tumor stage and others. Women with early stage of disease may be seen less frequently for follow-up visits than those women with locally advanced stages. Our results from SEER-Medicare data support the idea of risk-controlled follow-up strategies for groups of women. Conclusion: The methodology we proposed in this study allows one to determine individual follow-up scheduling based on a parametric hazard function that incorporates known prognostic factors.^

Analysis of recurrent failure times: A time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This research proposes to use a nonhomogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. This method assumes that repeated events occur for each individual, with given covariates, according to a nonhomogeneous Yule process with intensity function λx(t) = λ 0(t) · exp( x′β). One of the advantages of using a non-homogeneous Yule process for recurrent events is that it assumes that the recurrent rate is proportional to the number of events that occur up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. ^ Model comparisons between the proposed method and other existing recurrent models are addressed by simulation. One example concerning recurrent myocardial infarction events compared between two distinct populations, Mexican-American and Non-Hispanic Whites in the Corpus Christi Heart Project is examined. ^

The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^

A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

Time to renal disease and end-stage renal disease in PROFILE: a multiethnic lupus cohort.

BACKGROUND: Renal involvement is a serious manifestation of systemic lupus erythematosus (SLE); it may portend a poor prognosis as it may lead to end-stage renal disease (ESRD). The purpose of this study was to determine the factors predicting the development of renal involvement and its progression to ESRD in a multi-ethnic SLE cohort (PROFILE). METHODS AND FINDINGS: PROFILE includes SLE patients from five different United States institutions. We examined at baseline the socioeconomic-demographic, clinical, and genetic variables associated with the development of renal involvement and its progression to ESRD by univariable and multivariable Cox proportional hazards regression analyses. Analyses of onset of renal involvement included only patients with renal involvement after SLE diagnosis (n = 229). Analyses of ESRD included all patients, regardless of whether renal involvement occurred before, at, or after SLE diagnosis (34 of 438 patients). In addition, we performed a multivariable logistic regression analysis of the variables associated with the development of renal involvement at any time during the course of SLE.In the time-dependent multivariable analysis, patients developing renal involvement were more likely to have more American College of Rheumatology criteria for SLE, and to be younger, hypertensive, and of African-American or Hispanic (from Texas) ethnicity. Alternative regression models were consistent with these results. In addition to greater accrued disease damage (renal damage excluded), younger age, and Hispanic ethnicity (from Texas), homozygosity for the valine allele of FcgammaRIIIa (FCGR3A*GG) was a significant predictor of ESRD. Results from the multivariable logistic regression model that included all cases of renal involvement were consistent with those from the Cox model. CONCLUSIONS: Fcgamma receptor genotype is a risk factor for progression of renal disease to ESRD. Since the frequency distribution of FCGR3A alleles does not vary significantly among the ethnic groups studied, the additional factors underlying the ethnic disparities in renal disease progression remain to be elucidated.

Prevalence of Premature Ovarian Failure in Women with Tuberous Sclerosis

Tuberous Sclerosis Complex (TSC) is an autosomal dominant tumor suppressor disorder characterized by hamartomas, or benign growths, in various organ systems. Inactivating mutations in either the TSC1 or the TSC2 gene cause most cases of TSC. Recently, the use of ovarian specific conditional knock-out mouse models has demonstrated a crucial role of the TSC genes in ovarian function. Mice with complete deletion of Tsc1 or Tsc2 showed accelerated ovarian follicle activation and subsequent premature follicular depletion, consistent with the human condition premature ovarian failure (POF). POF is defined in women as the cessation of menses before the age of 40 and elevated levels of follicle stimulating hormone (FSH). The prevalence of POF is estimated to be 1%, affecting a substantial number of women in the general population. Nonetheless, the etiology of most cases of POF remains unknown. Based on the mouse model results, we hypothesized that the human TSC1 and TSC2 genes are likely to be crucial for ovarian development and function. Moreover, since women with TSC already have one inactivated TSC gene, we further hypothesized that they may show a higher prevalence of POF. To test this hypothesis, we surveyed 1000 women with TSC belonging to the Tuberous Sclerosis Alliance, a national support organization. 182 questionnaires were analyzed for information on menstrual and reproductive function, as well as TSC. This self-reported data revealed 8 women (4.4%) with possible POF, as determined by menstrual history report and additional supportive data. This prevalence is much higher than 1% in the general population. Data from all women suggested other reproductive pathology associated with TSC such as a high rate of miscarriage (41.2%) and menstrual irregularity of any kind (31.2%). These results establish a previously unappreciated effect of TSC on women’s reproductive health. Moreover, these data suggest that perturbations in the cellular pathways regulated by the TSC genes may play an important role in reproductive function.

Trastuzumab use and risk of congestive heart failure in older breast cancer patients

Trastuzumab is a humanized-monoclonal antibody, developed specifically for HER2-neu over-expressed breast cancer patients. Although highly effective and well tolerated, it was reported associated with Congestive Heart Failure (CHF) in clinical trial settings (up to 27%). This leaves a gap where, Trastuzumab-related CHF rate in general population, especially older breast cancer patients with long term treatment of Trastuzumab remains unknown. This thesis examined the rates and risk factors associated with Trastuzumab-related CHF in a large population of older breast cancer patients. A retrospective cohort study using the existing Surveillance, Epidemiology and End Results (SEER) and Medicare linked de-identified database was performed. Breast cancer patients ≥ 66 years old, stage I-IV, diagnosed in 1998-2007, fully covered by Medicare but no HMO within 1-year before and after first diagnosis month, received 1st chemotherapy no earlier than 30 days prior to diagnosis were selected as study cohort. The primary outcome of this study is a diagnosis of CHF after starting chemotherapy but none CHF claims on or before cancer diagnosis date. ICD-9 and HCPCS codes were used to pool the claims for Trastuzumab use, chemotherapy, comorbidities and CHF claims. Statistical analysis including comparison of characteristics, Kaplan-Meier survival estimates of CHF rates for long term follow up, and Multivariable Cox regression model using Trastuzumab as a time-dependent variable were performed. Out of 17,684 selected cohort, 2,037 (12%) received Trastuzumab. Among them, 35% (714 out of 2037) were diagnosed with CHF, compared to 31% (4784 of 15647) of CHF rate in other chemotherapy recipients (p<.0001). After 10 years of follow-up, 65% of Trastuzumab users developed CHF, compared to 47% in their counterparts. After adjusting for patient demographic, tumor and clinical characteristics, older breast cancer patients who used Trastuzumab showed a significantly higher risk in developing CHF than other chemotherapy recipients (HR 1.69, 95% CI 1.54 - 1.85). And this risk is increased along with the increment of age (p-value < .0001). Among Trastuzumab users, these covariates also significantly increased the risk of CHF: older age, stage IV, Non-Hispanic black race, unmarried, comorbidities, Anthracyclin use, Taxane use, and lower educational level. It is concluded that, Trastuzumab users in older breast cancer patients had 69% higher risk in developing CHF than non-Trastuzumab users, much higher than the 27% increase reported in younger clinical trial patients. Older age, Non-Hispanic black race, unmarried, comorbidity, combined use with Anthracycline or Taxane also significantly increase the risk of CHF development in older patients treated with Trastuzumab. ^

Robust effect sizes and their confidence intervals for group difference between trajectories in hierarchical linear growth model

Hierarchical linear growth model (HLGM), as a flexible and powerful analytic method, has played an increased important role in psychology, public health and medical sciences in recent decades. Mostly, researchers who conduct HLGM are interested in the treatment effect on individual trajectories, which can be indicated by the cross-level interaction effects. However, the statistical hypothesis test for the effect of cross-level interaction in HLGM only show us whether there is a significant group difference in the average rate of change, rate of acceleration or higher polynomial effect; it fails to convey information about the magnitude of the difference between the group trajectories at specific time point. Thus, reporting and interpreting effect sizes have been increased emphases in HLGM in recent years, due to the limitations and increased criticisms for statistical hypothesis testing. However, most researchers fail to report these model-implied effect sizes for group trajectories comparison and their corresponding confidence intervals in HLGM analysis, since lack of appropriate and standard functions to estimate effect sizes associated with the model-implied difference between grouping trajectories in HLGM, and also lack of computing packages in the popular statistical software to automatically calculate them. ^ The present project is the first to establish the appropriate computing functions to assess the standard difference between grouping trajectories in HLGM. We proposed the two functions to estimate effect sizes on model-based grouping trajectories difference at specific time, we also suggested the robust effect sizes to reduce the bias of estimated effect sizes. Then, we applied the proposed functions to estimate the population effect sizes (d ) and robust effect sizes (du) on the cross-level interaction in HLGM by using the three simulated datasets, and also we compared the three methods of constructing confidence intervals around d and du recommended the best one for application. At the end, we constructed 95% confidence intervals with the suitable method for the effect sizes what we obtained with the three simulated datasets. ^ The effect sizes between grouping trajectories for the three simulated longitudinal datasets indicated that even though the statistical hypothesis test shows no significant difference between grouping trajectories, effect sizes between these grouping trajectories can still be large at some time points. Therefore, effect sizes between grouping trajectories in HLGM analysis provide us additional and meaningful information to assess group effect on individual trajectories. In addition, we also compared the three methods to construct 95% confident intervals around corresponding effect sizes in this project, which handled with the uncertainty of effect sizes to population parameter. We suggested the noncentral t-distribution based method when the assumptions held, and the bootstrap bias-corrected and accelerated method when the assumptions are not met.^