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.

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. ^