A SAS macro for parametric and semiparametric mixture cure models

Application of Mixture and Non-mixture Cure Models in Survival Analysis of Patients With COVID-19

Background Due to the emergence of new COVID-19 mutations and an increase in re-infection rates, it has become an important priority for the medical community to identify the factors affecting the short- and long-term survival of patients. This study aimed to determine the risk factors of short- and long-term survival in patients with COVID-19 based on mixture and non-mixture cure models. Methodology In this study, the data of 880 patients with COVID-19 confirmed with polymerase chain reaction in Fereydunshahr city (Isfahan, Iran) from February 20, 2020, to December 21, 2021, were gathered, and the vital status of these patients was followed for at least one year. Due to the high rate of censoring, mixture and non-mixture cure models were applied to estimate the survival. Akaike information criterion values were used to evaluate the fit of the models. Results In this study, the mean age of the patients was 48.9 ± 21.23 years, and the estimated survival rates on the first day, the fourth day, the first week, the first month, and at one year were 0.997, 0.982, 0.973, 0.936, and 0.928, respectively. Among the parametric models, the log-logistic mixed cure model with the logit link, which showed the lowest Akaike information criterion value, demonstrated the best fit. The variables of age and prescribed medication type were significant predictors of long-term survival, while occupation was influential in the short-term survival of patients. Conclusions According to the results of this study, it can be concluded that elderly patients should observe health protocols more strictly and consider receiving booster vaccine doses. The log-logistic cure model with a logit link can be used for survival analysis in COVID-19 patients, a fraction of whom have long-term survival.

The SNP rs460089 in the gene promoter of the drug transporter OCTN1 has prognostic value for treatment-free remission in chronic myeloid leukemia patients treated with imatinib

Membrane transporters are important determinants of drug bioavailability. Their expression and activity affect the intracellular drug concentration in leukemic cells impacting response to therapy. Pharmacogenomics represents genetic markers that reflect allele arrangement of genes encoding drug transporters associated with treatment response. In previous work, we identified SNP rs460089 located in the promotor of SLC22A4 gene encoding imatinib transporter OCTN1 as influential on response of patients with chronic myeloid leukemia treated with imatinib. Patients with rs460089-GC pharmacogenotype had significantly superior response to first-line imatinib treatment compared to patients with rs460089-GG. This study investigated whether pharmacogenotypes of rs460089 are associated with sustainability of treatment-free remission (TFR) in patients from the EUROpean Stop Kinase Inhibitor (EURO-SKI) trial. In the learning sample, 176 patients showed a significantly higher 6-month probability of molecular relapse free survival (MRFS) in patients with GC genotype (73%, 95% CI: 60-82%) compared to patients with GG (51%, 95% CI: 41-61%). Also over time, patients with GC genotype had significantly higher MRFS probabilities compared with patients with GG (HR: 0.474, 95% CI: 0.280-0.802, p = 0.0054). Both results were validated with data on 93 patients from the Polish STOP imatinib study. In multiple regression models, in addition to the investigated genotype, duration of TKI therapy (EURO-SKI trial) and duration of deep molecular response (Polish study) were identified as independent prognostic factors. The SNP rs460089 was found as an independent predictor of TFR.

Laplacian‐P‐splines for Bayesian inference in the mixture cure model

The mixture cure model for analyzing survival data is characterized by the assumption that the population under study is divided into a group of subjects who will experience the event of interest over some finite time horizon and another group of cured subjects who will never experience the event irrespective of the duration of follow‐up. When using the Bayesian paradigm for inference in survival models with a cure fraction, it is common practice to rely on Markov chain Monte Carlo (MCMC) methods to sample from posterior distributions. Although computationally feasible, the iterative nature of MCMC often implies long sampling times to explore the target space with chains that may suffer from slow convergence and poor mixing. Furthermore, extra efforts have to be invested in diagnostic checks to monitor the reliability of the generated posterior samples. A sampling‐free strategy for fast and flexible Bayesian inference in the mixture cure model is suggested in this article by combining Laplace approximations and penalized B‐splines. A logistic regression model is assumed for the cure proportion and a Cox proportional hazards model with a P‐spline approximated baseline hazard is used to specify the conditional survival function of susceptible subjects. Laplace approximations to the posterior conditional latent vector are based on analytical formulas for the gradient and Hessian of the log‐likelihood, resulting in a substantial speed‐up in approximating posterior distributions. The spline specification yields smooth estimates of survival curves and functions of latent variables together with their associated credible interval are estimated in seconds. A fully stochastic algorithm based on a Metropolis‐Langevin‐within‐Gibbs sampler is also suggested as an alternative to the proposed Laplacian‐P‐splines mixture cure (LPSMC) methodology. The statistical performance and computational efficiency of LPSMC is assessed in a simulation study. Results show that LPSMC is an appealing alternative to MCMC for approximate Bayesian inference in standard mixture cure models. Finally, the novel LPSMC approach is illustrated on three applications involving real survival data.

Cancer immunotherapy trial design with random delayed treatment effect and cure rate

Immunotherapies are increasingly used for treating patients with advanced-stage cancers. However, cancer immunotherapy trials often present delayed treatment effects and long-term survivors which result nonproportional hazard models and challenge the immunotherapy trial designs. In this article, we proposed a general random delayed cure rate model for designing cancer immunotherapy trials. A sample size formula is derived for a weighted log-rank test. The accuracy of sample size estimation is assessed and compared with the existing methods via simulation studies. The sensitivities for misspecifying the random delay time are also studied through simulations.

An improved method for the effect estimation of the intermediate event on the outcome based on the susceptible pre-identification

Background

In follow-up studies, the occurrence of the intermediate event may influence the risk of the outcome of interest. Existing methods estimate the effect of the intermediate event by including a time-varying covariate in the outcome model. However, the insusceptible fraction to the intermediate event in the study population has not been considered in the literature, leading to effect estimation bias due to the inaccurate dataset.

Methods

In this paper, we propose a new effect estimation method, in which the susceptible subpopulation is identified firstly so that the estimation could be conducted in the right population. Then, the effect is estimated via the extended Cox regression and landmark methods in the identified susceptible subpopulation. For susceptibility identification, patients with observed intermediate event time are classified as susceptible. Based on the mixture cure model fitted the incidence and time of the intermediate event, the susceptibility of the patient with censored intermediate event time is predicted by the residual intermediate event time imputation. The effect estimation performance of the new method was investigated in various scenarios via Monte-Carlo simulations with the performance of existing methods serving as the comparison. The application of the proposed method to mycosis fungoides data has been reported as an example.

Results

The simulation results show that the estimation bias of the proposed method is smaller than that of the existing methods, especially in the case of a large insusceptible fraction. The results hold for small sample sizes. Besides, the estimation bias of the new method decreases with the increase of the covariates, especially continuous covariates, in the mixture cure model. The heterogeneity of the effect of covariates on the outcome in the insusceptible and susceptible subpopulation, as well as the landmark time, does not affect the estimation performance of the new method.

Conclusions

Based on the pre-identification of the susceptible, the proposed new method could improve the effect estimation accuracy of the intermediate event on the outcome when there is an insusceptible fraction to the intermediate event in the study population.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-021-01378-8.

First-line atezolizumab plus nab-paclitaxel for unresectable, locally advanced, or metastatic triple-negative breast cancer: IMpassion130 final overall survival analysis

BACKGROUND

Guidelines recommend atezolizumab plus nab-paclitaxel (A + nP) for first-line treatment of unresectable, locally advanced, or metastatic triple-negative breast cancer expressing programmed death-ligand 1 (PD-L1) on tumor-infiltrating immune cells (IC), based on IMpassion130. We report the final overall survival (OS) and safety of that study as per the prespecified analysis plan.

PATIENTS AND METHODS

Patients were randomized to nP 100 mg/m² (days 1, 8, and 15 of a 28-day cycle) with atezolizumab 840 mg (A + nP) or placebo (P + nP; days 1 and 15), until progression or unacceptable toxicity. Coprimary endpoints were progression-free survival [intention-to-treat (ITT) and PD-L1 IC-positive populations] and OS (tested hierarchically in the ITT population and, if significant, in the PD-L1 IC-positive population).

RESULTS

Each arm comprised 451 patients; 666 (73.8%) had died by the final OS analysis cut-off (median follow-up, 18.8 months; interquartile range, 8.9-34.7 months). Median OS in the ITT population was 21.0 months [95% confidence interval (CI), 19.0-23.4 months] with A + nP, and 18.7 months (95% CI, 16.9-20.8 months) with P + nP [stratified hazard ratio (HR), 0.87; 95% CI, 0.75-1.02; P = 0.077]. Exploratory analysis in the PD-L1 IC-positive population showed a median OS of 25.4 months (95% CI, 19.6-30.7 months) with A + nP (n = 185) and 17.9 months (95% CI, 13.6-20.3 months) with P + nP (n = 184; stratified HR, 0.67; 95% CI, 0.53-0.86). Safety outcomes were consistent with previous analyses and the known toxicity profiles of each agent. Immune-mediated adverse events of special interest were reported in 58.7% and 41.6% of patients treated with A + nP and P + nP, respectively.

CONCLUSION

Although the OS benefit in the ITT population was not statistically significant, precluding formal testing, clinically meaningful OS benefit was observed with A + nP in PD-L1 IC-positive patients, consistent with prior interim analyses. This combination remained safe and tolerable with longer follow-up.

Study design of single-arm phase II immunotherapy trials with long-term survivors and random delayed treatment effect

In the traditional study design of a single-arm phase II cancer clinical trial, the one-sample log-rank test has been frequently used. A common practice in sample size calculation is to assume that the event time in the new treatment follows exponential distribution. Such a study design may not be suitable for immunotherapy cancer trials, when both long-term survivors (or even cured patients from the disease) and delayed treatment effect are present, because exponential distribution is not appropriate to describe such data and consequently could lead to severely underpowered trial. In this research, we proposed a piecewise proportional hazards cure rate model with random delayed treatment effect to design single-arm phase II immunotherapy cancer trials. To improve test power, we proposed a new weighted one-sample log-rank test and provided a sample size calculation formula for designing trials. Our simulation study showed that the proposed log-rank test performs well and is robust of misspecified weight and the sample size calculation formula also performs well.

geecure: An R-package for marginal proportional hazards mixture cure models

BACKGROUND AND OBJECTIVE

Most of available software packages for mixture cure models to analyze survival data with a cured fraction assume independent survival times, and they are not suitable for correlated survival times, such as clustered survival data. The objective of this paper is to present a software package to fit a marginal mixture cure model to clustered survival data with a cured fraction.

METHODS

We developed an R package geecure that fits the marginal proportional hazards mixture cure (PHMC) models to clustered right-censored survival data with a cured fraction. The dependence among the cure statuses and among the survival times of uncured patients within a cluster are modeled by working correlation matrices through the generalized estimating equations, and the Expectation-Solution algorithm is used to estimate the parameters. The variances of the estimated regression parameters are estimated by either a sandwich method or a bootstrap method.

RESULTS

The package geecure can fit the marginal PHMC model where the cumulative baseline hazard function is either a two-parameter Weibull distribution or specified nonparametrically. Fitting the parametric PHMC model with the Weibull baseline hazard function on average takes less time than fitting the semiparametric PHMC model does. Two variance estimation methods are comparable in the simulation study. The sandwich method takes much less time than the bootstrap method in variance estimation.

CONCLUSIONS

The package geecure provides an easy access to the marginal PHMC models for clustered survival data with a cured fraction in routine survival analysis. It is easy to use and will make the wide applications of the marginal PHMC models possible.

Environmental heavy metal as a potential risk factor for the progression of oral potentially malignant disorders in central Taiwan

OBJECTIVE

Oral cancer (OC) is a leading cause of death from cancer in men between the ages of 25 and 44 years in Taiwan. The overall 5-year survival rates for the four OC stages (I-IV) in Taiwan are approximately 70%, 30%, 20%, and 10%, respectively, indicating the importance of the early diagnosis of oral potentially malignant disorders (OPMDs). Previous studies indicated an association between the OC incidence and certain environmental heavy metal concentrations. If these associations do exist for OC, they may also be observed for OPMD. The purpose of this study is to explore the association between the development of OPMD to OC and environmental heavy metals. Oral submucous fibrosis (OSF) and oral leukoplakia (OL) are two major types of OPMD in Taiwan.

MATERIALS AND METHODS

A retrospective cohort study was conducted by Changhua Christian Hospital, the sole medical center in Changhua County, where 2725 male adult patients diagnosed with either OSF or OL between 2000 and 2014 were recruited. Data were analyzed by Cox regression and adjusted for smoking and betel-quid chewing.

RESULTS AND DISCUSSION

OPMD patients who resided in areas with high nickel concentrations (polluted levels) exhibited hazard ratios of 1.8-2 for OC relative to those who lived in areas with low nickel levels (P<0.01). Meanwhile, smokers with OPMDs had a hazard ratio of 2.8-2.9 relative to non-smokers. Betel-quid chewers had a 2.2-2.3 hazard ratio relative to non-chewers. Smoking, betel-quid chewing, and environmental nickel exposure are associated with an increased risk of OC development in OPMD patients. This study provides valuable findings on the environmental effects of heavy metals on human health. Enhanced surveillance of the condition of OPMD patients who have been exposed to high nickel concentrations may be crucial for OC prevention.

Mixture and Non-Mixture Cure Fraction Models Based on Generalized Gompertz Distribution under Bayesian Approach

The cure fraction models are generally used to model lifetime data with long term survivors. In a cohort of cancer patients, it has been observed that due to the development of new drugs some patients are cured permanently, and some are not cured. The patients who are cured permanently are called cured or long term survivors while patients who experience the recurrence of the disease are termed as susceptibles or uncured. Thus, the population is divided into two groups: a group of cured individuals and a group of susceptible individuals. The proportion of cured individuals after the treatment is typically known as the cure fraction. In this paper, we have introduced a three parameter Gompertz (viz. scale, shape and acceleration) or generalized Gompertz distribution in the presence of cure fraction, censored data and covariates for estimating the proportion of cure fraction through Bayesian Approach. Inferences are obtained using the standard Markov Chain Monte Carlo technique in openBUGS software.

A novel sample size formula for the weighted log-rank test under the proportional hazards cure model

The treatment of cancer has progressed dramatically in recent decades, such that it is no longer uncommon to see a cure or log-term survival in a significant proportion of patients with various types of cancer. To adequately account for the cure fraction when designing clinical trials, the cure models should be used. In this article, a sample size formula for the weighted log-rank test is derived under the fixed alternative hypothesis for the proportional hazards cure models. Simulation showed that the proposed sample size formula provides an accurate estimation of sample size for designing clinical trials under the proportional hazards cure models.

A Comparison between Cure Model and Recursive Partitioning: A Retrospective Cohort Study of Iranian Female with Breast Cancer

Background. Breast cancer which is the most common cause of women cancer death has an increasing incidence and mortality rates in Iran. A proper modeling would correctly detect the factors' effect on breast cancer, which may be the basis of health care planning. Therefore, this study aimed to practically develop two recently introduced statistical models in order to compare them as the survival prediction tools for breast cancer patients. Materials and Methods. For this retrospective cohort study, the 18-year follow-up information of 539 breast cancer patients was analyzed by "Parametric Mixture Cure Model" and "Model-Based Recursive Partitioning." Furthermore, a simulation study was carried out to compare the performance of mentioned models for different situations. Results. "Model-Based Recursive Partitioning" was able to present a better description of dataset and provided a fine separation of individuals with different risk levels. Additionally the results of simulation study confirmed the superiority of this recursive partitioning for nonlinear model structures. Conclusion. "Model-Based Recursive Partitioning" seems to be a potential instrument for processing complex mixture cure models. Therefore, applying this model is recommended for long-term survival patients.

Sample size calculation for testing differences between cure rates with the optimal log-rank test

In this article, sample size calculations are developed for use when the main interest is in the differences between the cure rates of two groups. Following the work of Ewell and Ibrahim, the asymptotic distribution of the weighted log-rank test is derived under the local alternative. The optimal log-rank test under the proportional distributions alternative is discussed, and sample size formulas for the optimal and standard log-rank tests are derived. Simulation results show that the proposed formulas provide adequate sample size estimation for trial designs and that the optimal log-rank test is more efficient than the standard log-rank test, particularly when both cure rates and percentages of censoring are small.

Application of a Non-Mixture Cure Rate Model for Analyzing Survival of Patients with Breast Cancer

BACKGROUND

As a result of significant progress made in treatment of many types of cancers during the last few decades, there have been an increased number of patients who do not experience mortality. We refer to these observations as cure or immune and models for survival data which include cure fraction are known as cure rate models or long-term survival models.

MATERIALS AND METHODS

In this study we used the data collected from 438 female patients with breast cancer registered in the Cancer Research Center in Shahid Beheshti University of Medical Sciences, Tehran, Iran. The patients had been diagnosed from 1992 to 2012 and were followed up until October 2014. We had to exclude some because of incomplete information. Phone calls were made to confirm whether the patients were still alive or not. Deaths due to breast cancer were regarded as failure. To identify clinical, pathological, and biological characteristics of patients that might have had an effect on survival of the patients we used a non-mixture cure rate model; in addition, a Weibull distribution was proposed for the survival time. Analyses were performed using STATA version 14. The significance level was set at P ≤ 0.05.

RESULTS

A total of 75 patients (17.1%) died due to breast cancer during the study, up to the last follow-up. Numbers of metastatic lymph nodes and histologic grade were significant factors. The cure fraction was estimated to be 58%.

CONCLUSIONS

When a cure fraction is not available, the analysis will be changed to standard approaches of survival analysis; however when the data indicate that the cure fraction is available, we suggest analysis of survival data via cure models.

Spontaneous Clearance of the Hepatitis C Virus Among Men Who Have Sex With Men

BACKGROUND

The probability of spontaneous hepatitis C virus (HCV) clearance ranges from 11% to 49%. Our previous cross-sectional study suggests that mode of acquisition explains some of this heterogeneity. We performed this prospective study to determine factors associated with spontaneous HCV clearance among men who have sex with men (MSM).

METHODS

A mixture-cure model was used to evaluate the probability of spontaneous HCV clearance among 101 MSM in the Multicenter AIDS Cohort Study with acute HCV infection between 1984 and 2012.

RESULTS

Spontaneous HCV clearance occurred in 46% of MSM (49% in non-injection drug users [IDUs] and 23% in IDUs). In the multivariable analysis, age <30 years (clearance ratio [CR] = 2.43; 95% confidence interval [CI], 1.53-3.87) and being human immunodeficiency virus (HIV) uninfected (CR = 2.97; 95% CI, 1.98-4.46) were independently associated with spontaneous clearance. Among men aged ≥30 years, being HIV uninfected, not having unprotected anal intercourse, older age, and being on highly active antiretroviral therapy were independently associated with higher clearance. The interferon lambda rs12979860 single nucleotide polymorphism (SNP) was not associated with spontaneous clearance among the 88 MSM who were not active IDUs (CR = 0.74; 95% CI, .46-1.21 for CC vs CT/TT genotype).

CONCLUSIONS

The high probability of spontaneous HCV clearance together with the lack of an association between the rs12979860 SNP and spontaneous clearance among MSM who do not use injection drugs suggests that the immune mechanisms involved with a successful response to acute HCV differ by mode of virus acquisition. Understanding potential mechanistic differences could be important for HCV vaccine development.

Rates and predictors of 5-year survival in a national cohort of asymptomatic elderly patients undergoing carotid revascularization

BACKGROUND

Current American Heart Association guidelines recommend carotid revascularization for asymptomatic patients on the basis of life expectancy.

OBJECTIVE

To determine the rates and predictors of 5-year survival in elderly patients with asymptomatic carotid artery stenosis who underwent either carotid artery stent placement (CAS) or carotid endarterectomy (CEA).

METHODS

The rates of 5-year survival were determined by use of Kaplan-Meier survival methods in a representative sample of fee-for-service Medicare beneficiaries ≥65 years of age who underwent CAS or CEA for asymptomatic carotid artery stenosis with postprocedural follow-up of 3.4 ± 1.7 years. Cox proportional hazards analysis was used to assess the relative risk of all-cause mortality for patients in the presence of selected comorbidities, including ischemic heart disease, chronic renal failure, and atrial fibrillation, after adjustment for potential confounders such as age, sex, race/ethnicity, and procedure type.

RESULTS

A total of 22,177 patients with asymptomatic carotid artery stenosis were treated with either CAS (n = 2144) or CEA (n = 20,033). The overall estimated 5-year survival rate (±SE) was 95.3 ± 0.00149; it was 95.5% and 93.8% in patients treated with CEA and CAS, respectively. After adjustment for potential confounders, relative risk of all-cause 5-year mortality was significantly higher among patients with atrial fibrillation (relative risk, 1.8; 95% confidence interval, 1.5-2.1) and those with chronic renal failure (relative risk, 2.1; 95% confidence interval, 1.7-2.6).

CONCLUSION

Risks and benefits must be carefully weighed before carotid revascularization in elderly patients with asymptomatic carotid artery stenosis who have concurrent atrial fibrillation or chronic renal failure.

Variations in genes involved in dormancy associated with outcome in patients with resected colorectal liver metastases

BACKGROUND

Tumor dormancy has been described as a state of hibernation. Dormancy can be switched to proliferation by different pathways, which may play a critical role in tumor recurrence. In this study, we investigated genetic variations within genes involved in tumor dormancy and their association with recurrence and outcome in patients with colorectal liver metastases (CLM) who underwent neoadjuvant bevacizumab-based chemotherapy.

PATIENTS AND METHODS

Genomic DNA was extracted from resected CLM (FFPE) from 149 patients. Single-nucleotide polymorphisms (SNPs) in 14 genes associated with dormancy were analyzed by direct Sanger DNA sequencing and evaluated for response, recurrence-free survival (RFS), overall survival (OS) and recurrence patterns.

RESULTS

NME1 rs34214448 C>A was significantly associated with RFS in univariable analysis (P = 0.039) and with intrahepatic recurrence (P = 0.014). NOTCH3 rs1044009 T>C and CD44 rs8193 C>T showed a significant difference in 3-year OS rates (P = 0.004 and P = 0.042, respectively). With respect to radiological response, CD44 rs8193 C>T variant genotypes were associated with a significantly higher response rate (P = 0.033). Recursive partitioning analyses revealed that Dll4 rs12441495 C>G, NME1 rs34214448 C>A and NOTCH3 rs1044009 T>C were the dominant SNPs predicting histological response, RFS and OS, respectively.

CONCLUSION

Our data suggest that gene variations within genes involved in tumor dormancy pathways are associated with response and outcome in patients with resected CLM. These data may lead to new and more effective treatment strategies targeting tumor dormancy.

Single-arm phase II trial design under parametric cure models

The current practice of designing single-arm phase II survival trials is limited under the exponential model. Trial design under the exponential model may not be appropriate when a portion of patients are cured. There is no literature available for designing single-arm phase II trials under the parametric cure model. In this paper, a test statistic is proposed, and a sample size formula is derived for designing single-arm phase II trials under a class of parametric cure models. Extensive simulations showed that the proposed test and sample size formula perform very well under different scenarios.

Variations in genes involved in immune response checkpoints and association with outcomes in patients with resected colorectal liver metastases

In patients with colorectal liver metastases (CLM), liver resection offers the possibility of cure and long-term survival. The liver is a highly immunogenic organ harboring ~80% of the body's tissue macrophages. Emerging data demonstrate a critical role of the immune response for cancer treatment. We investigated variations within genes involved in immune response checkpoints and their association with outcomes in patients with CLM who underwent neoadjuvant chemotherapy including bevacizumab and liver resection. Single-nucleotide polymorphisms (SNPs) in nine genes (CCL2, CCR2, LAG3, NT5E, PDCD1, CD274, IDO1, CTLA4 and CD24) were analyzed in genomic DNA from 149 patients with resected bevacizumab-pretreated CLM by direct Sanger DNA sequencing, and correlated with response, recurrence-free survival (RFS), overall survival (OS), probability of cure and recurrence patterns. IDO1 (indoleamine 2, 3-dioxygenase) rs3739319 G>A and CD24 rs8734 G>A showed a significant difference in 3-year OS rates. In addition, IDO1 rs3739319 G>A was significantly associated with extrahepatic recurrence. Recursive partitioning analyses revealed that IDO1 rs3739319 G>A was the dominant SNP predicting RFS and OS. Our data suggest that variants within genes involved in immune response checkpoints are associated with outcomes in patients with resected CLM and might lead to improved treatment strategies modulating anti-tumor immune response by targeting novel immune checkpoints.

Genetic variations in angiopoietin and pericyte pathways and clinical outcome in patients with resected colorectal liver metastases

BACKGROUND

Genes involved in the angiopoietin and pericyte pathways may become escape mechanisms under antivascular endothelial growth factor (anti-VEGF) therapy. The authors investigated whether variations within genes in these pathways are associated with clinical outcome in patients with colorectal liver metastases who undergo liver resection and receive perioperative, bevacizumab-based chemotherapy.

METHODS

Single nucleotide polymorphisms (SNPs) in 9 genes (angiopoietin-1 [ANGPT1]; ANGPT2; TEK tyrosine kinase, endothelial [TEK]; platelet-derived growth factor β [PDGFB]; β-type platelet-derived growth factor receptor [PDGFRB]; insulin-like growth factor 1 [IGF1]; transforming growth factor β1 [TGFB1]; RalA binding protein 1 [RALBP1]; and regulator of G-protein signaling 5 [RGS5]) were analyzed in samples of genomic DNA from 149 patients and were evaluated for associations with clinical outcome.

RESULTS

RALBP1 reference SNP 329007 (rs329007) A>G resulted in a significant difference in recurrence-free survival (A/A genotype, 14.0 months; A/G or G/G genotype, 9.2 months; hazard ratio [HR], 1.60; P = .024). PDGFB rs1800818 A>G was associated with 3-year overall survival rates (A/A genotype, 78%; A/G genotype, 69%; [HR 1.37]; G/G genotype, 53%; [HR 2.12]; P = .048). In multivariate analysis, RALBP1 rs329007 A>G remained significant (HR, 1.99; P = .002). PDGFB rs1800818 A>G and RALBP1 rs329007 A>G were correlated with radiologic response (A/A or A/G genotype, 86%; G/G genotype, 71% [P = .042]; A/A genotype, 78%; A/G or G/G genotype, 94% [P = .018], respectively). RALBP1 rs329007 A>G demonstrated significantly different rates of histologic response (A/A genotype: major histologic response, 35%; partial histologic response, 34%; no histologic response, 30%; A/G or G/G genotype: 46%, 13%, and 41%, respectively; P = .029). Recursive partitioning analysis revealed that ANGPT2 rs2442599 T>C and RALBP1 rs329007 A>G were the main SNPs that predicted histologic response and recurrence-free survival, whereas PDGFB rs1800818 A>G was the leading SNP that predicted overall survival. ANGPT2 rs2916702 C>T and rs2442631 G>A were significantly associated with the probability of achieving a cure.

CONCLUSIONS

The current data suggest that variations in genes involved in the angiopoietin and pericyte pathways may be predictive and/or prognostic biomarkers in patients with resected colorectal liver metastases who receive bevacizumab-based chemotherapy.

Explaining survival differences between two consecutive studies with allogeneic stem cell transplantation in patients with chronic myeloid leukemia

PURPOSE

In the two consecutive German studies III and IIIA on chronic myeloid leukemia, between 1995 and 2004, 781 patients were randomized to receive either allogeneic hematopoietic stem cell transplantation with a related donor or continued drug treatment. Despite comparable transplantation protocols and most centers participating in both studies, the post-transplant survival probabilities for patients transplanted in first chronic phase were significantly higher in study IIIA (144 patients) than in study III (113 patients). Prior to the decision on a combined analysis of both studies, reasons for this discrepancy had to be investigated.

METHODS

The Cox proportional hazard cure model was used to identify prognostic factors for post-transplant survival.

RESULTS

Donor-recipient matching for human leukocyte antigen, patient age, time between diagnosis and transplantation, and calendar time showed a significant influence on survival and/or the incidence of cure. Added as a further factor, affiliation to study IIIA had no significant impact any longer.

CONCLUSIONS

Discrepancies in influential prognostic factors explained the different post-transplant survival probabilities between the studies. The significance of calendar time suggests a lack of consistency of transplantation practice over time. Accordingly, the prerequisite for a common assessment of overall survival in the two randomized transplantation arms was not met. Moreover, our analyses provide an independent validation of established prognostic factors and their cutoffs. The statistical approach in investigating and modeling potential prognostic factors for survival sets an example for the examination of studies with unexpected outcome differences in concurrent treatment arms.

smcure: an R-package for estimating semiparametric mixture cure models

The mixture cure model is a special type of survival models and it assumes that the studied population is a mixture of susceptible individuals who may experience the event of interest, and cure/non-susceptible individuals who will never experience the event. For such data, standard survival models are usually not appropriate because they do not account for the possibility of cure. This paper presents an R package smcure to fit the semiparametric proportional hazards mixture cure model and the accelerated failure time mixture cure model.

Increasing use of radical prostatectomy for nonlethal prostate cancer in Sweden

PURPOSE

The number of patients in Sweden treated with radical prostatectomy for localized prostate cancer has increased exponentially. The extent to which this increase reflects treatment of nonlethal disease detected through prostate-specific antigen (PSA) screening is unknown.

EXPERIMENTAL DESIGN

We undertook a nationwide study of all 18,837 patients with prostate cancer treated with radical prostatectomy in Sweden from 1988 to 2008 with complete follow-up through 2009. We compared cumulative incidence curves, fit Cox regression and cure models, and conducted a simulation study to determine changes in treatment of nonlethal cancer, in cancer-specific survival over time, and effect of lead-time due to PSA screening.

RESULTS

The annual number of radical prostatectomies increased 25-fold during the study period. The 5-year cancer-specific mortality rate decreased from 3.9% [95% confidence interval (CI), 2.5-5.3] among patients diagnosed between 1988 and 1992 to 0.7% (95% CI, 0.4-1.1) among those diagnosed between 1998 and 2002 (P(trend) < 0.001). According to the cure model, the risk of not being cured declined by 13% (95% CI, 12%-14%) with each calendar year. The simulation study indicated that only about half of the improvement in disease-specific survival could be accounted for by lead-time.

CONCLUSION

Patients overdiagnosed with nonlethal prostate cancer appear to account for a substantial and growing part of the dramatic increase in radical prostatectomies in Sweden, but increasing survival rates are likely also due to true reductions in the risk of disease-specific death over time. Because the magnitude of harm and costs due to overtreatment can be considerable, identification of men who likely benefit from radical prostatectomy is urgently needed.

Sample size calculation for the proportional hazards cure model

In clinical trials with time-to-event endpoints, it is not uncommon to see a significant proportion of patients being cured (or long-term survivors), such as trials for the non-Hodgkins lymphoma disease. The popularly used sample size formula derived under the proportional hazards (PH) model may not be proper to design a survival trial with a cure fraction, because the PH model assumption may be violated. To account for a cure fraction, the PH cure model is widely used in practice, where a PH model is used for survival times of uncured patients and a logistic distribution is used for the probability of patients being cured. In this paper, we develop a sample size formula on the basis of the PH cure model by investigating the asymptotic distributions of the standard weighted log-rank statistics under the null and local alternative hypotheses. The derived sample size formula under the PH cure model is more flexible because it can be used to test the differences in the short-term survival and/or cure fraction. Furthermore, we also investigate as numerical examples the impacts of accrual methods and durations of accrual and follow-up periods on sample size calculation. The results show that ignoring the cure rate in sample size calculation can lead to either underpowered or overpowered studies. We evaluate the performance of the proposed formula by simulation studies and provide an example to illustrate its application with the use of data from a melanoma trial.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. In this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example.

Computing power and sample size for case-control association studies with copy number polymorphism: application of mixture-based likelihood ratio test

Recent studies suggest that copy number polymorphisms (CNPs) may play an important role in disease susceptibility and onset. Currently, the detection of CNPs mainly depends on microarray technology. For case-control studies, conventionally, subjects are assigned to a specific CNP category based on the continuous quantitative measure produced by microarray experiments, and cases and controls are then compared using a chi-square test of independence. The purpose of this work is to specify the likelihood ratio test statistic (LRTS) for case-control sampling design based on the underlying continuous quantitative measurement, and to assess its power and relative efficiency (as compared to the chi-square test of independence on CNP counts). The sample size and power formulas of both methods are given. For the latter, the CNPs are classified using the Bayesian classification rule. The LRTS is more powerful than this chi-square test for the alternatives considered, especially alternatives in which the at-risk CNP categories have low frequencies. An example of the application of the LRTS is given for a comparison of CNP distributions in individuals of Caucasian or Taiwanese ethnicity, where the LRTS appears to be more powerful than the chi-square test, possibly due to misclassification of the most common CNP category into a less common category.