Continuous Bayesian adaptive randomization based on event times with covariates by Cheung et al., Statistics in Medicine 2006; 25:55-70.
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Publications and source records attributed to Rick Chappell.
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PURPOSE: To compare the benefit achieved by concurrent chemoradiotherapy (CRT) and/or accelerated fractionation (AF) vs. radiotherapy (RT) alone with conventional fractionation (CF) for patients with T3-4N0-1M0 nasopharyngeal carcinoma (NPC). METHODS AND MATERIALS: All patients were irradiated with the same RT technique to > or =66 Gy at 2 Gy per fraction, conventional five fractions/week in the CF and CF+C (chemotherapy) arms, and accelerated six fractions/week in the AF and AF+C arms. The CF+C and AF+C patients were given the Intergroup 0099 regimen (concurrent cisplatin plus adjuvant cisplatin and 5-fluorouracil). RESULTS: Between 1999 and April 2004, 189 patients were randomly assigned; the trial was terminated early because of slow accrual. The median follow-up was 2.9 years. When compared with the CF arm, significant improvement in failure-free survival (FFS) was achieved by the AF+C arm (94% vs. 70% at 3 years, p = 0.008), but both the AF arm and the CF+C arm were insignificant (p > or = 0.38). Multivariate analyses showed that CRT was a significant factor: hazard ratio (HR) = 0.52 (0.28-0.97), AF per se was insignificant: HR = 0.68 (0.37-1.25); the interaction of CRT by AF was strongly significant (p = 0.006). Both CRT arms had significant increase in acute toxicities (p < 0.005), and the AF+C arm also incurred borderline increase in late toxicities (34% vs. 14% at 3 years, p = 0.05). CONCLUSIONS: Preliminary results suggest that concurrent chemoradiotherapy with accelerated fractionation could significantly improve tumor control when compared with conventional RT alone; further confirmation of therapeutic ratio is warranted.
PURPOSE: This randomized study compared the results achieved by concurrent chemoradiotherapy (CRT) versus radiotherapy (RT) alone for nasopharyngeal carcinoma (NPC) with advanced nodal disease. PATIENTS AND METHODS: Patients with nonkeratinizing/undifferentiated NPC staged T1-4N2-3M0 were randomized to CRT or RT. Both arms were treated with the same RT technique and dose fractionation. The CRT patients were given cisplatin 100 mg/m2 on days 1, 22, and 43, followed by cisplatin 80 mg/m2 and fluorouracil 1,000 mg/m2/d for 96 hours starting on days 71, 99, and 127. RESULTS: From 1999 to January 2004, 348 eligible patients were randomly assigned; the median follow-up was 2.3 years. The two arms were well-balanced in all prognostic factors and RT parameters. The CRT arm achieved significantly higher failure-free survival (72% v 62% at 3-year, P = .027), mostly as a result of an improvement in locoregional control (92% v 82%, P = .005). However, distant control did not improve significantly (76% v 73%, P = .47), and the overall survival rates were almost identical (78% v 78%, P = .97). In addition, the CRT arm had significantly more acute toxicities (84% v 53%, P < .001) and late toxicities (28% v 13% at 3-year, P = .024). CONCLUSION: Preliminary results confirmed that CRT could significantly improve tumor control, particularly at locoregional sites. However, there was significant increase in the risk of toxicities and no early gain in overall survival. Longer follow-up is needed to confirm the ultimate therapeutic ratio.
OBJECTIVE: The aim of the current study was to evaluate the safety and efficacy of a widely available bupivacaine continuous wound infusion system in gynecologic oncology patients undergoing laparotomy. METHODS: A prospective, randomized, double-blind, placebo-controlled trial was performed. After closure of the fascia, flexible soaker catheters were placed in the deep subcutaneous space. The infusion pump was filled with 290 mL of either 0.5% bupivacaine or normal saline, to infuse over 72 hours. Daily assessments of pain scores utilized the Wisconsin Brief Pain Inventory. All patients received intravenous narcotics via patient-controlled devices. RESULTS: Eighty surgeries were evaluated in a total of 79 women (40 per arm). Mean age was 56 years, with 79% having invasive gynecologic pathology. The two groups were not significantly different in terms of type of surgery, length of incision, estimated blood loss, operative time, or medical history. Postoperative outcomes, including wound toxicity, time to flatus, and hospital stay, did not differ. Study patients averaged 75 mg intravenously and 107 mg total narcotic use (morphine equivalent), whereas controls averaged 60 mg intravenously and 86 mg total (P = .40 intravenously; P = .25 total). Acetaminophen and intravenous ketorolac consumption were equal between groups. The Brief Pain Inventory score for "current pain" was 2.84 for bupivacaine patients and 3.14 for controls (P = .46; least = 0, most = 10). There was no individual postoperative day when "current pain" BPI scores differed. "Worst pain" and "least pain" Brief Pain Inventory scores showed similar results. CONCLUSION: The results suggest that although the continuous infusion system seems safe, it is not efficacious in this patient population.
Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Because mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left-truncated and right-censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. First, we develop a novel estimator for the gamma frailty parameter under left truncation. Using this estimator, we then derive a closed-form estimator for the marginal distribution of the non-terminal event. The large sample properties of the estimators are established via asymptotic theory. The methodology performs well with moderate sample sizes, both in simulations and in an analysis of data from a diabetes registry.
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PURPOSE: To investigate the maximal tolerated dose of a continuous 28-day iododeoxyuridine (IUdr) infusion combined with hyperfractionated accelerated radiotherapy (HART); to analyze the percentage of IUdr-thymidine replacement in peripheral granulocytes as a surrogate marker for IUdr incorporation into tumor cells; to measure the steady-state serum IUdr levels; and to assess the feasibility of continuous IUdr infusion and HART in the management of malignant glioma. METHODS AND MATERIALS: Patients were required to have biopsy-proven malignant glioma. Patients received 100 (n = 4), 200 (n = 3), 300 (n = 3), 400 (n = 6), 500 (n = 4), 625 (n = 5), or 781 (n = 6) mg/m(2)/d of IUdr by continuous infusion for 28 days. HART was started 7 days after IUdr initiation. The total dose was 70 Gy (1.2 Gy b.i.d. for 25 days with a 10-Gy boost [2.0 Gy for 5 Saturdays]). Weekly assays were performed to determine the percentage of IUdr-DNA replacement in granulocytes and serum IUdr levels using standard high performance liquid chromatography methods. Standard Phase I toxicity methods were used. RESULTS: Between June 1994 and August 1999, 31 patients were enrolled. No patient had Grade 3 or worse HART toxicity. Grade 3 or greater IUdr toxicity predominantly included neutropenia (n = 3), thrombocytopenia (n = 3), and elevated liver function studies (n = 3). The maximal tolerated dose was 625 mg/m(2)/d. Thymidine replacement in the peripheral granulocytes peaked at 3 weeks and increased with the dose (maximal thymidine replacement 4.9%). The steady-state plasma IUdr level increased with the dose (maximum, 1.5 microM). CONCLUSION: In our study, continuous long-term IUdr i.v. infusion had a maximal tolerated dose of 625 mg/m(2)/d. Granulocyte incorporation data verified the concept that prolonged IUdr infusion results in IUdr-DNA replacement that corresponds to a high degree of cell labeling. IUdr steady-state plasma levels increased with increasing dose and attained levels needed for clinical radiosensitization. Continuous IUdr infusion and HART were both feasible and well tolerated.
PURPOSE: To study the prognostic significance of primary tumor volume on local control of nasopharyngeal carcinoma. METHODS AND MATERIALS: Between 1998 and 2001, 308 consecutive patients with nasopharyngeal carcinoma treated with radical intent were staged with MRI. On the basis of the extent of tumor infiltration outlined by a diagnostic radiologist, the gross tumor volume of the primary and involved retropharyngeal nodes (GTV-P) was delineated by a radiation oncologist for three-dimensional conformal radiotherapy to the nasopharyngeal region using the Helax-TMS Planning System. All patients were treated with 2 Gy daily to a total dose of 70 Gy in 6-7 weeks. Additionally, chemotherapy was given to 128 patients (42%). RESULTS: The median GTV-P for the whole series was 22 cm(3) (range, 1.4-218 cm(3)). Although the GTV-P varied substantially within each T stage, the overall correlation between these two parameters was strongly significant (p <0.01), with the median GTV-P 2.7 cm(3) for T1, 13.2 cm(3) for T2, 28.1 cm(3) for T3, and 65.5 cm(3) for T4. With a median follow-up of 1.9 years (range, 0.1-3.9 years), the 3-year local failure-free rate was 87%. The 3-year local failure-free rate was 97% for patients with a GTV-P <15 cm(3) compared with 82% for those with a GTV-P > or =15 cm(3) (p <0.01). On multivariate analysis (with T stage as a covariate), GTV-P remained an independent prognostic factor for the local failure-free rate (hazard ratio, 1.01; 95% confidence interval, 1.00-1.02; p <0.01). CONCLUSION: Our data suggested that GTV-P is a strongly significant factor for predicting local control of nasopharyngeal carcinoma. The risk of local failure was estimated to increase by 1% for every 1 cm(3) increase in primary tumor volume.
BACKGROUND: In phase I cancer clinical trials, adjustment for patient differences in toxicity susceptibility can be carried out with stratification into risk groups. Separate trials conducted for each risk group can lead to conflicting decisions, in which higher doses are recommended for higher risk groups. Designs which covariate adjust often require assumptions that clinicians may be uncomfortable with. METHODS: We extend up-and-down designs, isotonic designs and the continual reassessment method (CRM) to multiple risk groups with two-way isotonic regression. The only assumption about the groups is that they can be ordered according to their toxicity risk. The first two extensions, in particular, are nonparametric and easy for clinicians to understand. RESULTS: Simulations were based on an ongoing helical tomotherapy trial. Seven different toxicity scenarios were considered. The proposed methods compared favorably to a covariate adjusted CRM. The extended up-and-down designs inherited the conservativeness from the original designs. CONCLUSION: Our experience demonstrates that the escalation rules of multiple risk groups can be linked, without a parametric assumption about the group toxicity curve, to borrow strength and to ensure nonconflicting dosage recommendations.
PURPOSE: In this single institution Phase II trial, we evaluated the efficacy of the vitamin D analogue, 1alpha-OH-D(2), in patients with advanced hormone-refractory prostate cancer. EXPERIMENTAL DESIGN: The patients initially received 1alpha-OH-D(2) at 12.5 micro g p.o. every day, which was dose adjusted for hypercalcemia. Given the cytostatic nature of the drug, the primary study end point was progression-free survival for a minimum of 6 months. The secondary end point was further characterization of drug toxicity. RESULTS: A total of 26 patients was enrolled. Using the intent-to-treat population, stable disease was seen for an average of 19.2 weeks (median 12 weeks, range 3-108 weeks). Twenty patients were evaluable for response. The one patient that achieved disease stabilization for >2 years elected to come off-study because of patient preference. His last disease evaluation showed no evidence of progression. No objective responses were seen. Previous and ongoing clinical observations strongly imply that PSA could be a misleading surrogate marker for clinical effect with this type of drug. Therefore, prostate-specific antigen was not used as a marker for disease response. Toxicity was as expected with mild hypercalcemia and associated symptoms like constipation and prerenal azotemia seen in some patients. Six (30%) evaluable patients experienced stable disease for >6 months, suggesting possible cytostatic activity. CONCLUSION: The results of this and other trials suggest further clinical investigation in this disease with vitamin D analogues alone or in combination with other agents, such as chemotherapy, should be pursued.
Epidemiological data from the Hong Kong Cancer Registry for the period 1980-99 were analyzed. Altogether 21,768 new cases of nasopharyngeal carcinoma (NPC) and 8,664 related deaths were registered. In both genders, the peak incidence occurred in the 50-59 years age group, and this age distribution pattern remained similar throughout. The age-standardized incidence rate steadily decreased from 28.5 in 1980-84 to 20.2 in 1995-99 per 100,000 males, and from 11.2-7.8 per 100,000 females, resulting in a total decrease of 29% for males and 30% for females over this 20-year period. The magnitude of total decrease in NPC mortality amounted to 43% and 50%, respectively, as the age-standardized mortality rate steadily decreased from 13.7 in 1980-84 to 7.8 in 1995-99 per 100,000 males, and from 4.5-2.2 per 100,000 females. The age-standardized mortality/incidence ratio also decreased from the peak of 0.48 in 1980-84 to 0.39 in 1995-99 for males, and from 0.40-0.29 for females. Females had significantly lower age-standardized incidence (male/female ratio 2.5-2.6, p < 0.01) and mortality (male/female ratio 3.0-3.5, p< 0.01) throughout the whole period. Furthermore, females had consistently lower mortality/incidence ratio: 0.29 vs. 0.39 in 1995-99. These data are highly suggestive of significant improvement in prevention and control of NPC in Hong Kong. Closer scrutiny of the differences in intrinsic and extrinsic factors between the genders might help to show important factors affecting oncogenesis and prognosis. Possible ways for further reduction of incidence and mortality are discussed.
CONTEXT: Hearing impairment affects many older adults, but the incidence is unknown. OBJECTIVE: To determine the 5-year incidence and progression of hearing impairment. DESIGN: A longitudinal, population-based study of adults aged 48 to 92 years at baseline examination. Hearing sensitivity was measured twice, 5 years apart. SETTING: Testing was conducted at the Beaver Dam Community Hospital, Beaver Dam, Wis. PARTICIPANTS: A total of 1636 participants without hearing loss and 1085 participants with hearing loss at the baseline examination in 1993-1995 were reexamined in 1998-2000. MAIN OUTCOME MEASURES: The examinations included otoscopy, screening tympanometry, and tone air- and bone-conduction audiometry. Incidence of hearing impairment was defined as a pure-tone average (PTA) of thresholds at 500, 1000, 2000, and 4000 Hz (PTA 0.5, 1, 2, and 4 kHz) greater than 25 dB HL (hearing level) in either ear at follow-up among those without hearing loss at baseline. Progression was defined as a change of more than 5 dB in the PTA 0.5, 1, 2, and 4 kHz among those with hearing loss at baseline. RESULTS: The 5-year incidence of hearing impairment was 21%. More than half of those with hearing loss at baseline experienced a decline in hearing. Age was an important risk factor for both incidence and progression. Male sex, occupation, and education were associated with the incidence of hearing loss after adjusting for age. CONCLUSIONS: Older adults have a high risk of developing hearing loss. Among those with hearing loss, most experience further declines in hearing sensitivity over time. These data indicate that hearing impairment is an important public health problem and underscore the need for appropriate hearing screening and treatment.
BACKGROUND AND PURPOSE: To compare the rectal wall and bladder volume in the high dose region with or without the use of a balloon catheter with both three-dimensional (3D)-conformal and intensity modulated radiation therapy (CRT, IMRT) approaches in the treatment of prostate cancer. MATERIAL AND METHODS: Five patients with a wide range of prostate volumes and treated with primary external beam radiation therapy for localized prostate cancer were selected for analysis. Pinnacle treatment plans were generated utilizing a 3D conformal six-field design and an IMRT seven coplanar-field plan with a novel, three-step optimization and with ultrasound localization. Separate plans were devised with a rectal balloon deflated or air inflated with and without inclusion of the seminal vesicles (SV) in the target volume. The prescription dose was 76Gy in 38 fractions of 2Gy each. Cumulative dose-volume histograms (DVHs) were analyzed for the planning target volume (PTV), rectal wall, and bladder with an inflated (60cc air) or deflated balloon with and without SV included. The volumes of rectal wall and bladder above 60, 65, and 70Gy with each treatment approach were evaluated. RESULTS: Daily balloon placement was well-tolerated with good patient positional reproducibility. Inflation of the rectal balloon in all cases resulted in a significant decrease in the absolute volume of rectal wall receiving greater than 60, 65, or 70Gy. The rectal sparing ratio (RSR), consisting of a structure's high dose volume with the catheter inflated, divided by the volume with the catheter deflated, was calculated for each patient with and without seminal vesicle inclusion for 3D-CRT and IMRT. For 3D-CRT, RSRs with SV included were 0.59, 0.59, and 0.56 and with SV excluded were 0.60, 0.58, and 0.54 at doses of greater than 60, 65, and 70Gy, respectively. Similarly, for IMRT, the mean RSRs were 0.59, 0.59, and 0.63 including SV and 0.71, 0.66, and 0.67 excluding SV at these same dose levels, respectively. Averaged over all conditions, inflation of the rectal balloon resulted in a significant reduction in rectal volume receiving > or =65Gy to a mean ratio of 0.61 (P=0.01) or, in other words, a mean fractional high dose rectal sparing of 39%. There was a slight overall increase to 1.13 in the relative volume of bladder receiving at least 65Gy; however, this was not significant (P=0.6). Use of an endorectal balloon with a non-image-guided 3D-CRT plan produced about as much rectal dose sparing as a highly conformal, image-guided IMRT approach without a balloon. However, inclusion of a balloon with IMRT produced further rectal sparing still. CONCLUSION: These results indicate that use of a rectal balloon with a 3D-CRT plan incorporating typical treatment margins will produce significant high dose rectal sparing that is comparable to that achieved by a highly conformal IMRT with ultrasound localization. Further sparing is achieved with the inclusion of a balloon catheter in an IMRT plan. Thus, in addition to a previously reported advantage of prostate immobilization, the use of a rectal displacement balloon during daily treatment results in high dose rectal wall sparing during both modestly and highly conformal radiotherapy. Such sparing could assist in controlling and limiting rectal toxicity during increasingly aggressive dose escalation.
We consider estimating the distribution of nonterminal event time that may be censored by a terminal event but not vice versa. This problem may arise in two scenarios: (1) clinical trials involving both terminal and nonterminal events, or (2) when the primary outcome of the trial is nonterminal but there exists informative dropout. Inference is complicated by the dependent censoring from mortality or informative dropout. In this paper, we show that the joint distribution of the events can be formulated such that only the association is parameterized, with the marginal distributions unspecified. A closed form estimator for the association parameter is obtained from a novel adaptation of Oakes' concordance estimating equation. Tests for independence and goodness-of-fit of the model are also developed. A computationally simple, consistent and asymptotically normal estimator for the marginal distribution of the nonterminal event is given. Simulations demonstrate that the methods work well with practical sample sizes. The proposals are illustrated with data from an AIDS clinical trial.
There has been considerable methodological research on response-adaptive designs for clinical trials but they have seldom been used in practice. The many reasons for this are summarized in an article by Rosenberger and Lachin, but the two main reasons generally cited are logistical difficulties and the potential for bias due to selection effects, "drift" in patient characteristics or risk factors over time, and other sources. Jennison and Turnbull consider a group sequential, response-adaptive design for continuous outcome variables that partially addresses these concerns while at the same time allowing for early stopping. The key advantage of a group sequential approach in which randomization probabilities are kept constant within sequential groups is that a stratified analysis will eliminate bias due to drift. In this article we consider binary outcomes and an algorithm for altering the allocation ratio that depends on the strength of the accumulated evidence. Specifically, patients are enrolled in groups of size n(Ak), n(Bk), k=1, 2, ...K, where n(Ak), n(Bk) are the sample sizes in treatment arms A and B in sequential group k. Patients are initially allocated in a 1:1 ratio. After the kth interim analysis, if the z-value comparing outcomes in the two treatment groups is less than 1.0 in absolute value, the ratio remains 1:1; if the z-value exceeds 1.0, the next sequential group is allocated in the ratio R(1) favoring the currently better-performing treatment; if the z-statistic exceeds 1.5, the allocation ratio is R(2), and if the z-value exceeds 2.0, the allocation ratio is R(3). If the O'Brien-Fleming monitoring boundary is exceeded the trial is terminated. Group sample-sizes are adjusted upward to maintain equal increments of information when allocation ratios exceed one. The z-statistic is derived from a weighted log-odds ratio stratified by sequential group. Simulation studies and theoretical calculations were performed under a variety of scenarios and allocation rules. Results indicate that the method maintains the nominal type I error rate even when there is substantial drift in the patient population. When a true treatment difference exists, a modest reduction in the number of patients assigned to the inferior treatment arm can be achieved at the expense of smaller increases in the total sample size relative to a nonadaptive design. Limitations, such as the impact of delays in observing outcomes, are discussed, as well as areas for further research. We conclude that responsive adaptive designs may be useful for some purposes, particularly in the presence of large treatment effects, although allowing early stopping minimizes the benefits. If such a design is undertaken, the randomization and analysis should be stratified in order to avoid bias due to time trends.
Daily transabdominal ultrasound-directed localization has proven valuable in correcting for setup error and organ motion in the treatment of prostate cancer with three-dimensional conformal radiation therapy (3DCRT). The present study sought to determine whether this transabdominal ultrasound technology could also be reliably applied in the post-operative adjuvant or salvage setting to improve the reproducibility of coverage of the intended volumes and to enhance conformal avoidance of adjacent normal structures. Sixteen consecutive patients who received external beam radiotherapy underwent daily localization using an optically guided 3D-ultrasound target localization system (SonArray, Zmed, Inc., Ashland, MA). Six of the above patients were treated in a post-prostatectomy setting, either adjuvantly or for salvage, while the remaining 10 with intact prostates were treated definitively. Because the bladder neck generally approximates the postoperative prostatic fossa, it was used during ultrasound localization as the primary reference structure for the post-prostatectomy patients. For patients treated definitively, the prostate was the primary reference structure. Daily shifts were recorded and port films were taken weekly immediately after ultrasound-based repositioning. By comparing port films taken after ultrasound localization, which evaluates for both set-up error and internal shift, with the original digitally reconstructed radiographs (DRRs), which represents a zero clinical set-up error situation, the degree of variability in organ position was determined. The average absolute, ultrasound-based shifts from the clinical set-up position in the anterior/posterior, lateral, and cranial/caudal directions for the post-prostatectomy patients were 5 +/- 4 mm SD, 3 +/- 3 mm SD, and 3 +/- 4 mm SD over the entire course of treatment, respectively. The average vector length shift was 8 +/- 4 mm SD. For patients treated with an intact prostate, the analogous average absolute shifts in the anterior/posterior, lateral, and cranial/caudal directions were 4 +/- 3 mm SD, 4 +/- 3 mm SD, and 4 +/- 3 mm SD over the entire course of treatment. The average vector length shift was 7 +/- 4 mm SD. Vector length shifts representing interfraction internal motion were estimated by comparing post-ultrasound port films with DRRs. These were 5 +/- 3 mm SD and 4 +/- 4mm SD for post-prostatectomy and intact prostate patients, respectively. These ultrasound-based displacements were not statistically different in patients with an intact prostate versus patients post-prostatectomy (p > 0.1). In conclusion, daily transabdominal 3D-ultrasound localization proved to be a clinically feasible method of correcting for set-up and internal motion displacements. The bladder neck, which serves as an adequate localization reference structure for the prostatic fossa, could be readily ultrasound imaged and repositioned as necessary. Daily internal motion errors that would have occurred if only pre-treatment port films were used were similar in magnitude to those observed for the patients with intact prostates and were of sufficient magnitude to support the use of daily pre-treatment ultrasound localization in the post-prostatectomy setting.
PURPOSE: To study the factors affecting the risk of symptomatic temporal lobe necrosis after different fractionation schedules. METHODS AND MATERIALS: One thousand thirty-two patients with T1-2 nasopharyngeal carcinoma treated with radical radiotherapy in Hong Kong during 1990-1995 were studied. They were treated at four different centers with similar techniques but different fractionation schedules: 984 patients were given 1 fraction daily throughout (q.d.), and 48 patients were irradiated twice daily (b.i.d.) for part of the course. The median total dose was 62.5 Gy (range 50.4-71.2), dose per fraction was 2.5 Gy (range 1.6-4.2), and overall treatment time (OTT) was 44 days (range 29-70). In addition, 500 patients received supplementary doses for parapharyngeal extension, 113 received booster doses by brachytherapy, and 114 received sequential chemotherapy using cisplatin-based regimes. RESULTS: Altogether, 24 patients developed symptomatic temporal lobe necrosis: 18 from the q.d. group and 6 from the b.i.d. group. The 5-year actuarial incidence ranged from 0% (after 66 Gy in 33 fractions within 44 days) to 14% (after 71.2 Gy in 40 fractions within 35 days). Multivariate analyses showed that the risk was significantly affected by the fractional effect of the product of total dose and dose per fraction (hazard ratio [HR] = 1.04, 95% confidence interval [CI] 1.02-1.05), OTT (HR 0.88, 95% CI 0.80-0.97), and b.i.d. scheduling (HR 13, 95% CI 3-54). Repeating the analyses for patients treated with the q.d. schedules confirmed the independent significance of OTT in addition to the product of total dose and dose per fraction. CONCLUSION: The tentative results suggest that in addition to fractional dose, the OTT also had significant impact on the risk of temporal lobe necrosis, and b.i.d. scheduling increased the hazard further.
We show that the nonparametric maximum likelihood estimate (NPMLE) of the regression coefficient from the joint likelihood (of the regression coefficient and the baseline survival) works well for the Cox proportional hazards model with left-truncated and interval-censored data, but the NPMLE may underestimate the baseline survival. Two alternatives are also considered: first, the marginal likelihood approach by extending Satten (1996, Biometrika 83, 355-370) to truncated data, where the baseline distribution is eliminated as a nuisance parameter; and second, the monotone maximum likelihood estimate that maximizes the joint likelihood by assuming that the baseline distribution has a nondecreasing hazard function, which was originally proposed to overcome the underestimation of the survival from the NPMLE for left-truncated data without covariates (Tsai, 1988, Biometrika 75, 319-324). The bootstrap is proposed to draw inference. Simulations were conducted to assess their performance. The methods are applied to the Massachusetts Health Care Panel Study data set to compare the probabilities of losing functional independence for male and female seniors.