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.^

Adaptive clinical trial design for targeted therapy development

The development of targeted therapy involve many challenges. Our study will address some of the key issues involved in biomarker identification and clinical trial design. In our study, we propose two biomarker selection methods, and then apply them in two different clinical trial designs for targeted therapy development. In particular, we propose a Bayesian two-step lasso procedure for biomarker selection in the proportional hazards model in Chapter 2. In the first step of this strategy, we use the Bayesian group lasso to identify the important marker groups, wherein each group contains the main effect of a single marker and its interactions with treatments. In the second step, we zoom in to select each individual marker and the interactions between markers and treatments in order to identify prognostic or predictive markers using the Bayesian adaptive lasso. In Chapter 3, we propose a Bayesian two-stage adaptive design for targeted therapy development while implementing the variable selection method given in Chapter 2. In Chapter 4, we proposed an alternate frequentist adaptive randomization strategy for situations where a large number of biomarkers need to be incorporated in the study design. We also propose a new adaptive randomization rule, which takes into account the variations associated with the point estimates of survival times. In all of our designs, we seek to identify the key markers that are either prognostic or predictive with respect to treatment. We are going to use extensive simulation to evaluate the operating characteristics of our methods.^

Analyzing left-truncated right-censored data with uncertain onset time with parametric models

Prevalent sampling is an efficient and focused approach to the study of the natural history of disease. Right-censored time-to-event data observed from prospective prevalent cohort studies are often subject to left-truncated sampling. Left-truncated samples are not randomly selected from the population of interest and have a selection bias. Extensive studies have focused on estimating the unbiased distribution given left-truncated samples. However, in many applications, the exact date of disease onset was not observed. For example, in an HIV infection study, the exact HIV infection time is not observable. However, it is known that the HIV infection date occurred between two observable dates. Meeting these challenges motivated our study. We propose parametric models to estimate the unbiased distribution of left-truncated, right-censored time-to-event data with uncertain onset times. We first consider data from a length-biased sampling, a specific case in left-truncated samplings. Then we extend the proposed method to general left-truncated sampling. With a parametric model, we construct the full likelihood, given a biased sample with unobservable onset of disease. The parameters are estimated through the maximization of the constructed likelihood by adjusting the selection bias and unobservable exact onset. Simulations are conducted to evaluate the finite sample performance of the proposed methods. We apply the proposed method to an HIV infection study, estimating the unbiased survival function and covariance coefficients. ^

Modified 3+3 design for phase I clinical trials

Phase I clinical trial is mainly designed to determine the maximum tolerated dose (MTD) of a new drug. Optimization of phase I trial design is crucial to minimize the number of enrolled patients exposed to unsafe dose levels and to provide reliable information to the later phases of clinical trials. Although it has been criticized about its inefficient MTD estimation, nowadays the traditional 3+3 method remains dominant in practice due to its simplicity and conservative estimation. There are many new designs that have been proven to generate more credible MTD estimation, such as the Continual Reassessment Method (CRM). Despite its accepted better performance, the CRM design is still not widely used in real trials. There are several factors that contribute to the difficulties of CRM adaption in practice. First, CRM is not widely accepted by the regulatory agencies such as FDA in terms of safety. It is considered to be less conservative and tend to expose more patients above the MTD level than the traditional design. Second, CRM is relatively complex and not intuitive for the clinicians to fully understand. Third, the CRM method take much more time and need statistical experts and computer programs throughout the trial. The current situation is that the clinicians still tend to follow the trial process that they are comfortable with. This situation is not likely to change in the near future. Based on this situation, we have the motivation to improve the accuracy of MTD selection while follow the procedure of the traditional design to maintain simplicity. We found that in 3+3 method, the dose transition and the MTD determination are relatively independent. Thus we proposed to separate the two stages. The dose transition rule remained the same as 3+3 method. After getting the toxicity information from the dose transition stage, we combined the isotonic transformation to ensure the monotonic increasing order before selecting the optimal MTD. To compare the operating characteristics of the proposed isotonic method and the other designs, we carried out 10,000 simulation trials under different dose setting scenarios to compare the design characteristics of the isotonic modified method with standard 3+3 method, CRM, biased coin design (BC) and k-in-a-row design (KIAW). The isotonic modified method improved MTD estimation of the standard 3+3 in 39 out of 40 scenarios. The improvement is much greater when the target is 0.3 other than 0.25. The modified design is also competitive when comparing with other selected methods. A CRM method performed better in general but was not as stable as the isotonic method throughout the different dose settings. The results demonstrated that our proposed isotonic modified method is not only easily conducted using the same procedure as 3+3 but also outperforms the conventional 3+3 design. It can also be applied to determine MTD for any given TTL. These features make the isotonic modified method of practical value in phase I clinical trials.^

Instrumental variable method for the causal relationship between soluble receptor for advanced glycation end-products (sRAGE) and risk of pancreatic cancer

This thesis project is motivated by the potential problem of using observational data to draw inferences about a causal relationship in observational epidemiology research when controlled randomization is not applicable. Instrumental variable (IV) method is one of the statistical tools to overcome this problem. Mendelian randomization study uses genetic variants as IVs in genetic association study. In this thesis, the IV method, as well as standard logistic and linear regression models, is used to investigate the causal association between risk of pancreatic cancer and the circulating levels of soluble receptor for advanced glycation end-products (sRAGE). Higher levels of serum sRAGE were found to be associated with a lower risk of pancreatic cancer in a previous observational study (255 cases and 485 controls). However, such a novel association may be biased by unknown confounding factors. In a case-control study, we aimed to use the IV approach to confirm or refute this observation in a subset of study subjects for whom the genotyping data were available (178 cases and 177 controls). Two-stage IV method using generalized method of moments-structural mean models (GMM-SMM) was conducted and the relative risk (RR) was calculated. In the first stage analysis, we found that the single nucleotide polymorphism (SNP) rs2070600 of the receptor for advanced glycation end-products (AGER) gene meets all three general assumptions for a genetic IV in examining the causal association between sRAGE and risk of pancreatic cancer. The variant allele of SNP rs2070600 of the AGER gene was associated with lower levels of sRAGE, and it was neither associated with risk of pancreatic cancer, nor with the confounding factors. It was a potential strong IV (F statistic = 29.2). However, in the second stage analysis, the GMM-SMM model failed to converge due to non- concaveness probably because of the small sample size. Therefore, the IV analysis could not support the causality of the association between serum sRAGE levels and risk of pancreatic cancer. Nevertheless, these analyses suggest that rs2070600 was a potentially good genetic IV for testing the causality between the risk of pancreatic cancer and sRAGE levels. A larger sample size is required to conduct a credible IV analysis.^

External validation study of a clinical prediction rule for ambulation outcomes after traumatic spinal cord injury

The main objective of this study was to determine the external validity of a clinical prediction rule developed by the European Multicenter Study on Human Spinal Cord Injury (EM-SCI) to predict the ambulation outcomes 12 months after traumatic spinal cord injury. Data from the North American Clinical Trials Network (NACTN) data registry with approximately 500 SCI cases were used for this validity study. The predictive accuracy of the EM-SCI prognostic model was evaluated using calibration and discrimination based on 231 NACTN cases. The area under the receiver-operating-characteristics curve (ROC) curve was 0.927 (95% CI 0.894 – 0.959) for the EM-SCI model when applied to NACTN population. This is lower than the AUC of 0.956 (95% CI 0.936 – 0.976) reported for the EM-SCI population, but suggests that the EM-SCI clinical prediction rule distinguished well between those patients in the NACTN population who were able to achieve independent ambulation and those who did not achieve independent ambulation. The calibration curve suggests that higher the prediction score is, the better the probability of walking with the best prediction for AIS D patients. In conclusion, the EM-SCI clinical prediction rule was determined to be generalizable to the adult NACTN SCI population.^

The risk prediction for SPM and its impact on the survival in patients with head and neck squamous cell carcinoma

Head and Neck Squamous Cell Carcinoma (HNSCC) is the sixth common malignancy in the world, with high rates of developing second primary malignancy (SPM) and moderately low survival rates. This disease has become an enormous challenge in the cancer research and treatments. For HNSCC patients, a highly significant cause of post-treatment mortality and morbidity is the development of SPM. Hence, assessment of predicting the risk for the development of SPM would be very helpful for patients, clinicians and policy makers to estimate the survival of patients with HNSCC. In this study, we built a prognostic model to predict the risk of developing SPM in patients with newly diagnosed HNSCC. The dataset used in this research was obtained from The University of Texas MD Anderson Cancer Center. For the first aim, we used stepwise logistic regression to identify the prognostic factors for the development of SPM. Our final model contained cancer site and overall cancer stage as our risk factors for SPM. The Hosmer-Lemeshow test (p-value= 0.15>0.05) showed the final prognostic model fit the data well. The area under the ROC curve was 0.72 that suggested the discrimination ability of our model was acceptable. The internal validation confirmed the prognostic model was a good fit and the final prognostic model would not over optimistically predict the risk of SPM. This model needs external validation by using large data sample size before it can be generalized to predict SPM risk for other HNSCC patients. For the second aim, we utilized a multistate survival analysis approach to estimate the probability of death for HNSCC patients taking into consideration of the possibility of SPM. Patients without SPM were associated with longer survival. These findings suggest that the development of SPM could be a predictor of survival rates among the patients with HNSCC.^

Optimal, minimax, and Bayesian two-stage designs in two-dose phase II clinical trials

Background: For most cytotoxic and biologic anti-cancer agents, the response rate of the drug is commonly assumed to be non-decreasing with an increasing dose. However, an increasing dose does not always result in an appreciable increase in the response rate. This may especially be true at high doses for a biologic agent. Therefore, in a phase II trial the investigators may be interested in testing the anti-tumor activity of a drug at more than one (often two) doses, instead of only at the maximum tolerated dose (MTD). This way, when the lower dose appears equally effective, this dose can be recommended for further confirmatory testing in a phase III trial under potential long-term toxicity and cost considerations. A common approach to designing such a phase II trial has been to use an independent (e.g., Simon's two-stage) design at each dose ignoring the prior knowledge about the ordering of the response probabilities at the different doses. However, failure to account for this ordering constraint in estimating the response probabilities may result in an inefficient design. In this dissertation, we developed extensions of Simon's optimal and minimax two-stage designs, including both frequentist and Bayesian methods, for two doses that assume ordered response rates between doses. ^ Methods: Optimal and minimax two-stage designs are proposed for phase II clinical trials in settings where the true response rates at two dose levels are ordered. We borrow strength between doses using isotonic regression and control the joint and/or marginal error probabilities. Bayesian two-stage designs are also proposed under a stochastic ordering constraint. ^ Results: Compared to Simon's designs, when controlling the power and type I error at the same levels, the proposed frequentist and Bayesian designs reduce the maximum and expected sample sizes. Most of the proposed designs also increase the probability of early termination when the true response rates are poor. ^ Conclusion: Proposed frequentist and Bayesian designs are superior to Simon's designs in terms of operating characteristics (expected sample size and probability of early termination, when the response rates are poor) Thus, the proposed designs lead to more cost-efficient and ethical trials, and may consequently improve and expedite the drug discovery process. The proposed designs may be extended to designs of multiple group trials and drug combination trials.^

Study on the effect of metformin in patients of metastatic renal cell cancer with diabetes receiving tyrosine kinase inhibitor therapy

Objective: The primary objective of our study was to study the effect of metformin in patients of metastatic renal cell cancer (mRCC) and diabetes who are on treatment with frontline therapy of tyrosine kinase inhibitors. The effect of therapy was described in terms of overall survival and progression free survival. Comparisons were made between group of patients receiving metformin versus group of patients receiving insulin in diabetic patients of metastatic renal cancer on frontline therapy. Exploratory analyses were also done comparing non-diabetic patients of metastatic renal cell cancer receiving frontline therapy compared to diabetic patients of metastatic renal cell cancer receiving metformin therapy. ^ Methods: The study design is a retrospective case series to elaborate the response rate of frontline therapy in combination with metformin for mRCC patients with type 2 diabetes mellitus. The cohort was selected from a database, which was generated for assessing the effect of tyrosine kinase inhibitor therapy associated hypertension in metastatic renal cell cancer at MD Anderson Cancer Center. Patients who had been started on frontline therapy for metastatic renal cell carcinoma from all ethnic and racial backgrounds were selected for the study. The exclusion criteria would be of patients who took frontline therapy for less than 3 months or were lost to follow-up. Our exposure variable was treatment with metformin, which comprised of patients who took metformin for the treatment of type 2 diabetes at any time of diagnosis of metastatic renal cell carcinoma. The outcomes assessed were last available follow-up or date of death for the overall survival and date of progression of disease from their radiological reports for time to progression. The response rates were compared by covariates that are known to be strongly associated with renal cell cancer. ^ Results: For our primary analyses between the insulin and metformin group, there were 82 patients, out of which 50 took insulin therapy and 32 took metformin therapy for type 2 diabetes. For our exploratory analysis, we compared 32 diabetic patients on metformin to 146 non-diabetic patients, not on metformin. Baseline characteristics were compared among the population. The time from the start of treatment until the date of progression of renal cell cancer and date of death or last follow-up were estimated for survival analysis. ^ In our primary analyses, there was a significant difference in the time to progression of patients receiving metformin therapy vs insulin therapy, which was also seen in our exploratory analyses. The median time to progression in primary analyses was 1259 days (95% CI: 659-1832 days) in patients on metformin therapy compared to 540 days (95% CI: 350-894) in patients who were receiving insulin therapy (p=0.024). The median time to progression in exploratory analyses was 1259 days (95% CI: 659-1832 days) in patients on metformin therapy compared to 279 days (95% CI: 202-372 days) in non-diabetic group (p-value <0.0001). ^ The median overall survival was 1004 days in metformin group (95% CI: 761-1212 days) compared to 816 days (95%CI: 558-1405 days) in insulin group (p-value<0.91). For the exploratory analyses, the median overall survival was 1004 days in metformin group (95% CI: 761-1212 days) compared to 766 days (95%CI: 649-965 days) in the non-diabetic group (p-value<0.78). Metformin was observed to increase the progression free survival in both the primary and exploratory analyses (HR=0.52 in metformin Vs insulin group and HR=0.36 in metformin Vs non-diabetic group, respectively). ^ Conclusion: In laboratory studies and a few clinical studies metformin has been proven to have dual benefits in patients suffering from cancer and type 2-diabetes via its action on the mammalian target of Rapamycin pathway and effect in decreasing blood sugar by increasing the sensitivity of the insulin receptors to insulin. Several studies in breast cancer patients have documented a beneficial effect (quantified by pathological remission of cancer) of metformin use in patients taking treatment for breast cancer therapy. Combination of metformin therapy in patients taking frontline therapy for renal cell cancer may provide a significant benefit in prolonging the overall survival in patients with metastatic renal cell cancer and diabetes. ^

Assessing the patterns of colorectal cancer treatment, adherence to treatment guidelines and survival in Texas

Colorectal cancer (CRC) is the third leading cancer in both incidence and mortality in Texas. This study investigated the adherence of CRC treatment to standard treatment guidelines and the association between standard treatment and CRC survival in Texas. The author used Texas Cancer Registry (TCR) and Medicare linked data to study the CRC treatment patterns and factors associated with standard treatment in patients who were more than 65 years old and were diagnosed in 2001 through 2007. We also determined whether adherence to standard treatment affect patients' survival. Multiple logistic regression and Cox regression analysis were used to analyze our data. Both regression models are adjusted for demographic characteristics and tumor characteristics. We found that for the 3977 regional colon cancer patients 80 years old or younger, 60.2% of them received chemotherapy, in adherence to the recommended treatment guidelines. People with younger age, female gender, higher education and lower comorbidity score are more likely adherent to this surgery guideline. Patients' adherence to chemotherapy in this cohort have better survival compared to those who are not (HR: 0.76, 95% CI: 0.68-0.84). For the 12709 colon cancer patients treated with surgery, 49.3% have more than 12 lymph nodes removed, in adherence to the treatment guidelines. People with younger age, female gender, higher education, regional stage, lager tumor size and lower comorbidity score are more likely to adherent to this surgery guideline. Patients with more than 12 lymph nodes removed in this cohort have better survival (HR: 0.86, 95% CI: 0.82-0.91). For the 1211 regional rectal cancer patients 80 years old or younger, 63.2% of them were adherent to radiation treatment. People with smaller tumor size and lower comorbidity score are more likely to adherent to this radiation guideline. There is no significant survival difference between radiation adherent patients and non-adherent patients (HR: 1.03, 95% CI: 0.82-1.29). For the 1122 regional rectal cancer patients 80 years old or younger who were treated with surgery, 76.0% of them received postoperative chemotherapy, in adherence to the treatment guidelines. People with younger age and smaller comorbidity score are related with higher adherence rate. Patients adherent with adjuvant chemotherapy in this cohort have better survival than those were not adherent (HR: 0.60, 95% CI: 0.45-0.79).^

Classification of cellular malignancy associated changes in cervical cancer

Cervical cancer is the leading cause of death and disease from malignant neoplasms among women in developing countries. Even though the Pap smear has significantly decreased the number of deaths from cervical cancer in the past years, it has its limitations. Researchers have developed an automated screening machine which can potentially detect abnormal cases that are overlooked by conventional screening. The goal of quantitative cytology is to classify the patient's tissue sample based on quantitative measurements of the individual cells. It is also much cheaper and potentially can take less time. One of the major challenges of collecting cells with a cytobrush is the possibility of not sampling any existing dysplastic cells on the cervix. Being able to correctly classify patients who have disease without the presence of dysplastic cells could improve the accuracy of quantitative cytology algorithms. Subtle morphologic changes in normal-appearing tissues adjacent to or distant from malignant tumors have been shown to exist, but a comparison of various statistical methods, including many recent advances in the statistical learning field, has not previously been done. The objective of this thesis is to use different classification methods applied to quantitative cytology data for the detection of malignancy associated changes (MACs). In this thesis, Elastic Net is the best algorithm. When we applied the Elastic Net algorithm to the test set, we combined the training set and validation set as "training" set and used 5-fold cross validation to choose the parameter for Elastic Net. It has a sensitivity of 47% at 80% specificity, an AUC 0.52, and a partial AUC 0.10 (95% CI 0.09-0.11).^

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.^

The assumptions and effects of conservative procedures in low -dose risk assessment for setting safety standards

Conservative procedures in low-dose risk assessment are used to set safety standards for known or suspected carcinogens. However, the assumptions upon which the methods are based and the effects of these methods are not well understood.^ To minimize the number of false-negatives and to reduce the cost of bioassays, animals are given very high doses of potential carcinogens. Results must then be extrapolated to much smaller doses to set safety standards for risks such as one per million. There are a number of competing methods that add a conservative safety factor into these calculations.^ A method of quantifying the conservatism of these methods was described and tested on eight procedures used in setting low-dose safety standards. The results using these procedures were compared by computer simulation and by the use of data from a large scale animal study.^ The method consisted of determining a "true safe dose" (tsd) according to an assumed underlying model. If one assumed that Y = the probability of cancer = P(d), a known mathematical function of the dose, then by setting Y to some predetermined acceptable risk, one can solve for d, the model's "true safe dose".^ Simulations were generated, assuming a binomial distribution, for an artificial bioassay. The eight procedures were then used to determine a "virtual safe dose" (vsd) that estimates the tsd, assuming a risk of one per million. A ratio R = ((tsd-vsd)/vsd) was calculated for each "experiment" (simulation). The mean R of 500 simulations and the probability R $<$ 0 was used to measure the over and under conservatism of each procedure.^ The eight procedures included Weil's method, Hoel's method, the Mantel-Byran method, the improved Mantel-Byran, Gross's method, fitting a one-hit model, Crump's procedure, and applying Rai and Van Ryzin's method to a Weibull model.^ None of the procedures performed uniformly well for all types of dose-response curves. When the data were linear, the one-hit model, Hoel's method, or the Gross-Mantel method worked reasonably well. However, when the data were non-linear, these same methods were overly conservative. Crump's procedure and the Weibull model performed better in these situations. ^

Age -period -cohort analysis: An extension of Cox's lifetable regression with time -dependent covariates

It is well known that an identification problem exists in the analysis of age-period-cohort data because of the relationship among the three factors (date of birth + age at death = date of death). There are numerous suggestions about how to analyze the data. No one solution has been satisfactory. The purpose of this study is to provide another analytic method by extending the Cox's lifetable regression model with time-dependent covariates. The new approach contains the following features: (1) It is based on the conditional maximum likelihood procedure using a proportional hazard function described by Cox (1972), treating the age factor as the underlying hazard to estimate the parameters for the cohort and period factors. (2) The model is flexible so that both the cohort and period factors can be treated as dummy or continuous variables, and the parameter estimations can be obtained for numerous combinations of variables as in a regression analysis. (3) The model is applicable even when the time period is unequally spaced.^ Two specific models are considered to illustrate the new approach and applied to the U.S. prostate cancer data. We find that there are significant differences between all cohorts and there is a significant period effect for both whites and nonwhites. The underlying hazard increases exponentially with age indicating that old people have much higher risk than young people. A log transformation of relative risk shows that the prostate cancer risk declined in recent cohorts for both models. However, prostate cancer risk declined 5 cohorts (25 years) earlier for whites than for nonwhites under the period factor model (0 0 0 1 1 1 1). These latter results are similar to the previous study by Holford (1983).^ The new approach offers a general method to analyze the age-period-cohort data without using any arbitrary constraint in the model. ^

False -positives and false-negatives in tests for trend

False-positive and false-negative values were calculated for five different designs of the trend test and it was demonstrated that a design suggested by Portier and Hoel in 1984 for a different problem produced the lowest false-positive and false-negative rates when applied to historical spontaneous tumor rate data for Fischer Rats. ^