Testing for differences in changes in the presence of censoring: parametric and non-parametric methods

Variations in Risk of End-Stage Renal Disease and Risk of Mortality in an International Study of Patients With Type 1 Diabetes and Advanced Nephropathy

OBJECTIVE

Patients with type 1 diabetes and diabetic nephropathy are targets for intervention to reduce high risk of end-stage renal disease (ESRD) and deaths. This study compares risks of these outcomes in four international cohorts.

RESEARCH DESIGN AND METHODS

In the 1990s and early 2000s, Caucasian patients with type 1 diabetes with persistent macroalbuminuria in chronic kidney disease stages 1-3 were identified in the Joslin Clinic (U.S., 432), Finnish Diabetic Nephropathy Study (FinnDiane) (Finland, 486), Steno Diabetes Center Copenhagen (Denmark, 368), and INSERM (France, 232) and were followed for 3-18 years with annual creatinine measurements to ascertain ESRD and deaths unrelated to ESRD.

RESULTS

During 15,685 patient-years, 505 ESRD cases (rate 32/1,000 patient-years) and 228 deaths unrelated to ESRD (rate 14/1,000 patient-years) occurred. Risk of ESRD was associated with male sex; younger age; lower estimated glomerular filtration rate (eGFR); higher albumin/creatinine ratio, HbA_1c, and systolic blood pressure; and smoking. Risk of death unrelated to ESRD was associated with older age, smoking, and higher baseline eGFR. In adjusted analysis, ESRD risk was highest in Joslin versus reference FinnDiane (hazard ratio [HR] 1.44, P = 0.003) and lowest in Steno (HR 0.54, P < 0.001). Differences in eGFR slopes paralleled risk of ESRD. Mortality unrelated to ESRD was lowest in Joslin (HR 0.68, P = 0.003 vs. the other cohorts). Competing risk did not explain international differences in the outcomes.

CONCLUSIONS

Despite almost universal renoprotective treatment, progression to ESRD and mortality in patients with type 1 diabetes with advanced nephropathy are still very high and differ among countries. Finding causes of these differences may help reduce risk of these outcomes.

Synergism between circulating tumor necrosis factor receptor 2 and HbA(1c) in determining renal decline during 5-18 years of follow-up in patients with type 1 diabetes and proteinuria

OBJECTIVE

We studied the serum concentration of tumor necrosis factor receptor 2 (TNFR2) and the rate of renal decline, a measure of the intensity of the disease process leading to end-stage renal disease (ESRD).

RESEARCH DESIGN AND METHODS

A cohort of 349 type 1 diabetic patients with proteinuria was followed for 5-18 years. Serum TNFR2, glycated hemoglobin A1c (HbA1c), and other characteristics were measured at enrollment. We used a novel analytic approach, a joint longitudinal-survival model, fitted to serial estimates of glomerular filtration rate (eGFR) based on serum creatinine (median seven per patient) and time to onset of ESRD (112 patients) to estimate the rate of renal decline (eGFR loss).

RESULTS

At enrollment, all patients had chronic kidney disease stage 1-3. The mean (±SD) rate of eGFR loss during 5-18 years of follow-up was -5.2 (±4.9) mL/min/1.73 m(2)/year. Serum TNFR2 was the strongest determinant of renal decline and ESRD risk (C-index 0.79). The rate of eGFR loss became steeper with rising concentration of TNFR2, and elevated HbA1c augmented the strength of this association (P = 0.030 for interaction). In patients with HbA1c ≥10.1% (87 mmol/mol), the difference in the rate of eGFR loss between the first and fourth quartiles of TNFR2 was 5.4 mL/min/1.73 m(2)/year, whereas it was only 1.9 in those with HbA1c <7.9% (63 mmol/mol).

CONCLUSIONS

Circulating TNFR2 is a major determinant of renal decline in patients with type 1 diabetes and proteinuria. Elevated HbA1c magnifies its effect. Although the mechanisms of this synergism are unknown, our findings allow us to stratify patients according to risk of ESRD.

Performance of selected nonparametric tests for discrete longitudinal data under different patterns of missing data

Comparison of changes over time of a continuous response variable between treatment groups is often of main interest in clinical trials. When the distributional properties of the continuous response variable are not regular enough, or when the response is discrete, nonparametric techniques have been used. The relative performances of selected repeated measures nonparametric two-sample tests proposed by Wei and Lachin, Koziol, Wei and Johnson, and the adapted Wilcoxon Rank-Sum test are compared through simulations based on quality of life data. The Wilcoxon Rank-Sum test is the most powerful and is not significantly affected by the different patterns of missing data.

Differential role of basal keratinocytes in UV-induced immunosuppression and skin cancer

Cyclobutane pyrimidine dimers (CPDs) and 6-4 photoproducts (6-4PPs) comprise major UV-induced photolesions. If left unrepaired, these lesions can induce mutations and skin cancer, which is facilitated by UV-induced immunosuppression. Yet the contribution of lesion and cell type specificity to the harmful biological effects of UV exposure remains currently unclear. Using a series of photolyase-transgenic mice to ubiquitously remove either CPDs or 6-4PPs from all cells in the mouse skin or selectively from basal keratinocytes, we show that the majority of UV-induced acute effects to require the presence of CPDs in basal keratinocytes in the mouse skin. At the fundamental level of gene expression, CPDs induce the expression of genes associated with repair and recombinational processing of DNA damage, as well as apoptosis and a response to stress. At the organismal level, photolyase-mediated removal of CPDs, but not 6-4PPs, from the genome of only basal keratinocytes substantially diminishes the incidence of skin tumors; however, it does not affect the UVB-mediated immunosuppression. Taken together, these findings reveal a differential role of basal keratinocytes in these processes, providing novel insights into the skin's acute and chronic responses to UV in a lesion- and cell-type-specific manner.

Small-sample inference for incomplete longitudinal data with truncation and censoring in tumor xenograft models

In cancer drug development, demonstrating activity in xenograft models, where mice are grafted with human cancer cells, is an important step in bringing a promising compound to humans. A key outcome variable is the tumor volume measured in a given period of time for groups of mice given different doses of a single or combination anticancer regimen. However, a mouse may die before the end of a study or may be sacrificed when its tumor volume quadruples, and its tumor may be suppressed for some time and then grow back. Thus, incomplete repeated measurements arise. The incompleteness or missingness is also caused by drastic tumor shrinkage (<0.01 cm3) or random truncation. Because of the small sample sizes in these models, asymptotic inferences are usually not appropriate. We propose two parametric test procedures based on the EM algorithm and the Bayesian method to compare treatment effects among different groups while accounting for informative censoring. A real xenograft study on a new antitumor agent, temozolomide, combined with irinotecan is analyzed using the proposed methods.

Sensitivity analysis of longitudinal binary quality of life data with drop-out: an example using the EORTC QLQ-C30

Analysing quality of life data (QOL) may be complicated for several reasons. Quality of life data not only involves repeated measures but is also usually collected on ordered categorical responses. In addition, it is evident that not all patients provide the same number of assessments, due to attrition caused by death or other medical reasons. In the recent statistical literature, increasing attention is given to methods which can handle non-continuous outcomes in the presence of missing data. The aim of this paper is to investigate the effect on statistical conclusions of applying different modelling techniques to QOL data generated from an EORTC phase III trial. Treatment effects and treatment differences are of major concern. First, a random-effects model is fitted, relating a binary longitudinal response (derived from the physical functioning scale of the QLQ-C30) to several covariates. In a second approach, marginal models are fitted, retaining the response variable and the mean structure used before. The fitted marginal models only differ with respect to the considered estimation procedure: generalized estimating equations (GEE); weighted generalized estimating equations (WGEE), and maximum likelihood (ML).

Statistical considerations in the intent-to-treat principle

This paper describes some of the statistical considerations in the intent-to-treat design and analysis of clinical trials. The pivotal property of a clinical trial is the assignment of treatments to patients at random. Randomization alone, however, is not sufficient to provide an unbiased comparison of therapies. An additional requirement is that the set of patients contributing to an analysis provides an unbiased assessment of treatment effects, or that any missing data are ignorable. A sufficient condition to provide an unbiased comparison is to obtain complete data on all randomized subjects. This can be achieved by an intent-to-treat design wherein all patients are followed until death or the end of the trial, or until the outcome event is reached in a time-to-event trial, irrespective of whether the patient is still receiving or complying with the assigned treatment. The properties of this strategy are contrasted with those of an efficacy subset analysis in which patients and observable patient data are excluded from the analysis on the basis of information obtained postrandomization. I describe the potential bias that can be introduced by such postrandomization exclusions and the pursuant effects on type I error probabilities. Especially in a large study, the inflation in type I error probability can be severe, 0.50 or higher, even when the null hypothesis is true. Standard statistical methods for the analysis of censored or incomplete observations all require the assumption of missing at random to some degree, and none of these methods adjust for the potential bias introduced by post hoc subset selection. Nor is such adjustment possible unless one posits a model that relates the missing observations to other observed information for each subject-models that are inherently untestable. Further, the subset selection bias is confounded with the subset-specific treatment effect, and the two components are not identifiable without additional untestable assumptions. Methods for sensitivity analysis to assess the impact of bias in the efficacy subset analysis are described. It is generally believed that the efficacy subset analysis has greater power than the intent-to-treat analysis. However, even when the efficacy subset analysis is assumed to be unbiased, or have a true type I error probability equal to the desired level alpha, situations are described where the intent-to-treat analysis in fact has greater power than the efficacy subset analysis. The intent-to-treat design, wherein all possible patients continue to be followed, is especially powerful when an effective treatment arrests progression of disease during its administration. Thus, a patient benefits long after the patient becomes noncompliant or the treatment is terminated. In such cases, a landmark analysis using the observations from the last patient evaluation is likely to prove more powerful than life-table or longitudinal analyses. Examples are described.

Worst-rank score analysis with informatively missing observations in clinical trials

Many randomized clinical trials schedule subjects to undergo some assessment at a fixed time (or times) after the initiation of treatment. Often, these follow-up measurements may be missing for some subjects because a disease-related event occurred prior to the time of the follow-up observation. For example, a study of congestive heart failure may schedule patients to undergo exercise testing at 12 weeks, but this measurement may be missing for those who died of heart disease during the study. In such cases, the measurements are informatively missing because mortality from heart disease and a decline in exercise both indicate progression of the underlying disease. It is inappropriate, therefore, to treat these missing observations as missing-at-random and ignore them in the analysis. In one approach to this problem, investigators have included such patients in the analysis of the follow-up data by assigning a rank that represents a "worst-rank score" relative to those actually observed. Some, however, have criticized this procedure as having the potential to produce biased results. In this paper, we explore the statistical properties of such an analysis. We show under a specific model that the imputation of a worst-rank score for informatively missing observations provides an unbiased test against a restricted alternative. We also describe generalizations that employ the actual times of the informative event. We present an example from a study of congestive heart failure. Last, we discuss the implications of this approach and of other methods.

A comparison of the random-effects pattern mixture model with last-observation-carried-forward (LOCF) analysis in longitudinal clinical trials with dropouts

The last-observation-carried-forward imputation method is commonly used for imputting data missing due to dropouts in longitudinal clinical trials. The method assumes that outcome remains constant at the last observed value after dropout, which is unlikely in many clinical trials. Recently, random-effects regression models have become popular for analysis of longitudinal clinical trial data with dropouts. However, inference obtained from random-effects regression models is valid when the missing-at-random dropout process is present. The random-effects pattern-mixture model, on the other hand, provides an approach that is valid under more general missingness mechanisms. In this article we describe the use of random-effects pattern-mixture models under different patterns for dropouts. First, subjects are divided into groups depending on their missing-data patterns, and then model parameters are estimated for each pattern. Finally, overall estimates are obtained by averaging over the missing-data patterns and corresponding standard errors are obtained using the delta method. A typical longitudinal clinical trial data set is used to illustrate and compare the above methods of data analyses in the presence of missing data due to dropouts.

Statistical approaches to experimental design and data analysis of in vivo studies

The objective of any experiment is to obtain an unbiased and precise estimate of a treatment effect in an efficient manner. Statistical aspects of the design, conduct, and analysis of the experiment play a major role in determining whether this goal is met. We highlight some of the more important statistical issues that pertain to in vivo studies. Particular emphasis is placed on the role of randomization, the number of animals, the utilization of repeated measures data, adjustments for missing data, and dealing with multiple causes of death or treatment failure. The discussion is not intended to be a comprehensive guide to all the statistical issues that can occur in animal experiments. Rather, the objective is to acquaint researchers with components of the experiment that will require careful statistical thought.