Exact and asymptotic tests for homogeneity in several 2 x 2 tables

This paper presents the results of a Monte Carlo study comparing the performance, in terms of size and power, of six exact and six asymptotic tests for the homogeneity of odds ratios in several 2 x 2 contingency tables. With a small sample size or sparse data structure, the exact tests performed better than the asymptotic tests because they maintained the nominal size and, in some situations, had slightly higher power. Among the exact tests, we recommend the Zelen, Pearson chi-square and scores tests. Among the asymptotic tests, the Breslow-Day and Pearson chi-square tests were slightly better in some situations than the unconditional and conditional score tests. However, both exact and asymptotic tests had low power for small strata sizes, even with moderate to large heterogeneity of odds ratios. Corroborating previous findings, the asymptotic unconditional likelihood ratio test was too liberal in terms of size.

Persistently seronegative men from whom HIV-1 has been isolated are genetically and immunologically distinct

Studies in both monkeys and humans have suggested that transient infection with HIV-1 can occur without provoking a measurable humoral immune response. The objective of this study was to look for genetic and immunologic correlates of transient HIV-1 infection in antibody-negative men from whom HIV-1 had been isolated. The distributions of MHC class I, class II, and TAP (transporter protein associated with antigen processing) region genes were compared between 23 persistently seronegative men from whom HIV-1 was isolated at least once (isol+/Ab-) and 137 men who seroconverted. A subset of 13 of the 23 isol+/Ab- men were compared to 27 seronegative men for distribution of CD25+CD4+ and CD25+CD8+ cells in the absence of exogenous immunologic stimulation. The prevalences of the TAP1.4, and a combination of TAP1.4, and TAP2.3 variants were significantly higher in the isol+/Ab- men. The proportion of CD8+ cells that expressed CD25+ antigen was also significantly higher in the isol+/Ab- men than in the seronegative men. We conclude that isol+/Ab- men may be genetically and immunologically distinct from HIV-1 susceptible men. We hypothesize that activated CD8+ cells may have cleared HIV-1 infection in these men through genetically mediated influences of the TAP genes on the presentation of peptides by HLA class I molecules.

Exact power computation for dose-response studies

The toxicity of an agent or the therapeutic effect of a drug may be assessed by a dose-response study. We present a method for computing the exact power of exact and large sample statistical tests employed for binary response data from such a study. This method, based on recursive polynomial multiplications, enables fast computation of exact power for studies with up to a moderately large sample size. We demonstrate the efficiency of our method using three examples. The method is suitable for the design and power analysis of dose-response studies in which the usual asymptotic approximations are suspect.

Exact analysis for paired binary data

This paper provides an efficient algorithm to generate exact distributions for the bivariate logistic model with common and sub-unit-specific covariates. The algorithm can be used to analyze correlated paired binary response data from studies lacking a large sample size. Possible applications include a clinical trial with two distinct binary outcomes, a binary outcome cross-over or two-time point cohort study, and a pair-matched prospective study with binary outcome. Analysis of data from an ophthalmologic study is provided to illustrate the method. Extension to three or more correlated binary responses is also outlined.

Efficient power computation for exact and mid-P tests for the common odds ratio in several 2 x 2 tables

When designing a study that may generate a set of sparse 2 x 2 tables, or when confronted with 'negative' results upon exact analysis of such tables, we need to compute the power of exact tests. In this paper we provide an efficient approach for computing exact unconditional power for four exact tests on the common odds ratio in a series of 2 x 2 tables. These tests are the traditional exact test; a test based on a probability ordering of the sample space; and two tests based on ordering the sample space according to distance from the mean, or median. For each test, we consider both a conservative version and a mid-P adjusted version. We explore three computational options for power determination: exact power computation, calculation of exact upper and lower bounds for power, and Monte Carlo confidence bounds for power. We present an interactive program implementing these options. For study design, the program may be run several times to arrive at a sample configuration with adequate power.

An assessment of the use of anthropometric measures for predicting low birth weight

We report results of an evaluation of two anthropometric surrogates, viz chest circumference and mid-arm circumference, of birth weight. Optimal criteria for predicting birth weight below 2000 g and below 2500 g were provided by use of chest circumference alone. However, even the best criterion was not very sensitive indicating that use of anthropometric surrogates may have a limited practical value.

Carcinoma of the male breast in Tanzania

This is a retrospective study of male mammary carcinoma in Tanzania based on biopsy material received from 1974 to 1987 at the Tanzania Cancer Registry. In a series of 1104 cases of breast cancer, 76 or 6.5% were male. This compares with approximately 1% in Western literature, and a similar or higher percentage in some other African countries. In Africa, medical facilities are limited, and appropriate surgical treatment, radiotherapy, and chemotherapy are difficult to procure. By the time cases reach the main hospitals, the cancer is often in a very advanced stage. Thus, there is a need to ensure early referral of cases. Further, for disseminated carcinoma, the more frequent use of orchidectomy should be considered. Orchidectomy is a simple and potentially effective procedure that can be undertaken at any hospital.

Evaluation of exact and asymptotic interval estimators in logistic analysis of matched case-control studies

We compare six methods for constructing confidence intervals for a single parameter in stratified logistic regression. Three of these are based on inversion of standard asymptotic tests--namely, the Wald, the score, and the likelihood ratio tests. The other three are based on the exact distribution of the sufficient statistic for the parameter of interest. These include the traditional exact method of constructing confidence intervals, and two others, the mid-P and mean-P methods, which are modifications of this procedure that aim at reducing the conservative bias of the exact method. Using efficient algorithms, the six methods are compared by determination of their exact coverage levels in a series of conditional sample spaces. An incident case-control study of lung cancer in women is used to further illustrate the differences among the various methods. Computation of coverage functions is seen as a useful graphical diagnostic tool for assessing the appropriateness of different methods. The mid-P and the score methods are seen to have better coverage properties than the other four.

A quasi-exact test for comparing two binomial proportions

The use of the Fisher exact test for comparing two independent binomial proportions has spawned an extensive controversy in the statistical literature. Many critics have faulted this test for being highly conservative. Partly in response to such criticism, some statisticians have suggested the use of a modified, non-randomized version of this test, namely the mid-P-value test. This paper examines the actual type I error rates of this test. For both one-sided and two-sided tests, and for a wide range of sample sizes, we show that the actual levels of significance of the mid-P-test tend to be closer to the nominal level as compared with various classical tests. The computational effort required for the mid-P-test is no more than that needed for the Fisher exact test. Further, the basis for its modification is a natural adjustment for discreteness; thus the test easily generalizes to r x c contingency tables and other discrete data problems.

A comparison of exact, mid-P, and score tests for matched case-control studies

A recently developed algorithm for generating the distribution of sufficient statistics for conditional logistic models can be put to a twofold use. First, it provides an avenue for performing inference for matched case-control studies that does not rely on the assumption of a large sample size. Second, joint distributions generated by this algorithm can be used to make comparisons of various inferential procedures that are free from Monte Carlo sampling errors. In this paper, these two features of the algorithm are utilized to compare small-sample properties of the exact, mid-P value, and score tests for a conditional logistic model with two unmatched binary covariates. Both uniparametric and multiparametric tests, performed at a nominal significance level of .05, were studied. It was found that the actual significance levels of the mid-P test tend to be closer to the nominal level when compared with those of the other two tests.

A microcomputer program for exact and asymptotic analysis of several 2 x 2 tables

A microcomputer program for analysis of a binomial proportion and the common odds ratio in a series of 2 x 2 tables is presented. This program utilizes both exact and asymptotic methods to provide point estimates, P values, and confidence intervals. Modifications of the exact method based on the concept of a mid-P value are also included. The program allows the user to compare the exact coverage properties of various methods of computing confidence intervals. Use of an improved algorithm provides considerable gains in computational efficiency.

A note on interrater agreement

We investigate the properties of a measure of interrater agreement originally proposed by Rogot and Goldberg. Unlike commonly used measures, this measure not only adjusts for chance agreement, but it also standardizes for both perfect agreement as well as for perfect disagreement. Further, one can also use this measure to assess category specific conditional agreement, and thus apply it to situations with missing main diagonal data. We provide an asymptotic method for inference with this measure.

Efficacy of intensive chemotherapy for acute myelogenous leukemia associated with a preleukemic syndrome

One hundred ninety-six patients with acute myelogenous leukemia (AML) were treated with intensive induction chemotherapy using similar daunorubicin/cytarabine/thioguanine regimens. Treatment results of 44 patients who had a documented preleukemic syndrome or cytopenia present for more than 2 months before developing over AML were compared with 152 patients with de novo AML. Eighteen (41%) patients with preleukemia evolving into AML achieved complete remission compared with 111 (73%) patients with de novo AML (P less than .01). Patients with preleukemia-AML had a significantly longer period to recovery of granulocytes. Multivariate analysis indicated that presence of a previous preleukemic syndrome and advancing age were independent poor prognostic indicators for achieving remission. For patients who achieved remission, disease-free survival and overall survival were also inferior for patients with previous preleukemia; disease-free survival was 17 +/- 17% at 3 years compared with 29 +/- 10% in patients with de novo AML (P = .02). These data indicate that intensive chemotherapy has limited efficacy in patients with AML following a preleukemic syndrome. Durable remissions may be achieved in some patients.

Exact inference for matched case-control studies

In an epidemiological study with a small sample size or a sparse data structure, the use of an asymptotic method of analysis may not be appropriate. In this paper we present an alternative method of analyzing data for case-control studies with a matched design that does not rely on large-sample assumptions. A recursive algorithm to compute the exact distribution of the conditional sufficient statistics of the parameters of the logistic model for such a design is given. This distribution can be used to perform exact inference on model parameters, the methodology of which is outlined. To illustrate the exact method, and compare it with the conventional asymptotic method, analyses of data from two case-control studies are also presented.

Exact versus asymptotic analysis for a matched case-control study

We compare exact and asymptotic methods for variable selection in matched case-control studies. Data from a study of melanoma among the employees of the Lawrence Livermore National Laboratory illustrate the comparisons. Relative to large sample methods, the exact method almost always yielded larger p-values. The differences in p-values became more pronounced with inclusion of more variables in the logistic model. Thus, when the sample size is not large, and there are many covariates under study, use of the exact method tends to select more parsimonious models and avoids overfit of the data.