Properties of alternative estimators of familial correlations under variable sibship size.

Selected distributional properties of a variety of estimators of familial correlations (spouse, parent-child, and sibling) were investigated numerically, focusing particularly on sibling correlations under variable sibship size. Maximum likelihood estimators were evaluated for each of the three familial relationships. An additional parent-offspring estimator was studied using a parent-midoffspring estimate pooled over variable sibship size. For sibling intraclass correlations, three estimators based on analysis of variance and three pairwise estimators using different weighting functions for variable sibship sizes were investigated. Correlations were estimated from data simulated under eight sampling conditions (each replicated 1,000 times) using two sets of true parameter values, moderate and large sample sizes, and normal versus highly non-normal sample distributions of data. The estimators are nearly unbiased and efficient, but none of the sibling correlation estimators are normally distributed in small samples. Estimates from highly non-normal data are nearly unbiased but are less efficient than those from normal data.

Environmental index in genetic epidemiology: an investigation of its role, adequacy, and limitations.

The concept of environmental index is briefly reviewed. With a biologically plausible theoretical model, the consequences of indices being based on incomplete information about the familial environment are investigated. It is shown that using partial indices on all family members leads to both an underestimation of the familial environmental component of variance, also called cultural heritability, and, although to a possibly lesser extent, an overestimation of the genetic heritability. It is further shown that so long as complete indices are available on both parents, using identically partial indices on children will yield nearly undistorted parameter estimates. These conclusions were arrived at by using a special case of the model and may not apply in general.

Heterogeneity in the biological and cultural determinants of high-density lipoprotein cholesterol in five North American populations: the Lipid Research Clinics Family Study.

Heterogeneity in the source of familial resemblance for high-density lipoprotein (HDL) cholesterol in 5 different Lipid Research Clinics (Cincinnati, Iowa, Minnesota, Oklahoma and Stanford) was assessed using a general linear model for cultural and biological inheritance. No evidence of heterogeneity was found in any of the parameters of the model. Under the most parsimonious hypothesis, using data pooled over all clinics, genetic and cultural heritability were both significant and were estimated to be 0.52 +/- 0.04 and 0.09 +/- 0.02, respectively; there was cultural transmission but no maternal effects; marital and nontransmitted sibship environmental resemblance were significant.

Path analysis under generalized marital resemblance: evaluation of the assumptions underlying the mixed homogamy model by the Monte Carlo method.

Path analysis of nuclear family data has been widely applied to resolve genetic and environmental sources of familial resemblance. Here we report the results of a systematic evaluation of the effects of departures from five modeling assumptions often made when analyzing nuclear family data; i) the observed environmental index is unaffected by the genotype, ii) the basis of marital resemblance is correctly specified in the model, iii) there are no intergenerational differences in either the genetic or cultural heritability, iv) there is no genetic dominance, and v) there is no genotype by family environment interaction. "Deterministic simulations" identified various situations where model misspecification could lead to substantial bias in the estimation of the heritabilities. For these situations, "stochastic simulations" were performed to determine whether the "goodness-of-fit" test used in path analysis would correctly reject the misspecified model. In samples of 500 nuclear families, each comprising two parents and two children, the goodness-of-fit test was found to be sensitive to misspecifications of the source of marital resemblance and the existence of intergenerational differences in heritabilities, although reduced power would make the test less sensitive in smaller samples. The test was largely insensitive to misspecifications of possible genetic effects on the environmental index, and to the existence of multiplicative interaction between the genotype and familial environment. When genetic effects on the index are ignored, the genetic heritability (h2) is underestimated, the cultural heritability (c2) is overestimated, but h2+c2 remains unchanged. Neglecting the interaction was found to result in an overestimate of h2.

Nonrandom sampling in genetic epidemiology: an implementation of the Hanis-Chakraborty method for multifactorial analysis.

The method of Hanis and Chakraborty: [Statistics in Medicine 6:629-646, 1987] is known to yield unbiased estimates of familial correlations from family data ascertained according to just about any method of nonrandom sampling. For multifactorial analysis of such family data, the method is implemented here so as to provide a unique solution, handle variable sibship sizes, and provide likelihood ratio tests of hypotheses. Simulation results are presented to illustrate the utility of the proposed implementation.

On the properties of maximum likelihood estimators of familial correlations under variable sibship size.

Selected distributional properties of the maximum likelihood estimator and its z-transformation of three familial correlations (parental, parent-offspring, filial) were investigated numerically for the case of nuclear families with variable sibship size. This investigation was based on six different sets of the three correlations, and four different sample sizes, defining 24 sampling conditions, which were replicated 1,000 times each. It was found that the distributional properties of the correlation estimator are affected by the magnitude of the correlations even in large samples although approximate normality is achieved locally. Fisher's z-transformation, here used only in its interclass form, achieves reduction of skewness, stabilization of variance, and approach to normality already in small samples, except for the filial correlation (where it may be deemed inappropriate) in smaller samples. For both the correlation estimator and its z-transformation, the (estimated) relative efficiency was shown to be high (better than 90% in most sampling conditions), suggesting that the estimated minimum variance bound is a satisfactory estimator of the sampling variance. It is concluded that the maximum likelihood estimation of familial correlations under variable sibship size is feasible and, when prudently applied, especially in the form of their z-transformations, provides an appropriate method in analyses of family studies.

Multifactorial analysis of family data ascertained through truncation: a comparative evaluation of two methods of statistical inference.

When family data are ascertained through single selection based on truncation, a prevailing method of analysis is to condition the likelihood function on the proband's actual phenotypic value. An alternative method conditions the likelihood function on the event that the proband's measurement lies in the truncation region. Both methods are contrasted here by using Monte Carlo simulations; identical sets of data were analyzed using both methods. The results suggest that, under either method, (1) parameter estimates are nearly unbiased and (2) likelihood-ratio tests of null hypotheses are approximately distributed as chi 2. However, conditioning on the proband's actual phenotypic value yields considerably less efficient estimates and reduced power for hypothesis tests. A corresponding result also holds under complete ascertainment. It is argued, therefore, that whenever sufficient information is available on the nature of truncation, the alternative approach should be used.

A Monte Carlo evaluation of three statistical methods used in path analysis.

Results of a Monte Carlo study to investigate the properties of three statistical methods used extensively in path analysis of family data are presented. All three methods are based on the maximum likelihood principle and involve the assumptions of multivariate normality and large sample (asymptotic) statistical properties. The methods differ, however, in the specification of the likelihood function. Given a set of correlation estimates, method 1 maximizes the likelihood function under the stipulation that the estimates are independent. Method 2 differs from the former by allowing for covariances among the correlation estimators. Method 3 involves (direct) maximization of the likelihood function for the individual family observations assuming multivariate normality for the vector of family observations. The Monte Carlo study investigated validity of the test statistics and confidence intervals and evaluated the relative efficiency and bias of the parameter estimates based on 1,000 replications of each of several simulation conditions. The effects of violating the two basic assumptions, multivariate normality and asymptotic theory, were investigated by comparing results for non-normally vs normally distributed family data and for small vs large sample sizes. It is shown that method 3 provides valid statistical inferences under multivariate normality and that it is generally robust against minor departures from normality. Method 2 is also robust against minor deviations from normality, but it is sensitive to small sample sizes. Method 1 yields highly conservative test statistics under all conditions studied.

Nonrandom sampling in genetic epidemiology: maximum likelihood methods for multifactorial analysis of quantitative data ascertained through truncation.

Three types of nonrandom sampling of family data are described, and appropriate maximum likelihood methods are proposed for each. The three types arise depending on whether the selection of probands, based on truncation, is applied directly to the phenotypic distribution, to the distribution of a correlated trait, or to the liability distribution of an associated disease. Family data ascertained through random and nonrandom sampling can be analyzed together in a unified approach. Results of a Monte Carlo study are presented that demonstrate the utility of the proposed methods. In particular, likelihood ratio tests of null hypotheses are shown to be distributed as chi-square, even in samples as small as 50 families (with variable sibship size).

Evaluation of path analysis through computer simulation: effect of incorrectly assuming independent distribution of familial correlations.

Path analysis of family data has been widely applied to resolve genetic and environmental patterns of familial resemblance. A prevalent statistical approach in path analysis has been, first, to estimate the familial correlations and, second, by assuming these estimates to be independently distributed, define a likelihood function from which maximum likelihood estimates of model parameters can be obtained and likelihood ratio tests of hypotheses performed. Although it is generally known that the independence assumption does not hold when multiple familial correlations are estimated from the same family data, this statistical method has still been used in these situations owing, in part, to the lack of any viable alternatives and, in part, to the lack of any knowledge about the specific quantitative effects of not meeting the assumption of independence. Here, using computer-simulation methods, we evaluate the robustness of this statistical method to deviations from the assumption of independence. In general, we found that the failure to meet the assumption of independence leads to a conservative test of the goodness-of-fit of the path model, although likelihood ratio tests of specific null hypotheses were at times liberal, at times conservative, and at times nearly exact. Although the test statistics were found to be distorted, the parameter estimates using this method were nearly unbiased.

The Cincinnati Lipid Research Clinic family study: cultural and biological determinants of lipids and lipoprotein concentrations.

A general linear model is described here for cultural and biological inheritance of lipids and lipoproteins. This model involves 10 parameters to be estimated from a total of 17 correlations, leaving ample degrees of freedom to test the goodness of fit. The model fits very well to each of the five lipid and lipoprotein variables analyzed here from a Lipid Research Clinic family data set. Both genetic and cultural inheritance are significant for each trait with the single exception that triglyceride levels fail to support genetic inheritance. Under the most parsimonious hypothesis, the genetic heritability (h2) ranges from .194 +/- .092 for triglyceride to .624 +/- .093 for low-density lipoprotein-cholesterol. Cultural heritability ranges from .070 +/- .030 for total cholesterol to .149 +/- .034 for triglyceride.

The use of multiple thresholds and segregation analysis in analyzing the phenotypic heterogeneity of multifactorial traits.

(1) Three models based on multifactorial inheritance are introduced to account for phenotypic heterogeneities. These models are used to determine whether subforms of a triat are: (a) different degrees of the same process, (b) non-familial environmental variants of the same process, and (c) independently transmitted processes. (2) The parameters of each model consist of two population prevalences and either one, two, or three correlation coefficients which reflect the three hypotheses given above. The models are formulated so that a likelihood ratio test may be performed to discriminate between them. (3) The following types of analyses are described: (a) analysis of prevalence data with separate population prevalence estimates, (b) analysis of prevalence data with the proband a parent with specified spouse, (c) analysis of prevalence data with the proband an offspring with specified parents, and (d) the full segregation distribution of families using Complex Segregation Analysis. (4) When compared with the Analysis of Prevalences, Complex Segregation Analysis has the following advantages: (a) the number of degrees of freedom for parameter estimates is greater and separate estimates of the population prevalences are not necessary, (b) standard errors of the parameters are smaller, and (c) the power to discriminate models is increased. (5) Phenotypic heterogeneities such as age of onset, severity, and sex effect can be more completely understood by the methods of analyses described above. The nosology of familial disorders can also be clarified, and environments relevant to the transmission of the trait can be detected. This approach is particularly suitable for the analysis for behavioural traits since it does not require the assumption that environmental effects common to relatives be ignored. (6) Finally, our experience indicates that incorporating both prevalence and pedigree data into a single analysis decreases the time required to perform the analysis.

The use of steroids in Bell's palsy: a prospective controlled study.

A prospective, controlled, double-blind study was designed to evaluate the effect of steroid treatment on the natural history of Bell's palsy. Fifty-one patients were included in the study between 1972 and 1974. The patients were evaluated and started on treatment within two days of onset of Bell's palsy and followed for six months. Treatment was given in randomized double-blind fashion and consisted of either vitamins or a total of 410 mg of prednisone plus vitamins in descending doses over 10 days. The recovery of facial motor function was determined by three physicians who had no knowledge of the treatment received by the patients. They examined photographs of the patients taken six months after onset of paralysis in eight positions of facial function and categorized them as to complete fair, or poor recovery of facial function. These results of this evaluation were submitted to the biostatistician who broke the treatment code. The results of this study demonstrate no statistically significant beneficial effect of steroid therapy upon recovery from Bell's palsy. Factors considered included the patients' age, sex, the presence of pain, ageusia, hyperacusis, diabetes, hypertension, the progression and degree of palsy, the results of nerve excitability and salivary flow tests, and the time at which recovery was first noted or became complete. Bell's palsy remains without a proven efficacious treatment.

Natural history of bell's palsy: the salivary flow test and other prognostic indicators.

Fifty-one patients with Bell's palsy were evaluated within two days of onset and followed for six months without surgical intervention or effective medical treatment in order to observe the natural history of the disease. Sixty-three percent had a complete return while 37 percent had incomplete return. Age, the presence of pain, and taste alterations had no prognostic value. The progression of the palsy, response to maximal stimulation and salivary flow testing were approximately 80 percent accurate in predicting outcome. The salivary flow test was the most useful prognostic indicator since salivary flow became reduced within two days of onset in the patients likely to develop denervation while the other tests did not become altered until 3 to 14 days after onset. In patients with Bell's palsy, the salivation test seems to be the only method capable of predicting denervation before it begins; therefore, it should be ideal for selecting patients for appropriate treatment.