The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments.

Mean corrected higher order sample moments are asymptotically normally distributed. It is shown that both in the literature and popular software the estimates of their asymptotic covariance matrices are incorrect. An introduction to the infinitesimal jackknife is given and it is shown how to use it to correctly estimate the asymptotic covariance matrices of higher order sample moments. Another advantage in using the infinitesimal jackknife is the ease with which it may be used when stacking or sub-setting estimators. The estimates given are used to test the goodness of fit of a non-linear factor analysis model. A computationally accelerated form for infinitesimal jackknife estimates is given.

The nonsingularity of γ in covariance structure analysis of nonnormal data.

Covariance structure analysis of nonnormal data is important because in practice all data are nonnormal. When applying covariance structure analysis to nonnormal data, it is generally assumed that the asymptotic covariance matrix Γ for the nonredundant terms in the sample covariance matrix S is nonsingular. It is shown this need not be the case, which raises a question of how restrictive this assumption may be and how difficult it may be to verify it. It is shown that Γ is nonsingular whenever sampling is from a nonsingular distribution, including any distribution defined by a density function. In the discrete case necessary and sufficient conditions are given for the nonsingularity of Γ, and it is shown how to demonstrate Γ is nonsingular with high probability. Thus, the nonsingularity of Γ assumption is mild and one should feel comfortable about making it. These observations also apply to the asymptotic covariance matrix Γ that arises in structural equation modeling.

A cluster-based factor rotation.

A new oblique factor rotation method is proposed, the aim of which is to identify a simple and well-clustered structure in a factor loading matrix. A criterion consisting of the complexity of a factor loading matrix and a between-cluster dissimilarity is optimized using the gradient projection algorithm and the k-means algorithm. It is shown that if there is an oblique rotation of an initial loading matrix that has a perfect simple structure, then the proposed method with Kaiser's normalization will produce the perfect simple structure. Although many rotation methods can also recover a perfect simple structure, they perform poorly when a perfect simple structure is not possible. In this case, the new method tends to perform better because it clusters the loadings without requiring the clusters to be perfect. Artificial and real data analyses demonstrate that the proposed method can give a simple structure, which the other methods cannot produce, and provides a more interpretable result than those of widely known rotation techniques.

Primary androgen deprivation (AD) followed by active surveillance (AS) for newly diagnosed prostate cancer (PC): A retrospective study.

BACKGROUND: Active surveillance (AS) is only recommended for Low-Risk prostate cancer (PC) with <34% biopsies positive. Studies describing the long-term outcome of men treated with androgen deprivation (AD) followed by AS are sparse. MATERIALS AND METHODS: One hundred two men were treated with 12 months of AD in a medical oncology clinic specializing in PC between 1998 and 2007 and were followed for a median of 7.25 years. The biopsy complete response rate after AD and the incidence of disease progression while on subsequent AS was assessed. Baseline age, D'Amico risk category, PSA velocity, percentage core biopsies, and prostate volume were evaluated as potential predictors of disease progression. RESULTS: D'Amico risk category for the 102 men: Low: n = 22, Intermediate: n = 30, and High: n = 50. Medians: Age 67.3, PSA 7.8, Gleason 3 + 4, >50% core biopsies positive, stage T1c. Seventy men had a clear biopsy and 31 of these had disease progression leading to additional treatment after a median of 52 months. D'Amico risk category of the 57 men with a positive biopsy after AD or disease progression on AS was: Low: n = 4 (18%), Intermediate: n = 16 (53%), and High: n = 37 (74%). No PC deaths occurred. Three men had clinical progression. In stepwise logistic regression analysis only higher D'Amico risk category and lower prostate volume predicted disease progression. CONCLUSIONS: Despite a high prevalence of ≥50% core biopsies positive at baseline, AD induces durable remissions in most men with Low-Risk and about half with Intermediate-Risk PC.

Continuous orthogonal complement functions and distribution-free goodness of fit tests in moment structure analysis.

It is shown that for any full column rank matrix X 0 with more rows than columns there is a neighborhood [Formula: see text] of X 0 and a continuous function f on [Formula: see text] such that f(X) is an orthogonal complement of X for all X in [Formula: see text]. This is used to derive a distribution free goodness of fit test for covariance structure analysis. This test was proposed some time ago and is extensively used. Unfortunately, there is an error in the proof that the proposed test statistic has an asymptotic χ (2) distribution. This is a potentially serious problem, without a proof the test statistic may not, in fact, be asymptoticly χ (2). The proof, however, is easily fixed using a continuous orthogonal complement function. Similar problems arise in other applications where orthogonal complements are used. These can also be resolved by using continuous orthogonal complement functions.

Exploratory Bi-factor Analysis: The Oblique Case.

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford (Psychometrika 47:41-54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler (Psychometrika 76:537-549, 2011) introduced an exploratory form of bi-factor analysis that does not require one to provide an explicit bi-factor structure a priori. They use exploratory factor analysis and a bifactor rotation criterion designed to produce a rotated loading matrix that has an approximate bi-factor structure. Among other things this can be used as an aid in finding an explicit bi-factor structure for use in a confirmatory bi-factor analysis. They considered only orthogonal rotation. The purpose of this paper is to consider oblique rotation and to compare it to orthogonal rotation. Because there are many more oblique rotations of an initial loading matrix than orthogonal rotations, one expects the oblique results to approximate a bi-factor structure better than orthogonal rotations and this is indeed the case. A surprising result arises when oblique bi-factor rotation methods are applied to ideal data.

Primary intermittent androgen deprivation as initial therapy for men with newly diagnosed prostate cancer.

BACKGROUND: The purpose of this study was to describe the long-term incidence of cancer progression and mortality in men with localized prostate cancer treated with primary androgen deprivation (AD). METHODS: A retrospective chart review, from a medical oncology practice specializing in prostate cancer, was conducted of 73 men eligible for surgery or radiation treated with induction AD. Entry criteria consisted of a minimum of 9 months of induction AD, treatment initiation before 1999, clinical stage < T3, and outcome defined as the incidence of delayed local therapy, cancer progression, cancer mortality, and mortality from other causes. RESULTS: Median follow-up was 12 years. Fifteen men were at low risk, 38 were at intermediate risk, and 20 were at high risk. Three men (4%) experienced metastatic disease and died of prostate cancer after 3.5, 7.7, and 11 years, respectively. Two men were in the intermediate-risk category and 1 was high risk. Nineteen men (26%) died of non-prostate cancer causes. None had metastatic disease at the time of death. Of the remaining 51 survivors, none has experienced bone metastasis. Twenty-one men (29%) required no further therapy after the first induction course of AD. Twenty-four men (33%) maintained a prostate-specific antigen (PSA) level < 5.0 ng/mL with 2 to 5 cycles of intermittent AD. Twenty-eight men (38%) underwent delayed local therapy after a median of 5.5 years. Median follow-up after local therapy was 6.2 years. Three of these men experienced subsequent rising PSA levels but none has progressed to bone metastasis. Sixteen of 20 men (80%) in the high-risk category but only 12 of 53 men (23%) in the low- and intermediate-risk categories had delayed local therapy. CONCLUSIONS: Primary intermittent AD is feasible for men with localized prostate cancer. Men who are younger and men with high-risk disease undergo delayed local therapy more frequently.

Exploratory Bi-factor Analysis.

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger. The bi-factor model has a general factor and a number of group factors. The purpose of this paper is to introduce an exploratory form of bi-factor analysis. An advantage of using exploratory bi-factor analysis is that one need not provide a specific bi-factor model a priori. The result of an exploratory bi-factor analysis, however, can be used as an aid in defining a specific bi-factor model. Our exploratory bi-factor analysis is simply exploratory factor analysis using a bi-factor rotation criterion. This is a criterion designed to produce perfect cluster structure in all but the first column of a rotated loading matrix. Examples are given to show how exploratory bi-factor analysis can be used with ideal and real data. The relation of exploratory bi-factor analysis to the Schmid-Leiman method is discussed.

Prostate-cancer-specific survival and clinical progression-free survival in men with prostate cancer treated intermittently with testosterone-inactivating pharmaceuticals.

OBJECTIVES: More than 85% of men with prostate cancer die of other causes. An effective method is needed to distinguish fatal forms of prostate cancer from benign variants. METHODS: We performed a retrospective chart review from a medical oncology practice specializing in prostate cancer. All men with negative bone scans, prostate-specific antigen (PSA) level less than 100 ng/mL, adequate records for review, and who started taking testosterone inactivating pharmaceutical (TIP) agents before January 2000 were included in the study. Six factors were evaluated as potential predictors of prostate cancer-specific mortality: PSA nadir greater than 0.05 ng/mL while taking TIP, PSA doubling time of less than 12 months, Gleason score, stage, baseline PSA level greater than 20 ng/mL, and age. RESULTS: The study criteria were met by 160 men. The median follow-up was 10 years. The median age, PSA level, PSA nadir, and PSA doubling time was 65.6 years, 9.6 ng/mL, 0.03 ng/mL, and 10 months, respectively. Of the 160 men, 39 died of prostate cancer. Death from prostate cancer was far more common (78% versus 11%) and accelerated (median of 4 years versus 7 years) for men with a PSA nadir greater than 0.05 ng/mL than for those with a lower nadir. Multivariate Cox regression analysis indicated that the hazard ratio for prostate cancer-specific mortality in men with a PSA nadir greater than 0.05 ng/mL was 11.6 (P <0.0001). The hazard ratio for men with a PSA doubling time of less than 12 months was 2.9 (P = 0.04). Gleason score, stage, baseline PSA level greater than 20 ng/mL, and age were not statistically significant. CONCLUSIONS: Of the factors studied, the PSA nadir while taking a TIP was the best predictor of prostate cancer-specific mortality.

Intermittent use of testosterone inactivating pharmaceuticals using finasteride prolongs the time off period.

PURPOSE: Men with prostate cancer treated intermittently with TIP benefit from improved quality of life when TOP with recovered testosterone is prolonged. We examined factors influencing the duration of TOP. MATERIALS AND METHODS: We retrospectively reviewed the charts of 101 men treated with intermittent TIP in a 9-year period. Men with positive bone scan, men in whom a PSA nadir of less than 0.1 ng/ml on TIP failed to be achieved and maintained and men in whom testosterone failed to recover to greater than 150 ng/dl during the first 12 months of TOP were excluded. Potential factors predicting prolonged TOP or accelerated time to AIPC were studied with Cox regression analysis. RESULTS: Patient characteristics were clinical stage T1c-T2a in 51 and T2b-T3b in 11, PSA relapse in 29, and T3c, D0 or D1 in 10. Median PSA was 7.6 ng/ml, Gleason score was 3 + 4 = 7 and TIP duration was 15.8 months. The 60 group 1 patients received finasteride and the 41 in group 2 received no finasteride. Median TOP in groups 1 and 2 was 31 and 15 months, respectively, using Kaplan-Meier analysis. Cox regression analysis indicated that longer TIP, finasteride and increased age predicted longer TOP. A slow PSA decrease while on TIP, higher baseline PSA and increased Gleason score predicted shorter TOP. Cox regression analysis indicated that only higher clinical stage but not finasteride predicted the earlier onset of AIPC. CONCLUSIONS: Finasteride doubles the duration of TOP. AIPC was not increased by finasteride after almost 9 years of observation.

The predictive role of blood glucose for mortality in subjects with cardiovascular disease.

Using the Framingham Heart Study data (United States, 1948-1978), the authors examined the association of blood glucose with 2-year all-cause, cardiovascular, and noncardiovascular mortality in subjects with documented cardiovascular disease. After adjustment for systolic blood pressure, cholesterol, body mass index, cigarette smoking, and use of antihypertensive agents, they found that glucose was a strong, independent predictor of mortality. However, the relations for men and women were qualitatively different. For men, adjusted mortality risk increased very rapidly through the normal range (from 4.12% at 3.89 mmol/liter (70 mg/dl) to 12.26% at 5.55 mmol/liter (100 mg/dl)) and was flat at 12.26% thereafter. For women, risk was flat at 3.65% through the normal range and then increased rapidly, reaching 8.34% at 6.99 mmol/liter (126 mg/d), but increased much more slowly thereafter. Exactly analogous relations held for cardiovascular mortality. For men and women combined, noncardiovascular mortality increased from 1.82% at 3.89 mmol/liter to 2.06% at 5.55 mmol/liter to 2.29% at 6.99 mmol/liter (p for trend = 0.009). These findings suggest that although 5.55 mmol/liter (normal) may be a useful mortality risk division (albeit with different implications for the two sexes), 6.99 mmol/liter (diabetic) is not, especially for men.

Independent component analysis as a rotation method: a very different solution to Thurstone's box problem.

In this paper we consider the well-known Thurstone box problem in exploratory factor analysis. Initial loadings and components are extracted using principal component analysis. Rotating the components towards independence rather than rotating the loadings towards simplicity allows one to accurately recover the dimensions of each box and also produce simple loadings. It is shown how this may be done using an appropriate rotation criterion and a general rotation algorithm. Methods from independent component analysis are used, and this paper may be viewed as an introduction to independent component analysis from the perspective of factor analysis.

Blood glucose: a strong risk factor for mortality in nondiabetic patients with cardiovascular disease.

BACKGROUND: The prognostic significance of blood glucose (BG) for nondiabetic patients in a stable chronic phase of cardiovascular disease (CVD) has been sparsely investigated, especially for glucose within the normal range. In particular, it is unknown if for these patients there is a graded relation of mortality to glucose or if there is a lower threshold. METHODS: We used the Framingham Heart Study 30-year data to determine 2-year all-cause, cardiovascular mortality (CVM), and non-CVM risk adjusted for age, sex, and typical cardiovascular risk factors (systolic blood pressure, total cholesterol, body mass index, cigarette smoking, and use of antihypertensive drugs) by levels of random whole BG for non-glucose-intolerant subjects (glucose intolerance includes diabetes mellitus) with existing CVD. RESULTS: There were steep graded relations of 2-year all-cause, CVM, and non-CVM to BG throughout the normal and subdiabetic range with no evidence of a lower threshold. Two-year mortality continuously increased from 2.99% at the bottom of the normal range (BG = 60 [plasma equivalent = 67] mg/dL) to 7.23% at the top of the normal range (89 [plasma equivalent = 100] mg/dL) (a 2.42-fold increase) and then continued to further continuously increase, reaching 11.38% at 119 [plasma equivalent = 133] mg/dL, the top of the glucose range considered (P for trend < .0001). There were analogous steep increases for CVM and non-CVM. CONCLUSIONS: Blood glucose, even within the normal range, is a strong independent predictor of 2-year all-cause, CVM, and non-CVM in nondiabetic subjects with CVD and therefore of prognostic significance for these high-risk patients.

Long-term outcome for men with androgen independent prostate cancer treated with ketoconazole and hydrocortisone.

PURPOSE: The combination of high dose ketoconazole and hydrocortisone (HDK) is active against androgen independent prostate cancer (AIPC). Median response times with HDK tend to be brief but a significant minority of AIPC patients benefit with extended responses. Well characterized response and survival information, especially in the cohort of patients who experience these longer, more durable, responses has not been previously reported. Characterization of this subgroup is of particular interest since men with long-term responses derive the greatest benefit from HDK therapy. MATERIALS AND METHODS: The medical records of 78 patients with AIPC treated with HDK between March 1991 and February 1999 were retrospectively reviewed. Baseline clinical and laboratory factors predictive of prolonged response and survival were identified. RESULTS: The median baseline prostate specific antigen (PSA) before the initiation of HDK was 25.1. The number of patients with zero, 1 to 3, and more than 3 lesions on bone scan were 25, 35 and 18, respectively. Median and mean time to PSA progression was 6.7 and 14.5 months. Median and mean survival time was 38.0 and 42.4 months, respectively. Response time and survival were highly correlated (r = 0.799). A total of 34 (44%) men had a greater than 75% decrease in PSA. The median survival times in men with more vs less than a 75% decrease were 60 vs 24 months, respectively. In a Cox proportional hazard regression, prolonged survival was predicted by percent PSA decrease, extent of disease on bone scan and baseline PSA. CONCLUSIONS: Ketoconazole can induce prolonged responses, occasionally lasting for years. Long responses are more likely to occur in men initiating HDK earlier in the course of disease before the cancer burden becomes excessive.

beta-Cell function: a key pathological determinant in polycystic ovary syndrome.

We report data from 60 patients with polycystic ovary syndrome (PCOS) who had undergone assessment of insulin resistance, pancreatic beta-cell function, obesity, and androgen levels to elucidate the complex relationships among these traits. Homeostasis model assessment was used to quantify insulin resistance and beta-cell function. A reference population was derived from the National Health and Nutrition Examination Study (NHANES III, 1988-1994). Indices of insulin resistance, insulin secretion, bioavailable testosterone, and body mass index all exhibited significant pairwise correlations. Multiple regression analysis clarified the phenotypic relationships, demonstrating that insulin resistance and bioavailable testosterone were independent predictors of beta-cell function; beta-cell function and obesity were independent predictors of insulin resistance; and beta-cell function was an independent predictor of bioavailable testosterone. Of note, comparison with normal women from NHANES revealed a significantly stronger relationship between beta-cell function and insulin resistance in PCOS, raising the possibility of an intrinsic defect in beta-cell function whereby increasing insulin resistance leads to a greater insulin response in PCOS than normal. The altered relationship of beta-cell function and insulin resistance coupled with the fact that beta-cell function, not insulin resistance, was a predictor of hyperandrogenemia suggests that beta-cell dysfunction may be a key pathogenic determinant in PCOS.

Relative impact of insulin resistance and obesity on cardiovascular risk factors in polycystic ovary syndrome.

Polycystic ovary syndrome (PCOS) affects 5% to 7% of women of reproductive age. Insulin resistance and obesity are components of this important syndrome that may contribute to excess cardiovascular risk. We analyzed data from 69 patients with PCOS who had undergone quantitative assessment of insulin sensitivity, blood pressure, lipid profiles, and androgen levels to determine the impact of insulin resistance and obesity on parameters of cardiovascular risk. Homeostasis model assessment (HOMA) was used to stratify patients in terms of insulin resistance. To obtain a reference population, we used data from the National Health and Nutrition Examination Study (NHANES III, 1988 to 1994). The most insulin-resistant tertile of patients exhibited higher body mass index (BMI), androgen levels, systolic and diastolic blood pressure (DBP), triglyceride (TG) levels, and decreased high-density lipoprotein cholesterol (HDL-C) levels. Insulin resistance, not BMI, was the main determinant of HDL-C and TG levels and systolic blood pressure (SBP) in PCOS. Among normal women, both BMI and insulin resistance influenced cardiovascular risk factors. Insulin resistance was a more significant predictor of TGs in women with PCOS than in normal women (P =.008). In contrast to normal women, insulin resistance in PCOS appears to be the prime determinant of abnormal lipids, blood pressure, and androgens. Thus, early detection of insulin resistance, as well as weight reduction, should be emphasized for all patients with PCOS.

Using splines to detect changes in PSA doubling times.

BACKGROUND: PSA doubling time (PSADT) can predict the likelihood of clinical progression in patients with biochemical relapse after surgery or radiation for prostate cancer. Changes in PSA doubling time in response to therapy may be of clinical or investigational significance. How does one estimate PSADT before and after the initiation of therapy and determine if any change is statistically significant or simply the result of random variation? These are the type of questions addressed. METHODS: Our technique uses a best-fitting spline (i.e., a broken-line approximation) to a graph of log PSA on time to estimate PSADTs before and after treatment initiation. A linear regression program is used to produce the fit and to evaluate the statistical significance of any change in PSADT. This method differs from previous methods in that it uses all the data, exploits the continuity of PSA at the time of treatment initiation, and allows one to make statistical significance statements about specific individuals. RESULTS: Our technique is illustrated with data from a pilot clinical trial using a nutritional supplement in 12 men with prostate cancer. A detailed analysis of the first patient shows how the data are handled, how two lines of computer code are sufficient to fit the spline model, and how the doubling times and statistical significance of a change are read from the computer output. In the study, 9 of 12 patients had a statistically significant increase in doubling time. Because the study is preliminary and used only to illustrate our method, no medical discussion of the study is included. The last section of the study, in part expository, is devoted to explaining the underlying principles for those who may want to know not only what to do, but why it works. CONCLUSIONS: The method presented here for determining changes in PSADT is both simple and broadly applicable. It allows the evaluation of the size and statistical significance of an observed change or increase in PSADT in response to therapy for prostate cancer. It can be done using essentially any statistical software and widely accepted statistical methods.