Daniele De Martini

Nitric oxide modulates in vivo and in vitro growth hormone release in acromegaly.

Nitric oxide (NO) has recently been shown to modulate pituitary secretion both in vivo and in vitro. The aim of this study was to investigate the effects of this chemical transmitter on spontaneous and growth-hormone-releasing hormone (GHRH)-induced growth hormone (GH) secretion in acromegalic patients, as well as from GH-secreting tumors maintained in vitro. The study was carried out in 7 acromegalic patients (46.2 +/- 2 years) and in 5 normal subjects (40.1 +/- 1.5 years). GH and prolactin (PRL) secretion were assayed during the administration of isosorbide dinitrate (ID, 5 mg, orally), an NO donor, GHRH, and ID plus GHRH. During ID, a significant (p < 0.05) increase (37%) over basal GH levels was only observed in acromegalics. There was no change in GH levels in response to GHRH or ID plus GHRH in either group. No significant change in PRL levels was observed in either group during ID, while GHRH, with or without ID, induced a slight increase in PRL levels in acromegalics only. Tumor specimens were obtained by selective transsphenoidal adenomectomy, and the cells were plated and incubated for 1, 2 and 24 h in the presence of sodium nitroprusside, a releaser of NO (SNP, 0.3 or 0.6 mM), of GHRH (10-8 M) or of both. SNP significantly (p < 0.001) increased GH levels in a dose-dependent manner (R = 0.99, p = 0.02), but was unable to modify the GH response to GHRH. In acromegalics, a significant correlation (R = 0.822, p < 0.045) and a correlation near the limit of significance (R = 0.73, NS) were observed respectively between the in vivo GH response to ID and the in vitro response to SNP at 24 h. No significant effect was observed on PRL secretion during SNP incubations, while GHRH produced a significant increase in PRL after 2 and 24 h incubation in acromegalics. These observations indicate that NO plays a stimulatory role in vivo and in vitro on GH secretion in acromegalic patients.

Adapting by calibration the sample size of a phase III trial on the basis of phase II data

The problem of estimating the sample size for a phase III trial on the basis of existing phase II data is considered, where data from phase II cannot be combined with those of the new phase III trial. Focus is on the test for comparing the means of two independent samples. A launching criterion is adopted in order to evaluate the relevance of phase II results: phase III is run if the effect size estimate is higher than a threshold of clinical importance. The variability in sample size estimation is taken into consideration. Then, the frequentist conservative strategies with a fixed amount of conservativeness and Bayesian strategies are compared. A new conservative strategy is introduced and is based on the calibration of the optimal amount of conservativeness - calibrated optimal strategy (COS). To evaluate the results we compute the Overall Power (OP) of the different strategies, as well as the mean and the MSE of sample size estimators. Bayesian strategies have poor characteristics since they show a very high mean and/or MSE of sample size estimators. COS clearly performs better than the other conservative strategies. Indeed, the OP of COS is, on average, the closest to the desired level; it is also the highest. COS sample size is also the closest to the ideal phase III sample size M(I) , showing averages and MSEs lower than those of the other strategies. Costs and experimental times are therefore considerably reduced and standardized. However, if the ideal sample size M(I) is to be estimated the phase II sample size n should be around the ideal phase III sample size, i.e. n ≥2M(I) /3.

Conservative Sample Size Estimation in Nonparametrics

Due to the uncertainty of the results of phase II trials, underpowered phase III trials are often planned. In recent literature the conservative approach for sample size estimation was proposed. Some authors, in the parametric framework, make use of the lower bound of the effect size for conservatively estimating the true power, and so the sample sizes. Here, we present a general bootstrap method for conservatively estimating, on the basis of phase II data, the sample size needed for a phase III trial. The method we propose is based on the use of nonparametric lower bounds for the true power of the test. A wide study is shown for comparing the performances of the new method in estimating the power of the Wilcoxon rank-sum test with those given by standard techniques based on the asymptotic normality of the test statistic. Results indicate that when the phase II sample size is around the ideal sample size for the phase III, the bootstrap provides better results than the other techniques. Since the method is general, it could be used for planning clinical trials for testing superiority, for testing noninferiority, and for more complicated situations, e.g., for testing multiple endpoints.Due to the uncertainty of the results of phase II trials, underpowered phase III trials are often planned. In recent literature the conservative approach for sample size estimation was proposed. Some authors, in the parametric framework, make use of the lower bound of the effect size for conservatively estimating the true power, and so the sample sizes. Here, we present a general bootstrap method for conservatively estimating, on the basis of phase II data, the sample size needed for a phase III trial. The method we propose is based on the use of nonparametric lower bounds for the true power of the test. A wide study is shown for comparing the performances of the new method in estimating the power of the Wilcoxon rank-sum test with those given by standard techniques based on the asymptotic normality of the test statistic. Results indicate that when the phase II sample size is around the ideal sample size for the phase III, the bootstrap provides better results than the other techniques. Since the method is general, it could be used for planning clinical trials for testing superiority, for testing noninferiority, and for more complicated situations, e.g., for testing multiple endpoints.

Reproducibility probability estimation and testing for the Wilcoxon rank-sum test

The reproducibility probability (RP) of a statistically significant outcome is the true power of a statistical test and its estimate is a useful indicator of the stability of the test result. RP-testing consists in testing statistical hypotheses using an RP-estimator as test statistic. In the parametric framework, the RP-based test and the classical one are equivalent, while in the nonparametric one to perform RP-testing is possible only approximately. In this work, we evaluate through a wide simulation study the performances of several semi-parametric and nonparametric RP-estimators (RPEs) for the Wilcoxon rank-sum (WRS) test. RPEs have two tasks: to perform RP-testing and to estimate the RP. To compare RPEs performances we adopt risk indexes (e.g. mean square error (MSE)) and an index of agreement between the outcomes of the WRS test and the RP-based test. Results indicate that the rate of disagreement tends to zero as the sample size increases; the overall rate of disagreement provided by semi-parametric RPEs with finite samples (size 20–200 per group) is 0.15%, and that of nonparametric ones is 0.58%. Concerning risk measures, there is not an RPE dominating the others; for high power values, nonparametric RPEs present the lowest MSE; on average, the semi-parametric RPE based on the upper bound of the variance of the test statistic performs best; nevertheless, the relative gains between the best and the worst are quite small (5–10%). To conclude, well-approximated RP-testing for the WRS test can be performed by adopting a semi-parametric RPE. Since nonparametric plug-in based RPEs perform well in presence of high reproducibility, their adoption is suggested for evaluating the stability of test results and, for example, those of clinical trials.The reproducibility probability (RP) of a statistically significant outcome is the true power of a statistical test and its estimate is a useful indicator of the stability of the test result. RP-testing consists in testing statistical hypotheses using an RP-estimator as test statistic. In the parametric framework, the RP-based test and the classical one are equivalent, while in the nonparametric one to perform RP-testing is possible only approximately. In this work, we evaluate through a wide simulation study the performances of several semi-parametric and nonparametric RP-estimators (RPEs) for the Wilcoxon rank-sum (WRS) test. RPEs have two tasks: to perform RP-testing and to estimate the RP. To compare RPEs performances we adopt risk indexes (e.g. mean square error (MSE)) and an index of agreement between the outcomes of the WRS test and the RP-based test. Results indicate that the rate of disagreement tends to zero as the sample size increases; the overall rate of disagreement provided by semi-parametr...

Robustness and corrections for sample size adaptation strategies based on effect size estimation

A study on the robustness of the adaptation of the sample size for a phase III trial on the basis of existing phase II data is presented—when phase III is lower than phase II effect size. A criterion of clinical relevance for phase II results is applied in order to launch phase III, where data from phase II cannot be included in statistical analysis. The adaptation consists in adopting the conservative approach to sample size estimation, which takes into account the variability of phase II data. Some conservative sample size estimation strategies, Bayesian and frequentist, are compared with the calibrated optimal γ conservative strategy (viz. COS) which is the best performer when phase II and phase III effect sizes are equal. The Overall Power (OP) of these strategies and the mean square error (MSE) of their sample size estimators are computed under different scenarios, in the presence of the structural bias due to lower phase III effect size, for evaluating the robustness of the strategies. When the structural bias is quite small (i.e., the ratio of phase III to phase II effect size is greater than 0.8), and when some operating conditions for applying sample size estimation hold, COS can still provide acceptable results for planning phase III trials, even if in bias absence the OP was higher. Main results concern the introduction of a correction, which affects just sample size estimates and not launch probabilities, for balancing the structural bias. In particular, the correction is based on a postulation of the structural bias; hence, it is more intuitive and easier to use than those based on the modification of Type I or/and Type II errors. A comparison of corrected conservative sample size estimation strategies is performed in the presence of a quite small bias. When the postulated correction is right, COS provides good OP and the lowest MSE. Moreover, the OPs of COS are even higher than those observed without bias, thanks to higher launch probability and a similar estimation performance. The structural bias can therefore be exploited for improving sample size estimation performances. When the postulated correction is smaller than necessary, COS is still the best performer, and it also works well. A higher than necessary correction should be avoided.A study on the robustness of the adaptation of the sample size for a phase III trial on the basis of existing phase II data is presented—when phase III is lower than phase II effect size. A criterion of clinical relevance for phase II results is applied in order to launch phase III, where data from phase II cannot be included in statistical analysis. The adaptation consists in adopting the conservative approach to sample size estimation, which takes into account the variability of phase II data. Some conservative sample size estimation strategies, Bayesian and frequentist, are compared with the calibrated optimal γ conservative strategy (viz. COS) which is the best performer when phase II and phase III effect sizes are equal. The Overall Power (OP) of these strategies and the mean square error (MSE) of their sample size estimators are computed under different scenarios, in the presence of the structural bias due to lower phase III effect size, for evaluating the robustness of the strategies. When the stru...

Stability criteria for the outcomes of statistical tests to assess drug effectiveness with a single study

At least two adequate and well-controlled clinical studies are usually required to support effectiveness of a certain treatment. In some circumstances, however, a single study providing strong results may be sufficient. Some statistical stability criteria for assessing whether a single study provides very persuasive results are known. A new criterion is introduced, and it is based on the conservative estimation of the reproducibility probability in addition to the possibility of performing statistical tests by referring directly to the reproducibility probability estimate. These stability criteria are compared numerically and conceptually. This work aims to help both regulatory agencies and pharmaceutical companies to decide if the results of a single study may be sufficient to establish effectiveness.

Prolactin decrease and shift to a normal-like isoform profile during treatment with quinagolide in a patient affected by an invasive prolactinoma.

Prolactin (PRL) circulates as multiple molecular weight variants: glycosylated phosphory lated, deamidated and sulphated forms. The profiles of the forms, as determined by isoelectrofocusing (IEF), differ in physiological and pathological conditions. The case of a 72-year-old woman affected by an invasive prolactinoma is described. The patient had undergone surgical treatment followed by radiotherapy at the age of 71 years. Bromocriptine therapy followed (up to 10 mg/die), but the PRL levels were still extremely high (over 13,000 µg/l as determined by IRMA, after dilution). We therefore treated the patient with quinagolide, at increasing dosages, from 150 µg/die on day 0 to 600 µg/die on day 220. This treatment progressively lowered PRL to 23.2 µg/l. In addition to a decrease in PRL levels, a progressive change in the IEF profile was also noted. Indeed, on day 0, the PRL isoforms were very acidic and during treatment they progres sively shifted toward a more basic range. For purpose of comparison PRL profiles were also determined in 8 women with pathological hyperprolactinaemia (group A, aged 16–50 years, PRL levels: 25.1–170.4 µg/l), in 6 normal women (group B, aged 25–29 years, PRL levels: 3.4–7.9 µg/l) and in 5 normal women during a TRH test (group C, aged 17–52 years, PRL levels: 2.7–10.3 µg/l). The profiles observed in group A had a single major peak at isoelectric point (pl) 6.5, while the group B and C profiles were more heterogeneous displaying multiple minor peaks, the majority of the molecules being in a more basic range (pi 6.9 for group B and pl 7.5 for group C). During treatment, the profiles of our subject at first resembled those of group A; subsequently, when the PRL levels had normalised, the profile resembled those noted in group B. Altered (immature?, more glycosilated?, less bioactive?) PRL molecules could be secreted by the tumour. These data show that quinagolide successfully reduced PRL levels, while inducing secretion of forms more similar to those found in women affected by pathological hyperprolactinaemia or in normal women.

Copula-Based Models for the Power of Independence Tests

ABSTRACT We consider independence tests and the methods to evaluate their efficiency. First, we observe that many of the most used independence tests are functions of the empirical copula, which is a sufficient statistic. Hence, the power of these tests, such as the tests based on Spearmans ρ, on Kendalls τ, and on Ginis γ, depend solely on the theoretical copula, and not on the marginal distributions. Then, we consider monotone dependence tests and we propose a parametric model to define the power function. Such a model is based on a path of copulas, from the copula of discordance to the copula of concordance, and can be characterized by the copula of the underlying joint distribution. Moreover, we introduce a consistent estimator of the path of copulas. Finally, we provide some examples of applications, and in particular, a bootstrap-plug-in estimator of the power curve, all useful for power comparison.

Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests

Several reproducibility probability (RP)-estimators for the binomial, sign, Wilcoxon signed rank and Kendall tests are studied. Their behavior in terms of MSE is investigated, as well as their performances for RP-testing. Two classes of estimators are considered: the semi-parametric one, where RP-estimators are derived from the expression of the exact or approximated power function, and the non-parametric one, whose RP-estimators are obtained on the basis of the nonparametric plug-in principle. In order to evaluate the precision of RP-estimators for each test, the MSE is computed, and the best overall estimator turns out to belong to the semi-parametric class. Then, in order to evaluate the RP-testing performances provided by RP estimators for each test, the disagreement between the RP-testing decision rule, i.e., “accept H0 if the RP-estimate is lower than, or equal to, 1/2, and reject H0 otherwise”, and the classical one (based on the critical value or on the p-value) is obtained. It is shown that the RP-based testing decision for some semi-parametric RP estimators exactly replicates the classical one. In many situations, the RP-estimator replicating the classical decision rule also provides the best MSE.

Profit Evaluations when Adaptation By Design is Applied

Adaptation by design consists in conservatively estimating the phase III sample size on the basis of phase II data; it is also called conservative sample size estimation (CSSE). The usual assumptions are that the effect size is the same in both phases and that phase II data are not used for phase III confirmatory analysis. CSSE has been introduced to increase the rate of successful trials, and it can be applied in most clinical areas. CSSE reduces the probability of underpowered experiments and can improve the overall success probability of phase II and III, but it also increases phase III sample size, increasing the time and cost of experiments. Thus, the balance between higher revenue and greater cost is the issue. A profit model was built assuming that CSSE was applied and considering income per patient, annual incidence, time on market, market share, phase III success probability, fixed cost of the 2 phases, and cost per patient under treatment. Profit turns out to be a random variable depending on phase II sample size and conservativeness. Profit moments are obtained in a closed formula. Profit utility, which is a linear function of profit expectation and volatility, is evaluated in accordance with the modern theory of investment performances. Indications regarding phase II sample size and conservativeness can be derived on the basis of utility, for example, through utility optimization. CSSE can be adopted in many different statistical problems, and consequently the profit evaluations proposed here can be widely applied.Background: Adaptation by design consists in conservatively estimating the phase III sample size on the basis of phase II data; it is also called conservative sample size estimation (CSSE). The usual assumptions are that the effect size is the same in both phases and that phase II data are not used for phase III confirmatory analysis. CSSE has been introduced to increase the rate of successful trials, and it can be applied in most clinical areas. CSSE reduces the probability of underpowered experiments and can improve the overall success probability of phase II and III, but it also increases phase III sample size, increasing the time and cost of experiments. Thus, the balance between higher revenue and greater cost is the issue. Methods: A profit model was built assuming that CSSE was applied and considering income per patient, annual incidence, time on market, market share, phase III success probability, fixed cost of the 2 phases, and cost per patient under treatment. Results: Profit turns out to be a random variable depending on phase II sample size and conservativeness. Profit moments are obtained in a closed formula. Profit utility, which is a linear function of profit expectation and volatility, is evaluated in accordance with the modern theory of investment performances. Indications regarding phase II sample size and conservativeness can be derived on the basis of utility, for example, through utility optimization. Conclusions: CSSE can be adopted in many different statistical problems, and consequently the profit evaluations proposed here can be widely applied.