Absolute precision confidence intervals for unstandardized mean differences using sequential stopping rules.

Societies and journals in psychology encourage use of confidence intervals (CIs) on effect sizes. Gaining a maximum of precision of the CI at a minimum cost is desirable. Methods are available to calculate a sample size to provide some percent "assurance" that the final CI will be no wider than a desired value under the fixed-sample rule (FSR), in which a sample size must be decided a priori. Such assurance is expensive, and still subject to failure. The desired width can be specified either in standardized or unstandardized units, and this article focuses on unstandardized widths. A sequential stopping rule (SSR) can generate a CI for a mean difference that is always the desired width, and the average use of subjects is about the same as the FSR sample size without assurance. Improper use of sequential sampling can lead to a CI that has degraded coverage - the interval may contain the population value only 90% of the time for a nominal 95% CI. SSR methods are available to deliver CIs that are within a certain tolerance of the nominal coverage or that are at least the nominal coverage on average. These methods can be assessed by simulations, and they involve a manipulation of the minimum sample size, the desired width, or the practical confidence coefficient used to calculate CIs during the SSR experiment. As with FSR, more exact CIs are generated when the population standard deviation can be estimated accurately.

Expected and empirical coverages of different methods for generating noncentral t confidence intervals for a standardized mean difference.

Different methods have been suggested for calculating "exact" confidence intervals for a standardized mean difference using the noncentral t distributions. Two methods are provided in Hedges and Olkin (1985, "H") and Steiger and Fouladi (1997, "S"). Either method can be used with a biased estimator, d, or an unbiased estimator, g, of the population standardized mean difference (methods abbreviated Hd, Hg, Sd, and Sg). Coverages of each method were calculated from theory and estimated from simulations. Average coverages of 95% confidence intervals across a wide range of effect sizes and across sample sizes from 5 to 89 per group were always between 85 and 98% for all methods, and all were between 94 and 96% with sample sizes greater than 40 per group. The best interval estimation was the Sd method, which always produced confidence intervals close to 95% at all effect sizes and sample sizes. The next best was the Hg method, which produced consistent coverages across all effect sizes, although coverage was reduced to 93-94% at sample sizes in the range 5-15. The Hd method was worse with small sample sizes, yielding coverages as low as 86% at n = 5. The Sg method produced widely different coverages as a function of effect size when the sample size was small (93-97%). Researchers using small sample sizes are advised to use either the Steiger & Fouladi method with d or the Hedges & Olkin method with g as an interval estimation method.

Variable criteria sequential stopping rule: Validity and power with repeated measures ANOVA, multiple correlation, MANOVA and relation to Chi-square distribution.

The variable criteria sequential stopping rule (vcSSR) is an efficient way to add sample size to planned ANOVA tests while holding the observed rate of Type I errors, αo, constant. The only difference from regular null hypothesis testing is that criteria for stopping the experiment are obtained from a table based on the desired power, rate of Type I errors, and beginning sample size. The vcSSR was developed using between-subjects ANOVAs, but it should work with p values from any type of F test. In the present study, the αo remained constant at the nominal level when using the previously published table of criteria with repeated measures designs with various numbers of treatments per subject, Type I error rates, values of ρ, and four different sample size models. New power curves allow researchers to select the optimal sample size model for a repeated measures experiment. The criteria held αo constant either when used with a multiple correlation that varied the sample size model and the number of predictor variables, or when used with MANOVA with multiple groups and two levels of a within-subject variable at various levels of ρ. Although not recommended for use with χ2 tests such as the Friedman rank ANOVA test, the vcSSR produces predictable results based on the relation between F and χ2. Together, the data confirm the view that the vcSSR can be used to control Type I errors during sequential sampling with any t- or F-statistic rather than being restricted to certain ANOVA designs.

The refined biomimetic NeuroDigm GEL™ model of neuropathic pain in a mature rat.

Background: Many humans suffering with chronic neuropathic pain have no objective evidence of an etiological lesion or disease. Frequently their persistent pain occurs after the healing of a soft tissue injury. Based on clinical observations over time, our hypothesis was that after an injury in mammals the process of tissue repair could cause chronic neural pain. Our objectives were to create the delayed onset of neuropathic pain in rats with minimal nerve trauma using a physiologic hydrogel, and characterize the rats' responses to known analgesics and a targeted biologic. Methods: In mature male Sprague Dawley rats (age 9.5 months) a percutaneous implant of tissue-derived hydrogel was placed in the musculofascial tunnel of the distal tibial nerve. Subcutaneous morphine (3 mg/kg), celecoxib (10 mg/kg), gabapentin (25 mg/kg) and duloxetine (10 mg/kg) were each screened in the model three times each over 5 months after pain behaviors developed. Sham and control groups were used in all screenings. A pilot study followed in which recombinant human erythropoietin (200 units) was injected by the GEL™ neural procedure site. Results: The GEL group gradually developed mechanical hypersensitivity lasting months. Morphine, initially effective, had less analgesia over time. Celecoxib produced no analgesia, while gabapentin and duloxetine at low doses demonstrated profound analgesia at all times tested. The injected erythropoietin markedly decreased bilateral pain behavior that had been present for over 4 months, p ≤ 0.001. Histology of the GEL group tibial nerve revealed a site of focal neural remodeling, with neural regeneration, as found in nerve biopsies of patients with neuropathic pain. Conclusion: The refined NeuroDigm GEL™ model induces a neural response resulting in robust neuropathic pain behavior. The analgesic responses in this model reflect known responses of humans with neuropathic pain. The targeted recombinant human erythropoietin at the ectopic neural lesion appears to alleviate the persistent pain behavior in the GEL™ model rodents.

Minimizing animal numbers: the variable-criteria sequential stopping rule.

The variable-criteria sequential stopping rule (SSR) allows an investigator to use a few subjects at a time to determine whether a planned experiment is worth pursuing without increasing the rate of false discoveries (type I errors). The SSR is appropriate whenever testing a null hypothesis if the experiment can be conducted in stages. The investigator adds a predetermined number of subjects at each stage and tests repeatedly for significance until the experiment is stopped because: (1) a significant effect is detected; (2) the effect is clearly not going to be significant; or (3) the predetermined maximal number of subjects has been reached. Two crucial features of the SSR are that it holds the probability of a type I error constant and maintains excellent power. The method is more efficient than is performing a typical significance test after a power analysis because SSR can require 30% fewer subjects to achieve the same power. The variable-criteria SSR provides a formal method for assuring the use of a minimal number of animals. This article provides practical examples of how to use the SSR in combination with a t test, one-way ANOVA, one-way ANOVA with a planned contrast as the focus of the stopping rule, or, in limited circumstances, multifactorial ANOVA.

Ethics and animal numbers: informal analyses, uncertain sample sizes, inefficient replications, and type I errors.

To obtain approval for the use vertebrate animals in research, an investigator must assure an ethics committee that the proposed number of animals is the minimum necessary to achieve a scientific goal. How does an investigator make that assurance? A power analysis is most accurate when the outcome is known before the study, which it rarely is. A 'pilot study' is appropriate only when the number of animals used is a tiny fraction of the numbers that will be invested in the main study because the data for the pilot animals cannot legitimately be used again in the main study without increasing the rate of type I errors (false discovery). Traditional significance testing requires the investigator to determine the final sample size before any data are collected and then to delay analysis of any of the data until all of the data are final. An investigator often learns at that point either that the sample size was larger than necessary or too small to achieve significance. Subjects cannot be added at this point in the study without increasing type I errors. In addition, journal reviewers may require more replications in quantitative studies than are truly necessary. Sequential stopping rules used with traditional significance tests allow incremental accumulation of data on a biomedical research problem so that significance, replicability, and use of a minimal number of animals can be assured without increasing type I errors.

The variable-criteria sequential stopping rule: generality to unequal sample sizes, unequal variances, or to large ANOVAs.

The variable-criteria sequential stopping rule (SSR) is a method for conducting planned experiments in stages after the addition of new subjects until the experiment is stopped because the p value is less than or equal to a lower criterion and the null hypothesis has been rejected, the p value is above an upper criterion, or a maximum sample size has been reached. Alpha is controlled at the expected level. The table of stopping criteria has been validated for a t test or ANOVA with four groups. New simulations in this article demonstrate that the SSR can be used with unequal sample sizes or heterogeneous variances in a t test. As with the usual t test, the use of a separate-variance term instead of a pooled-variance term prevents an inflation of alpha with heterogeneous variances. Simulations validate the original table of criteria for up to 20 groups without a drift of alpha. When used with a multigroup ANOVA, a planned contrast can be substituted for the global F as the focus for the stopping rule. The SSR is recommended when significance tests are appropriate and when the null hypothesis can be tested in stages. Because of its efficiency, the SSR should be used instead of the usual approach to the t test or ANOVA when subjects are expensive, rare, or limited by ethical considerations such as pain or distress.

Improved stopping rules for the design of efficient small-sample experiments in biomedical and biobehavioral research.

Sequential stopping rules (SSRs) should augment traditional hypothesis tests in many planned experiments, because they can provide the same statistical power with up to 30% fewer subjects without additional education or software. This article includes new Monte-Carlo-generated power curves and tables of stopping criteria based on the p values from simulated t tests and one-way ANOVAs. The tables improve existing SSR techniques by holding alpha very close to a target value when 1-10 subjects are added at each iteration. The emphasis is on small sample sizes (3-40 subjects per group) and large standardized effect sizes (0.8-2.0). The generality of the tables for dependent samples and one-tailed tests is discussed. SSR methods should be of interest to ethics bodies governing research when it is desirable to limit the number of subjects tested, such as in studies of pain, experimental disease, or surgery with animal or human subjects.

Intravenous angiotensin and salt appetite in rats.

Circulating angiotensin II is crucial for the activation of salt appetite after sodium depletion. We tested if angiotensin (ANG) II infused intravenously at 50 ng/kg/min overnight (chronic) can mimic the rapid salt appetite similar to furosemide and overnight sodium depletion. In experiment 1, rats received chronic ANG II or vehicle infusions all night with access to water and chow but no saline solution. In the morning, the infusions continued, but half of the vehicle-infused group was switched to ANG II (acute). Thirty minutes after the switch, all rats received 10 mg/kg furosemide SC. One hour later they were provided water and 0.3 M NaCl to drink. Rats infused with vehicle or acute ANG drank little, but the chronic ANG group drank 11+/-1 ml of saline in 90 min. In experiment 2, the furosemide was omitted, and a group receiving a chronic infusion of phenylephrine at 6.25 microg/kg/min was included. The chronic ANG group drank 10+/-1 ml saline in 90 min, but the phenylephrine group, which also incurred a significant negative sodium balance overnight, drank little. Thus, an overnight infusion of ANG II is sufficient to mimic the robust expression of salt appetite as observed after furosemide and overnight sodium depletion.

Differential effects of intravenous hyperosmotic solutes on drinking latency and c-Fos expression in the circumventricular organs and hypothalamus of the rat.

Hyperosmotic intravenous infusions of NaCl are more potent for inducing drinking and vasopressin (AVP) secretion than equally osmotic solutions of glucose or urea. The fact that all three solutes increased cerebrospinal fluid osmolality and sodium concentration led the investigators to conclude that critical sodium receptors or osmoreceptors for stimulating drinking and AVP secretion were outside the blood-brain barrier (BBB) in the circumventricular organs (CVOs). We tested an obvious prediction of this hypothesis: that all three solutes should increase c-Fos-like immunoreactivity (Fos-ir) inside the BBB, but that only NaCl should increase Fos-ir in the CVOs. We gave intravenous infusions of 3.0 Osm/l NaCl, glucose, or urea to rats for 11 or 22 min at 0.14 ml/min and perfused the rats for assay of Fos-ir at 90 min. Controls received isotonic NaCl at the same volume. Drinking latency was measured, but water was then removed. Drinking consistently occurred with short latency during hyperosmotic NaCl infusions only. Fos-ir in the forebrain CVOs, the subfornical organ, and organum vasculosum laminae terminalis was consistently elevated only by hyperosmotic NaCl. However, all three hyperosmotic solutes potently stimulated Fos-ir in the supraoptic and paraventricular nuclei of the hypothalamus inside the BBB. Hyperosmotic NaCl greatly elevated Fos-ir in the area postrema, but even glucose and urea caused moderate elevations that may be related to volume expansion rather than osmolality. The data provide strong support for the conclusion that the osmoreceptors controlling drinking are located in the CVOs.

Misuse of ANOVA with cumulative intakes.

Cumulative responses are important for the study of ingestive behavior. The total amounts consumed at several time points after experimental or control treatments are often analyzed using a mixed-model analysis of variance. The method used by some investigators to calculate the significance of this difference is invalid and may lead to serious errors of inference. Direct analysis of cumulative data can lead to grossly erroneous p-values for certain effects because data from early time points contribute disproportionately to the outcome. Analysis of uncumulated data yields the appropriate levels of significance and all of the same hypotheses can be tested.

Losartan blocks drinking and cFos expression induced by central ornithine vasotocin in rats.

We previously reported that an intracerebroventricular (icv) injection of the oxytocin receptor antagonist ornithine vasotocin (OVT) caused water and saline intakes, a pressor response, and Fos-like immunoreactivity (Fos-IR) in the median preoptic nucleus of the rat brain. In the present report, rats receiving an icv injection of isotonic saline vehicle followed by an icv injection of 10 microg of OVT 20 min later drank 5.5+/-1.1 ml of total water and saline intake in 60 min after the OVT; rats receiving 10 microg of losartan before the OVT drank only 0.9+/-0.3 ml of total fluid. In a separate study, rats were treated as above except that they were not allowed to drink and were perfused for analysis of Fos-IR in the median preoptic nucleus at 90 min. Fos-IR in the dorsal part of the median preoptic nucleus was significantly suppressed from 2.69+/-0.57 cells per 10,000 square mum in vehicle-treated rats to 0.89+/-0.20 in losartan-treated rats. Losartan alone had no effect on Fos-IR. Losartan did not reduce intake of saccharin in a dessert test. This suggests that the OVT-induced drinking may result from an activation or disinhibition of angiotensin type AT1 receptors in the median preoptic nucleus.

Subfornical organ disconnection alters Fos expression in the lamina terminalis, supraoptic nucleus, and area postrema after intragastric hypertonic NaCl.

The lamina terminalis was severed by a horizontal knife cut through the anterior commissure to determine the effects of a disconnection of the subfornical organ (SFO) on drinking and Fos-like immunoreactivity (Fos-ir) in the rat brain in response to an intragastric load of hypertonic saline (5 ml/kg of 1.5 M NaCl by gavage). After an initial load, knife-cut rats drank significantly less water than sham-cut rats, thus confirming a role for the SFO in osmotic drinking. After a second load at least 1 wk later, the rats were not allowed to drink after the gavage and were perfused for analysis of Fos-ir at 90 min. Compared with sham-cut rats, the knife-cut rats displayed significantly elevated Fos-ir in the main body of the SFO, in the dorsal cap of the organum vasculosum laminae terminalis, and in the ventral median preoptic nucleus after the hypertonic load. The knife cut significantly decreased Fos-ir in the supraoptic nucleus. Fos-ir was expressed mainly in the midcoronal and caudal parts of the area postrema of sham-cut rats, and this expression was greatly reduced in knife-cut rats. These findings strengthen the case for the presence of independently functioning osmoreceptors within the SFO and suggest that the structures of the lamina terminalis provide mutual inhibition during hypernatremia. They also demonstrate that the Fos-ir in the area postrema after intragastric osmotic loading is heavily dependent on the intact connectivity of the SFO.

Effects of forebrain circumventricular organ ablation on drinking or salt appetite after sodium depletion or hypernatremia.

In many previous studies, one or the other forebrain circumventricular organ, the subfornical organ (SFO) or organum vasculosum laminae terminalis (OVLT), was lesioned to test whether it was critical for the behavioral or physiological responses to sodium depletion and hypernatremia. These studies conflict in their conclusions. The present study was designed to create discrete lesions of both the SFO and OVLT in the same animals and to compare these with rats having a lesion of only the SFO or OVLT. Both the OVLT-lesioned group and the combined SFO + OVLT-lesioned group drank significantly more water and saline on a daily basis than Controls or SFO-lesioned rats. In both sodium depletion and hypertonic saline testing, rats with SFO lesions displayed transient deficits in salt appetite or thirst responses, whereas the rats with single OVLT lesions did not. In the sodium depletion test, but not in the hypernatremia test, rats with lesions of both the SFO and OVLT exhibited the largest deficit. The data support the hypothesis that a combined lesion eliminates redundancy and is more effective than a single lesion in sodium depletion tests. The interpretation of the OVLT lesion-only data may have been complicated by a tendency to drink more fluid on a daily basis, because some of those animals drank copious water in addition to saline even very early during the salt appetite test.

Lesions of the subfornical organ decrease the calcium appetite of calcium-deprived rats.

There are several indications that neurons in the rat's subfornical organ (SFO) are sensitive to internal calcium status. We investigated the role of the SFO in regulating calcium intake by comparing the consumption of 30 mM CaCl2 by rats with (a) lesions of >90% of the SFO, (b) lesions that left the SFO mostly intact but disconnected its rostroventral stalk, (c) misplaced lesions that spared most of the SFO, or (d) a sham lesion procedure. In one experiment involving calcium-replete rats, these four groups had similar CaCl2 intakes. In another experiment involving calcium-deprived rats, those with lesions of the SFO or its rostroventral stalk consumed less CaCl2 than did those with missed or sham lesions. The SFO therefore appears to play a role in the calcium appetite that accompanies calcium deprivation in rats, most likely through its rostroventral efferents, but it is not important for need-free calcium intake.

Effects of central oxytocin receptor blockade on water and saline intake, mean arterial pressure, and c-Fos expression in rats.

Central injection of ANG II has been proposed to have dual effects on salt appetite including a direct stimulatory effect and an indirect inhibitory effect through an activation of central oxytocinergic neurons. The inhibition was demonstrated by pretreating rats with central ornithine vasotocin (OVT; oxytocin antagonist) 30 min before a central ANG II injection. The OVT pretreatment produced a large increase in ANG II-induced saline intake. The present paper reports a failure to replicate that influential experiment. However, we also report for the first time that OVT by itself: 1) provokes drinking of both water and saline solution with a latency almost as short as that produced by ANG II; 2) produces a mild pressor response; and 3) increases c-Fos expression in the organum vasculosum laminae terminalis (OVLT) and the median preoptic nucleus (MnPO). Oxytocin activity may provide an inhibitory control of drinking responses as has been suggested, but the inhibition is tonic and includes both water and saline drinking. Inhibition of this tonic activity may stimulate drinking by increasing neural activity in the OVLT and MnPO.

Salt appetite of adrenalectomized rats after a lesion of the SFO.

Circumventricular organs such as the subfornical organ (SFO) may mediate the effects of circulating angiotensin (ANG) II on salt appetite under conditions of sodium depletion in the rat. We studied the effects of an electrolytic lesion of SFO on salt appetite after adrenalectomy (ADX) in Long-Evans rats. The SFO lesion had no effect on saline intake, but it did abolish water intake after acute peripheral treatments with 2 mg/kg of captopril or a 10 mg/kg of furosemide. These findings contrast with other recent data from this laboratory demonstrating large reductions in salt appetite in adrenal-intact rats with lesions of either SFO or the organum vasculosum laminae terminalis during acute iv infusions of ANG II. Thus, the SFO may contribute to the salt appetite response to circulating ANG II, but it is not essential for the response to adrenalectomy.

Forebrain circumventricular organs mediate salt appetite induced by intravenous angiotensin II in rats.

Two circumventricular organs, the subfornical organ (SFO) and organum vasculosum laminae terminalis (OVLT), may mediate salt appetite in response to acute intravenous infusions of angiotensin (ANG) II. Fluid intakes and mean arterial pressures were measured in rats with sham lesions or electrolytic lesions of the SFO or OVLT during an intravenous infusion of 30 ng/min ANG II. Beginning 21 h before the 90-min infusion, the rats were depleted of sodium with furosemide and given a total of 300 mg/kg captopril in 75 ml/kg water in three spaced gavages to block the usual salt appetite and to hydrate the rats. No other food or fluids were available for ingestion. Sham-lesioned rats drank 9.3+/-1.2 ml if 0.3 M NaCl alone was available and drank 8.9+/-1.6 ml of saline and 3.7+/-1.6 ml of water if both were available. Either SFO or OVLT lesions reduced the intakes of saline to <5 ml in both conditions and of water to <1 ml. Mean arterial pressure did not differ among the groups and was maintained above 100 mmHg after the depletion and captopril treatments because of the large doses of water. Thus, a full expression of salt appetite in response to an acute intravenous infusion of ANG II requires the integrity of both the SFO and OVLT.

Subfornical organ disconnection and Fos-like immunoreactivity in hypothalamic nuclei after intragastric hypertonic saline.

The subfornical organ (SFO) may act as a sodium- or osmoreceptor that drives hypothalamic and other nuclei to secrete vasopressin and to elicit drinking. However, in response to mild doses of hypertonic saline, Fos-like immunoreactivity (Fos-ir) is absent in the SFO whereas it is well expressed in the hypothalamic supraoptic (SON) and paraventricular (PVN) nuclei. This suggests that the hypothalamus may be activated in advance of the SFO. In this study, the fibers connecting the SFO and hypothalamus were disconnected by a wire knife cut so that Fos-ir could be examined in both the SFO and hypothalamus after an intragastric (ig) load of 0.5% of body weight of 0.6 M NaCl. Compared with Fos-ir in isotonic-loaded rats, Fos-ir after the hypertonic load was not significantly elevated in the SFO or median preoptic nucleus in sham-cut or knife-cut rats and was only slightly elevated in the OVLT in sham-cut rats. However, the hypertonic load in sham-cut rats greatly elevated Fos-ir in the SON and in the entire PVN, but this expression was reduced significantly by 30-50% in knife-cut rats. Thus, the connectivity between SFO and the hypothalamus is critical for the full expression of Fos-ir in the hypothalamus during moderate ig hypertonic saline loading even when the SFO itself does not yet express Fos-ir.