A framework for identifying treatment-covariate interactions in individual participant data network meta-analysis.

BACKGROUND: Stratified medicine seeks to identify patients most likely to respond to treatment. Individual participant data (IPD) network meta-analysis (NMA) models have greater power than individual trials to identify treatment-covariate interactions (TCIs). Treatment-covariate interactions contain "within" and "across" trial interactions, where the across-trial interaction is more susceptible to confounding and ecological bias. METHODS: We considered a network of IPD from 37 trials (5922 patients) for cervical cancer (2394 events), where previous research identified disease stage as a potential interaction covariate. We compare 2 models for NMA with TCIs: (1) 2 effects separating within- and across-trial interactions and (2) a single effect combining within- and across-trial interactions. We argue for a visual assessment of consistency of within- and across-trial interactions and consider more detailed aspects of interaction modelling, eg, common vs trial-specific effects of the covariate. This leads us to propose a practical framework for IPD NMA with TCIs. RESULTS: Following our framework, we found no evidence in the cervical cancer network for a treatment-stage interaction on the basis of the within-trial interaction. The NMA provided additional power for an across-trial interaction over and above the pairwise evidence. Following our proposed framework, we found that the within- and across-trial interactions should not be combined. CONCLUSION: Across-trial interactions are susceptible to confounding and ecological bias. It is important to separate the sources of evidence to check their consistency and identify which sources of evidence are driving the conclusion. Our framework provides practical guidance for researchers, reducing the risk of unduly optimistic interpretation of TCIs.

What is the optimal systemic treatment of men with metastatic, hormone-naive prostate cancer? A STOPCAP systematic review and network meta-analysis.

Background: Our prior Systemic Treatment Options for Cancer of the Prostate systematic reviews showed improved survival for men with metastatic hormone-naive prostate cancer when abiraterone acetate plus prednisolone/prednisone (AAP) or docetaxel (Doc), but not zoledronic acid (ZA), were added to androgen-deprivation therapy (ADT). Trial evidence also suggests a benefit of combining celecoxib (Cel) with ZA and ADT. To establish the optimal treatments, a network meta-analysis (NMA) was carried out based on aggregate data (AD) from all available studies. Methods: Overall survival (OS) and failure-free survival data from completed Systemic Treatment Options for Cancer of the Prostate reviews of Doc, ZA and AAP and from recent trials of ZA and Cel contributed to this comprehensive AD-NMA. The primary outcome was OS. Correlations between treatment comparisons within one multi-arm, multi-stage trial were estimated from control-arm event counts. Network consistency and a common heterogeneity variance were assumed. Results: We identified 10 completed trials which had closed to recruitment, and one trial in which recruitment was ongoing, as eligible for inclusion. Results are based on six trials including 6204 men (97% of men randomised in all completed trials). Network estimates of effects on OS were consistent with reported comparisons with ADT alone for AAP [hazard ration (HR) = 0.61, 95% confidence interval (CI) 0.53-0.71], Doc (HR = 0.77, 95% CI 0.68-0.87), ZA + Cel (HR = 0.78, 95% CI 0.62-0.97), ZA + Doc (HR = 0.79, 95% CI 0.66-0.94), Cel (HR = 0.94 95% CI 0.75-1.17) and ZA (HR = 0.90 95% CI 0.79-1.03). The effect of ZA + Cel is consistent with the additive effects of the individual treatments. Results suggest that AAP has the highest probability of being the most effective treatment both for OS (94% probability) and failure-free survival (100% probability). Doc was the second-best treatment of OS (35% probability). Conclusions: Uniquely, we have included all available results and appropriately accounted for inclusion of multi-arm, multi-stage trials in this AD-NMA. Our results support the use of AAP or Doc with ADT in men with metastatic hormone-naive prostate cancer. AAP appears to be the most effective treatment, but it is not clear to what extent and whether this is due to a true increased benefit with AAP or the variable features of the individual trials. To fully account for patient variability across trials, changes in prognosis or treatment effects over time and the potential impact of treatment on progression, a network meta-analysis based on individual participant data is in development.

Multiple imputation using linked proxy outcome data resulted in important bias reduction and efficiency gains: a simulation study.

BACKGROUND: When an outcome variable is missing not at random (MNAR: probability of missingness depends on outcome values), estimates of the effect of an exposure on this outcome are often biased. We investigated the extent of this bias and examined whether the bias can be reduced through incorporating proxy outcomes obtained through linkage to administrative data as auxiliary variables in multiple imputation (MI). METHODS: Using data from the Avon Longitudinal Study of Parents and Children (ALSPAC) we estimated the association between breastfeeding and IQ (continuous outcome), incorporating linked attainment data (proxies for IQ) as auxiliary variables in MI models. Simulation studies explored the impact of varying the proportion of missing data (from 20 to 80%), the correlation between the outcome and its proxy (0.1-0.9), the strength of the missing data mechanism, and having a proxy variable that was incomplete. RESULTS: Incorporating a linked proxy for the missing outcome as an auxiliary variable reduced bias and increased efficiency in all scenarios, even when 80% of the outcome was missing. Using an incomplete proxy was similarly beneficial. High correlations (> 0.5) between the outcome and its proxy substantially reduced the missing information. Consistent with this, ALSPAC analysis showed inclusion of a proxy reduced bias and improved efficiency. Gains with additional proxies were modest. CONCLUSIONS: In longitudinal studies with loss to follow-up, incorporating proxies for this study outcome obtained via linkage to external sources of data as auxiliary variables in MI models can give practically important bias reduction and efficiency gains when the study outcome is MNAR.

What impact do assumptions about missing data have on conclusions? A practical sensitivity analysis for a cancer survival registry.

BACKGROUND: Within epidemiological and clinical research, missing data are a common issue and often over looked in publications. When the issue of missing observations is addressed it is usually assumed that the missing data are 'missing at random' (MAR). This assumption should be checked for plausibility, however it is untestable, thus inferences should be assessed for robustness to departures from missing at random. METHODS: We highlight the method of pattern mixture sensitivity analysis after multiple imputation using colorectal cancer data as an example. We focus on the Dukes' stage variable which has the highest proportion of missing observations. First, we find the probability of being in each Dukes' stage given the MAR imputed dataset. We use these probabilities in a questionnaire to elicit prior beliefs from experts on what they believe the probability would be in the missing data. The questionnaire responses are then used in a Dirichlet draw to create a Bayesian 'missing not at random' (MNAR) prior to impute the missing observations. The model of interest is applied and inferences are compared to those from the MAR imputed data. RESULTS: The inferences were largely insensitive to departure from MAR. Inferences under MNAR suggested a smaller association between Dukes' stage and death, though the association remained positive and with similarly low p values. CONCLUSIONS: We conclude by discussing the positives and negatives of our method and highlight the importance of making people aware of the need to test the MAR assumption.

Multiple imputation for IPD meta-analysis: allowing for heterogeneity and studies with missing covariates.

Recently, multiple imputation has been proposed as a tool for individual patient data meta-analysis with sporadically missing observations, and it has been suggested that within-study imputation is usually preferable. However, such within study imputation cannot handle variables that are completely missing within studies. Further, if some of the contributing studies are relatively small, it may be appropriate to share information across studies when imputing. In this paper, we develop and evaluate a joint modelling approach to multiple imputation of individual patient data in meta-analysis, with an across-study probability distribution for the study specific covariance matrices. This retains the flexibility to allow for between-study heterogeneity when imputing while allowing (i) sharing information on the covariance matrix across studies when this is appropriate, and (ii) imputing variables that are wholly missing from studies. Simulation results show both equivalent performance to the within-study imputation approach where this is valid, and good results in more general, practically relevant, scenarios with studies of very different sizes, non-negligible between-study heterogeneity and wholly missing variables. We illustrate our approach using data from an individual patient data meta-analysis of hypertension trials. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Variance estimation for stratified propensity score estimators.

Propensity score methods are increasingly used to estimate the effect of a treatment or exposure on an outcome in non-randomised studies. We focus on one such method, stratification on the propensity score, comparing it with the method of inverse-probability weighting by the propensity score. The propensity score--the conditional probability of receiving the treatment given observed covariates--is usually an unknown probability estimated from the data. Estimators for the variance of treatment effect estimates typically used in practice, however, do not take into account that the propensity score itself has been estimated from the data. By deriving the asymptotic marginal variance of the stratified estimate of treatment effect, correctly taking into account the estimation of the propensity score, we show that routinely used variance estimators are likely to produce confidence intervals that are too conservative when the propensity score model includes variables that predict (cause) the outcome, but only weakly predict the treatment. In contrast, a comparison with the analogous marginal variance for the inverse probability weighted (IPW) estimator shows that routinely used variance estimators for the IPW estimator are likely to produce confidence intervals that are almost always too conservative. Because exact calculation of the asymptotic marginal variance is likely to be complex, particularly for the stratified estimator, we suggest that bootstrap estimates of variance should be used in practice.

Predicting the advent of ascites and other complications in primary biliary cirrhosis: a staged model approach.

BACKGROUND: Current survival models for primary biliary cirrhosis have limited precision for medium and long-term survival. Aim To describe a prognostic model for the advent of complications in primary biliary cirrhosis as the first approach to a staged prognostic model. METHODS: From an established database of 289 consecutive primary biliary cirrhosis patients referred to Royal Free Hospital over 12 years (mean follow-up of 4.1 years), baseline characteristics at referral were evaluated by Cox-proportional hazards regression modelling. RESULTS: The following complications occurred de novo: 85 ascites/peripheral oedema, 40 oesophagogastric varices, 63 encephalopathy, 29 spontaneous bacterial peritonitis and/or septicaemia, 59 symptomatic urinary tract infections. Age, albumin, log(10)(bilirubin), presence of ascites at referral, variceal bleeding within 6 weeks before referral, detection of oesophagogastric varices at or before referral were significant at multivariate analysis with different combinations and coefficients for each complication. The model for predicting ascites and/or peripheral oedema best fitted the observed data (ROC = 0.7682, S.E. = 0.0385). CONCLUSIONS: The known prognostic factors in primary biliary cirrhosis also model the advent of complications. In view of the prognostic importance of ascites and its more robust statistical model, ascites and/or peripheral oedema could represent, following validation, the most suitable staged model in primary biliary cirrhosis to improve precision in survival modelling.

Effect of lactation stage and concurrent pregnancy on milk composition in the bottlenose dolphin.

ALTHOUGH MANY TOOTHED WHALES (CETACEA: Odontoceti) lactate for 2-3 years or more, it is not known whether milk composition is affected by lactation stage in any odontocete species. We collected 64 pooled milk samples spanning 1-30 months postpartum from three captive bottlenose dolphins Tursiops truncatus. Milks were assayed for water, fat, crude protein (TN × 6.38) and sugar; gross energy was calculated. Ovulation and pregnancy were determined via monitoring of milk progesterone. Based on analysis of changes in milk composition for each individual dolphin, there were significant increases (P<0.05) in fat (in all three dolphins) and crude protein (in two of three), and a decrease (P<0.05) in water (in two of three) over the course of lactation, but the sugar content did not change. In all three animals, the energy content was positively correlated with month of lactation, but the percentage of energy provided by crude protein declined slightly but significantly (P<0.05). At mid-lactation (7-12 months postpartum, n=17), milk averaged 73.0±1.0% water, 12.8±1.0% fat, 8.9±0.5% crude protein, 1.0±0.1% sugar, 1.76±0.09 kcal g(-1) (=7.25 kJ g(-1)) and 30.3±1.3% protein:energy per cent. This protein:energy per cent was surprisingly high compared with other cetaceans and in relation to the growth rates of calves. Milk progesterone indicated that dolphins ovulated and conceived between 413 and 673 days postpartum, following an increase in milk energy density. The significance of these observed compositional changes to calf nutrition will depend on the amounts of milk produced at different stages of lactation, and how milk composition and yield are influenced by sampling procedure, maternal diet and maternal condition, none of which are known.

Phosphorus in Hawaiian kikuyugrass pastures and potential phosphorus release to water.

Pasture systems in Hawaii are based primarily on kikuyugrass (Pennisetum clandestinum Hochst. ex Chiov.). Relationships among kikuyugrass P concentration, animal P requirements, and various soil P determinations are needed to help identify source areas for implementing pasture management strategies to limit P loss via overland flow. A total of 51 rotationally stocked kikuyugrass pastures (>20 yr old) with contrasting soil chemical properties were sampled. A satisfactory predictive relationship between modified-Truog (MT)-extractable phosphorus (P(MT)) and dissolved (<0.45-mum pore diameter), molybdate-reactive phosphorus (DRP) desorbed from soil in a water extract (DRP(WE)) was found when 0- to 4-cm-depth data for the soil orders with medium to high DRP(WE) (two Mollisols and an Inceptisol) were pooled separately from those with low DRP(WE) (five Andisols, three Ultisols, and an Oxisol). The oxalate phosphorus saturation index (PSI(ox)) procedure was the best predictor of DRP(WE) across soil orders when oxalate-extractable molybdate-reactive phosphorus (RP(ox)) was used to calculate PSI(ox) (PSI(ox)RP) rather than when total oxalate-extractable phosphorus (TP(ox)) was used (PSI(ox)TP). There was little DRP(WE) until PSI(ox)RP exceeded 6% or PSI(ox)TP exceeded 8%. A more empirical dilute-acid phosphorus saturation index (PSI(MT)) was also calculated using P(MT) and MT-extractable iron (Fe(MT)) and aluminum (Al(MT)). The PSI(MT) procedure showed some utility in predicting DRP(WE), was positively related to the PSI(ox) procedures, and can be more readily performed in agronomic soil testing laboratories than PSI(ox). The present research suggests that while Hawaiian kikuyugrass pastures tend to be sufficient to high in forage P, potential soil P release to water only appeared to be a possible environmental concern for the Mollisol and Inceptisol sites.

Long-term ursodeoxycholic acid therapy for primary biliary cirrhosis: a follow-up to 12 years.

BACKGROUND: It is uncertain whether ursodeoxycholic acid therapy slows down the progression of primary biliary cirrhosis, according to two meta-analyses. However, the randomized trials evaluated had only a median of 24 months of follow-up. AIM: To evaluate long-term ursodeoxycholic acid therapy in primary biliary cirrhosis. METHODS: We evaluated 209 consecutive primary biliary cirrhosis patients, 69 compliant with ursodeoxycholic acid and 140 untreated [mean follow-up 5.79 (s.d. = 4.73) and 4.87 (s.d. = 5.21) years, respectively] with onset of all complications documented. Comparison was made following adjustment for baseline differences according to Cox modelling, Mayo and Royal Free prognostic models. RESULTS: Bilirubin and alkaline phosphatase concentrations improved with ursodeoxycholic acid (at 36 months, P = 0.007 and 0.018, respectively). Unadjusted Kaplan-Meier analysis showed benefit (P = 0.028), as 44 (31%) untreated and 15 (22%) ursodeoxycholic acid patients died or had liver transplantation. However, there was no difference when adjusted by Cox modelling (P = 0.267), Mayo (P = 0.698) and Royal Free models (P = 0.559). New pruritus or fatigue or other complications were not different, either before or after adjustment for baseline characteristics. CONCLUSIONS: Long-term ursodeoxycholic acid therapy did not alter disease progression in primary biliary cirrhosis patients despite a significant improvement in serum bilirubin and alkaline phosphatase consistent with, and similar to, those seen in ursodeoxycholic acid cohorts in randomized trials.

Bootstrap confidence intervals for relative risk parameters in affected-sib-pair data.

In affected-sib-pair (ASP) studies, parameters such as the locus-specific sibling relative risk, lambda(s), may be estimated and used to decide whether or not to continue the search for susceptibility genes. Typically, a maximum likelihood point estimate of lambda(s) is given, but since this estimate may have substantial variability, it is of interest to obtain confidence limits for the true value of lambda(s). While a variety of methods for doing this exist, there is considerable uncertainty over their reliability. This is because the discrete nature of ASP data and the imposition of genetic "possible triangle" constraints during the likelihood maximization mean that asymptotic results may not apply. In this paper, we use simulation to evaluate the reliability of various asymptotic and simulation-based confidence intervals, the latter being based on a resampling, or bootstrap approach. We seek to identify, from the large pool of methods available, those methods that yield short intervals with accurate coverage probabilities for ASP data. Our results show that many of the most popular bootstrap confidence interval methods perform poorly for ASP data, giving coverage probabilities much lower than claimed. The test-inversion, profile-likelihood, and asymptotic methods, however, perform well, although some care is needed in choice of nuisance parameter. Overall, in simulations under a variety of different genetic hypotheses, we find that the asymptotic methods of confidence interval evaluation are the most reliable, even in small samples. We illustrate our results with a practical application to a real data set, obtaining confidence intervals for the sibling relative risks associated with several loci involved in type 1 diabetes.

Estimation of admixture and detection of linkage in admixed populations by a Bayesian approach: application to African-American populations.

We describe a novel method for analysis of marker genotype data from admixed populations, based on a hybrid of Bayesian and frequentist approaches in which the posterior distribution is generated by Markov chain simulation and score tests are obtained from the missing-data likelihood. We analysed data on unrelated individuals from eight African-American populations, genotyped at ten marker loci of which two (FY and AT3) are linked (22 cM apart). Linkage between these two loci was detected by testing for association of ancestry conditional on parental admixture. The strength of this association was consistent with European gene flow into the African-American population between five and nine generations ago. To mimic the mapping of an unknown gene in an 'affecteds- only' analysis, a binary trait was constructed from the genotype at the AT3 locus and a score test was shown to detect linkage of this 'trait' with the FY locus. Mis-specification of the ancestry-specific allele frequencies - the probabilities of each allelic state given the ancestry of the allele - was detected at three of the ten marker loci. The methods described here have wide application to the analysis of data from admixed populations, allowing the effects of linkage and population structure (variation of admixture between individuals) to be distinguished. With more markers and a more complex statistical model, genes underlying ethnic differences in disease risk could be mapped by this approach.

Nutrient, fatty acid, amino acid and mineral analysis of natural prey of the Hawaiian monk seal, Monachus schauinslandi.

Proximate nutrients, gross energy content, mineral, amino acid and fatty acid composition were determined for teleost, cephalopod and crustacean prey of the Hawaiian monk seal. Crude protein was highest in the octopus, Octopus cyanea (80.0%), crude fat was highest in the Muraenid teleost, Gymnothorax eurostus (14.1%), whereas crude ash was highest in the lobster, Panulirus marginatus (11.6%). Gross energies ranged from 4.0 +/- 0.01 kcal g-1 in the Labrid teleost Bodianus bilulunatus to 6.0 +/- 0.12 kcal g-1 in the moray eel, Gymnothorax undulatus. Essential amino acids occurred in lower concentrations as a percentage of the total amino acids (35.8 +/- 2.6%) than non-essential amino acids (64.2 +/- 2.6%), but the ratio of individual amino acids to total amino acid concentrations were similar to those required by some monogastric terrestrial species and fingerling salmon. The fatty acid concentrations varied widely among species (range = 1.2-16.5 mg 100 mg-1); however, the teleosts had higher total fatty acids than the non-teleosts. This study indicates that, from a nutritional standpoint, some prey may be more beneficial to the Hawaiian monk seal; however, these prey are not necessarily the most abundant or available to some populations of the monk seal.

Prepartum nutrition and solar radiation in beef cattle: II. Residual effects on postpartum milk yield, immunoglobulin, and calf growth.

Residual effects of nutrition and solar radiation during the last two-thirds of gestation on postpartum milk yield, immunoglobulin (Ig) G and M in both colostrum and calf serum, and calf growth were determined in beef cattle. Nineteen mature, multiparous crossbred cows (Bos taurus) at d 90 of pregnancy were assigned to either low (LO, 70% NRC total energy intake) or high (HI, 110% NRC total energy intake) nutritional level (sudangrass hay) and to either shade (S) or no shade (NS) treatments in a 2 x 2 factorial experiment. After parturition, all cows were moved into a large paddock and managed uniformly. Calf weights and calf serum were collected within 1 d postpartum, thereafter at 2-wk intervals for the next 12 wk, and then at 4-wk intervals until weaning. Colostrum samples were taken from the cow and milk yields were determined by the "weigh-suckle-weigh" technique. Neither prepartum nutrition nor environment influenced lactational performance of the dam. Concentrations of IgG were elevated in the colostrum of LO cows (15.3 vs 7.8 g/100 mL, LO vs HI, respectively; P < or = .05) but were not affected by shading. The patterns of IgG concentration in the calf serum were not altered by prepartum nutrition or environment; however, the pattern of IgM concentrations was greater (P < or = .01) in calves from S cows than in those from NS cows. This difference in IgM profile did not seem to be due to any residual effect from prepartum treatments. Postnatal growth of calves from birth until weaning were similar across all prepartum treatments.(ABSTRACT TRUNCATED AT 250 WORDS)

Prepartum nutrition and solar radiation in beef cattle: I. Relationships of body fluid compartments, packed cell volume, plasma urea nitrogen, and estrogens to prenatal development.

Adaptations in body fluid pools during pregnancy were monitored in cows (n = 19) assigned to either low (LO, 70% NRC total feed intake) or high (HI, 110% NRC total feed intake) nutritional level (sudangrass hay) and to either shade (S) or no shade (NS) treatments in a 2 x 2 factorial experiment. Body water distribution (empty body water [EBW] by urea dilution; extracellular water [ECW] by thiosulfate dilution; intracellular water [ICW] by difference; plasma volume by Evans Blue dilution; interstitial water [ISW] by difference) was measured at 4-wk intervals beginning at 3 mo of pregnancy until birth and then immediately after birth. Both EBW and ICW in LO cows showed a steady decline (P < or = .05), whereas HI cows tended to maintain these body pools throughout gestation. Shading did not affect the pattern of change in EBW; however, it did produce a greater (P < or = .05) ICW in the S than in the NS cows throughout gestation. Generally, other body fluid pools (ECW, ISW, and plasma) were either not affected, or were just slightly affected, by shading or nutrition. Most of the body fluid pools (EBW, ECW, ICW, and ISW) inversely followed the seasonal changes in solar radiation. Calf birth weights were not affected by treatments but were moderately correlated to EBW (r = .49; P < or = .05) and ICW (r = .50; P < or = .05). Plasma urea nitrogen change, although not affected by nutrition, was affected (P < or = .05) by shading.(ABSTRACT TRUNCATED AT 250 WORDS)

Airway response to inhaled methacholine in normal human subjects.

The individual airway responsiveness to inhaled, nebulized methacholine (MeCh) was estimated in normal volunteers, measuring specific airway conductance (sGAW). The dose of MeCh was increased logarithmically until a 60-65% reduction from baseline sGAW or an asymptotic approach to a maximal response was attained. The concentration of MeCh that caused a 35% reduction in sGAW (PC35), the dose that caused a 62.5% reduction in sGAW, the slope of the straight, central part of the log-dose-response curve (LDRC), the slope of the straight, initial part of the dose-response curve, the maximal response attainable (Emax) and the dose causing a half-maximal response (ED50) were derived. These parameters were transformed as necessary to attain normality of distribution. Relationships between them were examined by measuring the correlations between their transformed values. The ED50 was taken to represent the least biased estimate of the sensitivity to MeCh. The PC35 was the best practical estimate of sensitivity. The Emax was taken to represent the least biased estimate of the reactivity to MeCh. The slope of the LDRC was the best practical estimate of reactivity. The sensitivity and reactivity varied independently in these normal subjects. Each was also independent of the baseline sGAW.