An extension to the Brun-Titchmarsh theorem

The Siegel-Walfisz theorem states that for any B > 0, we have ∑/p≤x/p≡a(mod k) 1 ∼ x/φ(k) lox x for k ≤ log B x and (k, a) = 1. This only gives an asymptotic formula for the number of primes over an arithmetic progression for quite small moduli k compared with x. However, if we are only concerned about upper bound, we have the Brun-Titchmarsh theorem, namely for any 1 ≤ k 0, s ≥ 1 and 1 ≤ k < x.In particular, for s ≤ log log (x/k), we have ∑/y<n≤x+y ≡ a (mod k)ω (n) < s 1 ≪ x/φ (k) log (x/k) (log log (x/k) + K)s-1/(s-1)! √ log log (x/k) + K and for any ε∈(0, 1) and s ≤ (1-ε) log log (x/k), we have. ∑/y<n≤x+y ≡ a (mod k)ω (n) < s 1 ≪ ε-1x/φ (k) log (x/k) (log log (x/k) +K)s-1/(s-1) !. © 2010. Published by Oxford University Press. All rights reserved.postprin

Longitudinal assessment of community psychobehavioral responses during and after the 2003 outbreak of severe acute respiratory syndrome in Hong Kong

Background. In previous literature, the stability and temporal evolution of psychobehavioral responses to an outbreak remained undefined, because of the exclusively cross-sectional nature of such study designs. Methods. Using random-digit dialing, we sampled 4481 Hong Kong residents in 6 population-based surveys that were conducted at different times during and after the 2003 outbreak of severe acute respiratory syndrome (SARS). Results. Respondents' State-Trait Anxiety Inventory score (range, 10-40) showed a decreasing temporal trend, from a high mean value of 24.8 during the peak of the Amoy Gardens outbreak to a postepidemic mean baseline value of 14.5. Those who perceived a higher likelihood of contracting or dying of SARS had significantly higher anxiety scores. Female respondents, individuals aged 30-49 years, and individuals with only a primary education or less were predisposed to greater anxiety. There was a positive dose-response gradient between anxiety level and uptake of personal protective measures. Males respondents, individuals at the extremes of age, and individuals with lower educational levels were less likely to engage in self-protective behavior. The presence of symptoms was the only consistent predictor for greater use of health services. There was remarkable stability in the magnitude and the direction of associations between predictors and outcomes over time. Conclusions. Our findings can assist in modifying public service announcements in the future, which should be tailored to psychobehavioral surveillance intelligence to achieve the desired behavioral outcomes. Future research should explore the use of more-sophisticated techniques, including structural equation modeling and game-theoretical frameworks, to analyze population psychology and behavior, and it should integrate such findings with transmission dynamics modeling. © 2005 by the Infectious Diseases Society of America. All rights reserved.published_or_final_versio

A prospective study of stage of change for general health promotion action and health-related lifestyle practices among Chinese adults

In a previous study we proposed the notion of general health promotion action (GHPA) defined as "a general intention and actual practices to take action aimed to promote health." GHPA is a subjective measure of health-promoting lifestyle which may reflect practices aimed to promote health and practices which are taken for non-health reasons but which nonetheless have health benefits. The present prospective study aimed to examine whether baseline stage of change for GHPA predicted health-related lifestyle practices at 24-month follow-up in a representative community-based cohort of 3129 Hong Kong Chinese adults. Overall, 37% of the subjects remained in the same stage, 43% had progressed to later stages, and 20% had regressed to earlier stages of change at follow-up. Baseline maintainers were the most likely to report desirable lifestyle practices at follow-up. They were significantly more likely to have exercised in the past month, consumed at least 2 portions of fruit a day, consumed at least 3 portions of vegetable a day, consumed at least 5 portions of fruit or vegetable a day, have had no episodes of binge drinking in the past month, and have had a dental examination at least once a year. The association remained significant after adjusting for age, gender, education, income and baseline level of respective lifestyle practices, with significantly increasing trends from precontemplation to maintenance stage. We conclude that the predictive validity of stage of change for GHPA was supported from these longitudinal findings, and further research on how GHPA can guide health promotion strategies is warranted. © 2006 Elsevier Ltd. All rights reserved.link_to_subscribed_fulltex

Training nurses and social workers in smoking cessation counseling: A population needs assessment in Hong Kong

To achieve greater coverage of elderly smokers and to shift entire populations toward cessation, the provider-client interface could be broadened beyond physicians to include nurses and social workers, who can be formally trained to provide such services. We carried out a population-based training needs assessment of the latter two groups in Hong Kong. Three thousand seven hundred eligible hospital-based nurses and 2,258 social workers who had elderly clients in Hong Kong were recruited in a knowledge, attitude, and practice (KAP) cross-sectional survey. We used multivariable logistic regression to identify predictors for two key outcomes-"initiation and advice" (ask and advise) and "follow-through" (assess, assist and arrange), based on the U.S. Agency for Health Care Policy Research framework. One thousand eight hundred forty-three (49.8%) nurses and 1,499 (66.4%) social workers responded. Nurses reported a much higher level of engagement in smoking cessation activities than social workers in all five steps of the AHCPR framework (P < 0.001). Nurses (mean score = 2.99 ± 0.40 on a 4-point Likert scale) had more positive attitudes to tobacco control and smoking cessation counseling compared to social workers (mean score = 2.79 ± 0.41; P < 0.001), whereas the latter group perceived themselves as more competent in handling such practice (mean score nurses = 2.36 ± 0.52, mean score social workers = 2.51 ± 0.39; P < 0.001). Both attitudinal and self-perceived competence scores predicted incremental gains in the likelihood of offering "follow-through" interventions in addition to those observed for "initiation and advice" actions. Our findings highlight a large degree of unmet need in Hong Kong's hospital-based nurses and social workers who work with the elderly regarding smoking cessation service provision and training. Future research should focus on developing and evaluating programs that encourage nurses and social workers to provide cessation interventions to exert a much greater collective impact than doctors can alone. © 2004 The Institute For Cancer Prevention and Elsevier Inc. All rights reserved.link_to_subscribed_fulltex

Effectiveness of an elderly smoking cessation counseling training program for social workers: A longitudinal study

Background: To achieve greater coverage of the elderly smoking population, the provider/client interface could be broadened to include other professional groups who work with the elderly. We evaluated the effectiveness of a 9-h smoking cessation counseling training program for social workers. Methods: We recruited 177 social workers and used a preintervention/postintervention longitudinal design, analyzed by multilevel, multivariable modeling to adjust for between-subjects covariables and within-subjects correlation in repeated measurements at baseline, 3 months, 6 months, and 12 months after training. Results: Overall, knowledge improved from a mean score of 6.70 ± 1.03 (± SD) at baseline to 7.35 ± 0.75 at 12 months (range, 0 to 8 correct responses), attitude from 2.84 ± 0.41 to 3.10 ± 0.48, and self-perceived competence from 2.49 ± 0.38 to 2.85 ± 0.36 (range, 1 to 4, where 4 is best). On multilevel modeling, three of the four "A"s (ask, advice, assist, arrange as per the Agency for Healthcare Research and Quality framework) registered significant gains from baseline to 12 months overall, whereas "advice" did not show any appreciable change. Conclusion: These findings demonstrate that our smoking cessation training program achieved sustained effectiveness in the first year after training in enhancing knowledge, positively shifting attitudes, boosting self-perceived competence, and increasing the self-reported frequency of practicing three of the four As in their routine interaction with elderly clients.link_to_subscribed_fulltex

Satisfaction with inpatient care in a population-based Hong Kong Chinese sample

Objective To measure self-reported inpatient experience in Hong Kong. Design Data were derived from the 2005 Thematic Household Survey. Setting and participants 24 364 non-institutional and 3390 institutionalised respondents aged at least 18 years systematically drawn to represent the Hong Kong adult population, 6.9% of whom were admitted at least once as an inpatient during the previous 12 months. Data from this group was analysed. Main outcome measure Picker Patient Experience Questionnaire-15. Results Overall, respondents scored their last inpatient episode 39.6 (range=0-100, the lower the score, the better the patient experience). Patients who sought care from private hospitals reported a lower Picker Patient Experience Questionnaire-15 score than those cared for in public facilities (31.1 vs 41.8 respectively, p<0.001). We observed substantial differences between public hospital geographic clusters that were confirmed by multivariable regression. When benchmarked against the UK, Germany and the USA, Hong Kong patients tended to report a significantly higher number of problems. Conclusions We found systematic differences between the level of satisfaction and type of problems reported by Hong Kong Chinese compared to those in Euro-American settings. The observed heterogeneities among different public hospitals, between the private and public sectors, and among subgroups of inpatients should provide an evidence based on which quality improvement initiatives can be designed and evaluated.link_to_subscribed_fulltex

Prognostic significance of time to prostate-specific antigen (PSA) nadir and its relationship to survival beyond time to PSA nadir for prostate cancer patients with bone metastases after primary androgen deprivation therapy

BACKGROUND: This study investigated the prognostic significance of time to the prostate-specific antigen nadir (TTPN) and its relationship to survival beyond TTPN in metastatic prostate cancer after primary androgen-deprivation therapy (ADT). METHODS: All metastatic prostate cancer patients treated with primary ADT from 2000 to 2009 were reviewed. The prognostic significance of TTPN in predicting progression-free survival (PFS) beyond TTPN and overall survival (OS) beyond TTPN was analyzed using the Cox regression model. The median PFS and OS were plotted against TTPN on a monthly interval. The PFS beyond TTPN and the OS beyond TTPN with reference to TTPN were calculated and presented. RESULTS: The study enrolled 419 patients with a median follow-up period of 38 months. The findings showed that TTPN was a significant prognostic indicator for both PFS beyond TTPN (hazard ratio [HR] 0.72, 95 % confidence interval [CI] 0.52-0.99, p = 0.04) and OS beyond TTPN (HR 0.65, 95 % CI 0.47-0.90, p = 0.01) according to Cox regression analyses. The relationship between TTPN and survival beyond TTPN consisted of three phases. In the first phase (17 months for PFS and >20 months for OS), the survival beyond TTPN increased exponentially with TTPN. CONCLUSIONS: In this study, TTPN was a good prognostic indicator for PFS beyond TTPN and OS beyond TTPN in metastatic prostate cancer cases after primary ADT. Different TTPNs had different implications for predicting survival beyond TTPN