Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

Randomized Trial for a Mobile Health Approach to Increase Uptake of Cervical Cancer Screening in Tanzania

Background: Largely due to low availability and uptake of screening in low- and middle-income countries, cervical cancer is the second ranked cancer among women in these countries. This is a tragedy because cervical cancer is one of the most preventable carcinomas. This thesis will investigate behaviour change methods, which capitalize on the recent exponential increase in ownership of mobile phones in Tanzania, to increase uptake of cervical cancer screening (CCS) in the Kilimanjaro region of Tanzania. Objectives: 1) To evaluate the effectiveness of behaviour change messages delivered via short message service (SMS) on the uptake of CCS in the Kilimanjaro region; 2) to evaluate the effectiveness of a transportation eVoucher on the uptake of CCS in the Kilimanjaro region; 3) to explore characteristics associated with CCS uptake in the Kilimanjaro region; and 4) to determine the attitudes towards and perceived benefit of behaviour change SMS messages and eVouchers intended to increase uptake of CCS. Methods: In the Kilimanjaro Region, 853 women participated in a randomized controlled trial. Baseline data was collected through self-report through systematic stratified random sampling. Participants were randomized to one of three groups: a control group, a group receiving behaviour change messages delivered via SMS, or a group receiving a travel eVoucher and identical SMS as the SMS group. A fieldworker recorded participants attending screening at the CCS clinics and administered a post-screening survey. The follow-up period was two months from the time of the participant’s enrolment. Logistic regression (both for the combined and stratified data sets) was used to determine associations between the behaviour change interventions, baseline characteristics and cervical cancer screening uptake. Results: All participants receiving SMS messages (SMS or eVoucher group) were more likely to attend cervical cancer screening in comparison with the control group. 83% of participants who attended screening shared the information contained in the messages with others. Conclusions: Behaviour change messages delivered via SMS and transportation eVouchers have the potential to increase uptake of cervical cancer screening in the Kilimanjaro region of Tanzania. Harnessing this potential will require implementing these interventions alongside other methods to achieve maximum impact.