Biostatistics & Epidemiology

Wednesday, August 14, 2019

Public Private Partnership

TYPES AND VARIATIONS OF PPPs:

PPP types depending on specific factors.

Source of funds for the private partner´s revenues: user-pays PPPs (mainly based on charges to users) versus government-pays PPPs (mainly based on government payments for the service).

Ownership of the PPP company or Special Purpose Vehicle (SPV): There are conventional PPPs (100 percent private ownership), institutional PPPs (publicly owned with 100 percent public ownership or under a JV or empresa mixta scheme with the public party controlling the PPP company), and other JVs or empresas mixtas.

Scope of the contract and/or object of the contract: Infrastructure PPPs or PPPs that include significant capital investment, where the main objective is developing and managing infrastructure over the long term; integrated PPPs when, in addition to the infrastructure, the private party is granted the right and obligation to operate a service; and O&M PPPs or service PPPs when there is neither capital investment nor development of new infrastructure by the private partner.

Relevance of private sector financing: Co-financed PPPs (PPP schemes where there is a material portion of public finance, usually in the form of grants), versus conventional PPPs.

PPPs may also be distinguished based on the past use of the site. From the perspective of the investor industry, the following alternative definitions are common.

Greenfield projects: Project investments that relate to a DBFOM that is recently awarded or under construction.

Brownfield projects: Project investments in infrastructure assets that existed before the time of procurement or that were previously greenfields, but are in operation at the time the investment is made.

Yellowfields or secondary stage: PPPs where the investment is related to significant renewals, refurbishment or a substantial expansion of the existing infrastructure.

A PPP with equity participation by the public party may be legally categorized as an empresa mixta, depending on the jurisdiction. Commonly, a JV or empresa mixta scheme will imply a significant participation of the public party in equity and significant participation in management, while a mere public equity participation, with no strategic influence in the PPP company, is not regarded as a JV by this Guide.

There are alternative uses of the terms Greenfield and Brownfield.

Tuesday, August 13, 2019

Least square mean

Least squares means (marginal means) vs. means Least square means is actually referred to as marginal means. In an analysis of covariance model, they are the group means after having controlled for a covariate (i.e. holding it constant at some typical value of the covariate, such as its mean value).

I made up the data in Table 1 above. There are two treatment groups (treatment A and treatment B) that are measured at two centers (Center 1 and Center 2). The mean value for Treatment A is simply the summation of all measures divided by the total number of observations (Mean for treatment A = 24/5 = 4.8); similarly the Mean for treatment B = 26/5 = 5.2. Mean for treatmeng A > Mean for treatment B. Table 2 shows the calculation of least squares means. First step is to calculate the means for each cell of treatment and center combination. The mean 9/3=3 for treatment A and center 1 combination; 7.5 for treatment A and center 2 combination; 5.5 for treatment B and center 1 combination; and 5 for treatment B and center 2 combination. After the mean for each cell is calculated, the least squares means are simply the average of these means. For treatment A, the LS mean is (3+7.5)/2 = 5.25; for treatment B, it is (5.5+5)/2=5.25. The LS Mean for both treatment groups are identical. It is easy to show the simple calculation of means and LS means in the above table with two factors. In clinical trials, the statistical model often needs to be adjusted for multiple factors including both categorical (treatment, center, gender) and continuous covariates (baseline measures). The calculation of LS mean is not easy to demonstrate. However, the LS mean should be used when the inferential comparison needs to be made. Typically, the means and LS means should point to the same direction (while with different values) for treatment comparison. Occasionally, they could point to the different directions (treatment A better than treatment B according to mean values; treatment B better than treatment A according to LS Mean).

Wednesday, January 2, 2019

Which statistical test to apply

Some names of the statistical tests:

Ref. Dtsch Arztebl Int 2010; 107(19): 343–8 DOI: 10.3238/arztebl.2010.0343

Edit:error in the picture

Mann Whitney U test is same as wilxon rank sum test

Wilcoxon Signed rank test is done in paired data

Ref. Dtsch Arztebl Int 2010; 107(19): 343–8 DOI: 10.3238/arztebl.2010.0343

PSM / COMMUNITY MEDICINE by Dr Abhishek Jaiswal is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at learnpsm@blogspot.com.
Permissions beyond the scope of this license may be available at jaiswal.fph@gmail.com.

Minimisation

The most important drawback of the randomization software is the problem of unmatched groups. In the process of randomization it is probable that the treatment groups develop significant differences in some prognostic factors, especially when the sample size is relatively small (<200). If these factors have important effects on the primary or secondary outcomes of the study, any important difference in the levels of these factors invalidate the trial results, and necessitate complicated statistical analysis with unreliable results. Various methods have been used to overcome the problem of unmatched trial groups including minimization and stratification, with minimization providing more acceptable results. With minimization the first subjects are enrolled randomly into one of groups. The subsequent subjects will be allocated to treatment groups after hypothetical allocation of each subject to every group, and then calculating an imbalance score. Using these imbalance scores, we can decide to which group the new subject must be allocated, to have the minimum amount of imbalance, in terms of prognostic factors. Pure minimization is indeed completely deterministic, that is, we can predict which group the next subject will be enrolled in, provided the factor levels of the new subject are known. This may invalidate the principle of trial blindness and introduce some bias into the trial. To overcome this shortcoming some elements of randomness are incorporated into the minimization algorithm, to make the prediction unlikely. Unfortunately the whole process of minimization is well beyond the skill of a typical clinical researcher, especially when the problem of unequal group allocations has to be taken into account. The difficulty in computation has resulted in a relatively less frequent use of minimization methods, in randomized clinical trials. The computer software can perform excellently in these situations, especially when the implementation has been logical. In the following sections, the aspects of two minimization programs are presented. Again the selection of these programs is based on the availability and ease of use.

Hosmer Lemeshow test

Proposed grouping based on the values of estimated probabilities.

2 grouping strategies:

Based on percentiles of estimated probabilities
Based on fixed values of estimated probabilities

With the first method, use of g=10 groups result in the first group containing
n1=n/10 subjects having the smallest estimated probabilities and the last group
containing n10=n/10 subjects having the largest estimated probabilities.

With the second method, use of g=10 groups results in cut points defined at the
values k/10, k=1,2……9 & the groups contain all subjects with estimated
probabilities between adjacent cut points.

Mann-Whitney U test

Mann-Whitney U test: It is the non-parametric alternative test to the unpaired t-test. It is a non-parametric test that is used to compare two sample means that come from the same population, and used to test whether two sample means are equal or not. Usually, the Mann-Whitney U test is used when the data is ordinal or when the assumptions of the t-test are not met.

Assumptions:

1. Sample drawn from the population is random
2. Observations are independent
3. Ordinal measurement scale

Wilcoxon sign test

Wilcoxon sign test: It is a type of test of significance done in paired data if the data is non-parametrically distributed or ordinal data. Compared to paired t-tests which analyzes if the average difference of two repeated measures is zero and require metric (interval or ratio) and normally distributed data.

The Wilcoxon signed rank test relies on the W-statistics. For large samples with n>10 paired observations the W-statistics approximates a Normal Distribution. The W statistics is a non-parametric test, thus it does not need multivariate normality in the data.

The first step of the Wilcoxon sign test is to calculate the differences of the repeated measurements and to calculate the absolute differences.

The next step of the Wilcoxon sign test is to order the cases by increasing absolute differences.

For the Wilcoxon signed rank test we can ignore cases where the difference is zero. For all other cases we assign their relative rank. In case of tied ranks the average rank is calculated. That is if rank 10 and 11 have the same observed differences both are assigned rank 10.5.

The next step of the Wilcoxon sign test is to sign each rank. If the original difference < 0 then the rank is multiplied by -1; if the difference is positive the rank stays positive.

The W-statistic is simply the sum of the signed ranks.