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As noted in earlier modules a key goal in applied biostatistics is to make inferences about unknown population parameters based on sample statistics. Strictly speaking a 95% confidence interval means that if we were to take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ). Suppose we want to generate a 95% confidence interval estimate for an unknown population mean.
Using algebra, we can rework this inequality such that the mean (μ) is the middle term, as shown below. In the health-related publications a 95% confidence interval is most often used, but this is an arbitrary value, and other confidence levels can be selected. With smaller samples (n< 30) the Central Limit Theorem does not apply, and another distribution called the t distribution must be used.
Suppose we wish to estimate the mean systolic blood pressure, body mass index, total cholesterol level or white blood cell count in a single target population. Descriptive statistics on variables measured in a sample of a n=3,539 participants attending the 7th examination of the offspring in the Framingham Heart Study are shown below. The table below shows data on a subsample of n=10 participants in the 7th examination of the Framingham offspring Study.
Suppose we compute a 95% confidence interval for the true systolic blood pressure using data in the subsample.
Suppose we wish to estimate the proportion of people with diabetes in a population or the proportion of people with hypertension or obesity. This formula is appropriate for large samples, defined as at least 5 successes and at least 5 failures in the sample.
Specific applications of estimation for a single population with a dichotomous outcome involve estimating prevalence, cumulative incidence, and incidence rates. The table below, from the 5th examination of the Framingham Offspring cohort, shows the number of men and women found with or without cardiovascular disease (CVD).
There are many situations where it is of interest to compare two groups with respect to their mean scores on a continuous outcome. We could begin by computing the sample sizes (n1 and n2), means 1 and 2), and standard deviations (s1 and s2) in each sample. The confidence interval will be computed using either the Z or t distribution for the selected confidence level and the standard error of the point estimate. Where Sp is the pooled estimate of the common standard deviation (assuming that the variances in the populations are similar) computed as the weighted average of the standard deviations in the samples. Suppose we want to compare mean systolic blood pressures in men versus women using a 95% confidence interval. The following table includes 95% confidence intervals for each characteristic, computed using the same formula we used for the confidence interval for the difference in mean systolic blood pressures.
The confidence interval for the difference in means provides an estimate of the absolute difference in means of the outcome variable of interest between the comparison groups.
We previously considered a subsample of n=10 participants attending the 7th examination of the Offspring cohort in the Framingham Heart Study.
Suppose we wish to construct a 95% confidence interval for the difference in mean systolic blood pressures between men and women using these data. The previous section dealt with confidence intervals for the difference in means between two independent groups. A single sample of participants and each participant is measured twice, once before and then after an intervention.
A goal of these studies might be to compare the mean scores measured before and after the intervention, or to compare the mean scores obtained with the two conditions in a crossover study. For example, we might be interested in the difference in an outcome between twins or between siblings. In the one sample and two independent samples applications participants are the units of analysis. However, with two dependent samples application,the pair is the unit (and not the number of measurements which is twice the number of units).
In the Framingham Offspring Study, participants attend clinical examinations approximately every four years. We can now use these descriptive statistics to compute a 95% confidence interval for the mean difference in systolic blood pressures in the population. A crossover trial is conducted to evaluate the effectiveness of a new drug designed to reduce symptoms of depression in adults over 65 years of age following a stroke. One can compute a risk difference, which is computed by taking the difference in proportions between comparison groups and is similar to the estimate of the difference in means for a continuous outcome.
The risk ratio (or relative risk) is another useful measure to compare proportions between two independent populations and it is computed by taking the ratio of proportions.
Note that this formula is appropriate for large samples (at least 5 successes and at least 5 failures in each sample). The following table contains data on prevalent cardiovascular disease (CVD) among participants who were currently non-smokers and those who were current smokers at the time of the fifth examination in the Framingham Offspring Study.
A randomized trial is conducted among 100 subjects to evaluate the effectiveness of a newly developed pain reliever designed to reduce pain in patients following joint replacement surgery. Using the data in the table below, compute the point estimate for the difference in proportion of pain relief of 3+ points.are observed in the trial. Compute the 95% confidence interval for the difference in proportions of patients reporting relief (in this case a risk difference, since it is a difference in cumulative incidence). The risk difference quantifies the absolute difference in risk or prevalence, whereas the relative risk is, as the name indicates, a relative measure.
The relative risk is a ratio and does not follow a normal distribution, regardless of the sample sizes in the comparison groups. Statistics Confidence level is used to establish the statistics confidence interval it makes easily reached of the given data.
A confidence interval is a range of values that describes the uncertainty surrounding an estimate.
One-sided confidence interval bound or limit since either the upper limit will be infinity or the lower limit will be minus infinity depending on whether it is a lower bound or an upper bound respectively. Calculating Confidence Intervals is a very importat operation within Confidence Intervals study. The confidence interval is a range of values that has a given probability of containing the true value of the association.
Confidence limits for the mean are an interval estimate for the mean, whereas the estimate of the mean varies from sample to sample. A confidence interval is an interval estimate of a population parameter and is used to indicate the reliability of an estimate. Background: HIV infected patients, especially those treated with antiretroviral (ARV) drugs, show an increA­ased risk and incidence of cardiovascular disease. Results: HIV infected patients show more advanced subclinical atherosclerosis in the carotid arteries (cIMT and plaques incidence).
Due to the continuous development of antiretroviral therapy in recent years and the significantly prolonged survival time of HIV infected patients, in addition to many other diseases coexisting with HIV infection, there have been numerous reports on increased risk of cardiovascular disease (CVD) in this subpopulation.
Considering the research results, there are no single CVD risk factors in the HIV infected subpopulation.
The study lasted from March 2008 to May 2009 and inA­cluded 72 HIV infected patients treated at the Clinic of Acquired Immune Disorders.
This paper presents the preliminary cross-sectional reA­sults of the study on atherosclerosis in 72 HIV infected paA­tients. The characteristics of the immunological and virological status of the study group are presented in Table 1. The study protocol included obtaining the informed patient consent, interview with questions about traditional and seA­lected non-traditional CVD risk factors, pharmacotherapy including cART, and symptoms of CVD: cerebrovascular and cardiac events, and intermittent claudication. Metabolic syndrome (MS) was recognized based on the NCEP ATP III (National Cholesterol Education Program Adult Treatment Panel III) criteria revised in 2004 and the assessment of waist circumference, typical for American standards, and the IDF (International Diabetes Federation) 2005 definition, with the waist circumference assessment typical for Europe [74,76]. Ischemic heart disease was recognized on the basis of the medical history, and a resting electrocardiogram (ECG) was performed in all patients. Quantitative variables were presented as an arithmetic mean, geometric mean or median, depending on normaliA­ty of distribution.
Due to the small number of ARV non-treated patients in the cohort, the differences between ARV treated and nonA­-treated patients were not analyzed in this study. Tables 2 and 3 show the statistical analysis of quantitatiA­ve variables in the studied cohort and the control group. Among the laboratory parameters relevant to the CVD risk assessment (Tables 2, 3), statistically significant changes in the lipid profile can be observed: in the study cohort, the level of all cholesterol fractions was significantly reA­duced and triglyceride concentration was higher, while in the hemostatic system, a significantly lower platelet count and fibrinogen concentration was recorded. Another risk factor is hyperlipoproteinemia, understood as hypercholesterolemia, hypertriglyceridemia or mixed diA­sorders.
The percentage of diagnosed hypertension was similar in the cohort and in the control group (Table 4). Based on the physical examination, medical history and available medical records, cardiovascular disease was diaA­gnosed in three of the cohort participants (4.2%). Table 6 presents the results of IMT measurements: mean, standard deviation, median, minimum and maximum IMT for the location (LCA, LB, RCA, RB) and cIMT in both groups - the cohort and the control group. In the group of HIV infected patients, the values of cIMT and IMT for each location (RB, LB, LCA and RCA) were significantly higher, as was the percentage of people in whom atherosclerotic plaques were found (Table 7).
Analysis of regression between cIMT and smoking as a categorical variable shows no correlation of smoking and cIMT (Table 8).
After dividing the cohort according to the assumed criteA­rion of treatment duration, a significant difference in the advancement of subclinical carotid atherosclerosis was reA­vealed.
MSM mode infected patients show a significantly higher cIMT value compared with a subgroup of those infected by intravenous drug use. The paper on the cohort of HIV infected patients evaluA­ating the cardiovascular risk and subclinical atheroscleA­rosis brought about a number of interesting observations. In the study group of HIV-positive patients, the rate of cardiovascular events is higher for men and lower for woA­men (0%) compared to the general population.
The frequency of symptomatic POAD, confirmed by ABI, is similar (1.3%) to the non-infected population of this age [3] and twice as low as in the other described HIV infecA­ted cohorts [23,60].
It is difficult to discuss the impact of HIV infection on the incidence of CVD in our cohort in a clear way given the sample size and the number of people with episodes (one of the CVD events happened before HIV infection was doA­cumented), and also taking into account the exposure to multiple risk factors, including such potent factors as age, gender and positive family history.
The prevailing classic risk factor in our cohort is smoking, followed by lipid disorders and hypertension.
Comparison of this young cohort with the results of epiA­demiological studies in Poland is not easy, as all major studies were conducted among the elderly population.
The second most important risk factors in our cohort are lipid disorders, which occur in a similar proportion in the cohort and the control group (53% vs.
The cause of low total cholesterol and both its fractions in HIV infected patients is not clear; possible explanations include the young age of the cohort, low BMI, improper diet and lifestyle, and coexisting hepatitis B and C, as well as cigarette smoking (effect on HDL).
Diabetes occurs in the two groups at a similar frequency as in the adult Polish population aged 18-59 [83]. A general assessment of body posture revealed significanA­tly higher WHR and significantly lower BMI in the cohort participants compared with the control group. Metabolic syndrome is significantly more frequently diaA­gnosed in the cohort, using both ATP III and IDF criteria, and this is consistent with previous reports.
There is no difference in the homocysteine concentration between the infected and control groups. Multivariate regression analysis revealed that cIMT is strongly affected by age, hypertension, non-HDL choleA­sterol and ARV treatment time.
Metabolic syndrome occurs slightly more often in infected patients, but we did not demonstrate its effect on subcliniA­cal atherosclerosis.
Many of the outcomes we are interested in estimating are either continuous or dichotomous variables, although there are other types which are discussed in a later module.
In practice, however, we select one random sample and generate one confidence interval, which may or may not contain the true mean.
This means that there is a 95% probability that the confidence interval will contain the true population mean. However, if the sample size is large (n > 30), then the sample standard deviations can be used to estimate the population standard deviation. Note that for a given sample, the 99% confidence interval would be wider than the 95% confidence interval, because it allows one to be more confident that the unknown population parameter is contained within the interval. The t distribution is similar to the standard normal distribution but takes a slightly different shape depending on the sample size. We select a sample and compute descriptive statistics including the sample size (n), the sample mean, and the sample standard deviation (s). The margin of error is very small (the confidence interval is narrow), because the sample size is large. Because the sample size is small, we must now use the confidence interval formula that involves t rather than Z. These diagnoses are defined by specific levels of laboratory tests and measurements of blood pressure and body mass index, respectively.
For example, we might be interested in comparing mean systolic blood pressure in men and women, or perhaps compare BMI in smokers and non-smokers.
For analysis, we have samples from each of the comparison populations, and if the sample variances are similar, then the assumption about variability in the populations is reasonable. The sample is large (> 30 for both men and women), so we can use the confidence interval formula with Z. Next we substitute the Z score for 95% confidence, Sp=19, the sample means, and the sample sizes into the equation for the confidence interval.

The following table contains descriptive statistics on the same continuous characteristics in the subsample stratified by sex. There is an alternative study design in which two comparison groups are dependent, matched or paired. Participants are usually randomly assigned to receive their first treatment and then the other treatment.
Symptoms of depression are measured on a scale of 0-100 with higher scores indicative of more frequent and severe symptoms of depression. When the outcome is dichotomous, the analysis involves comparing the proportions of successes between the two groups. The risk ratio is a good measure of the strength of an effect, while the risk difference is a better measure of the public health impact, because it compares the difference in absolute risk and, therefore provides an indication of how many people might benefit from an intervention. When constructing confidence intervals for the risk difference, the convention is to call the exposed or treated group 1 and the unexposed or untreated group 2. However, the natural log (Ln) of the sample RR, is approximately normally distributed and is used to produce the confidence interval for the relative risk. Basically, it is concerned with the collection, organization, interpretation, calculation, forecast and analysis of statistical data.
All confidence intervals include zero, the lower bounds are negative whereas the upper bounds are positive.
A 95% confidence interval provides a range of likely values for the parameter such that the parameter is included in the interval 95% of the time in the long term.
If we careful, constructing a one-sided confidence interval can provide a more effective statement than use of a two-sided interval would. This section will help you to get knowledge over this.Confidence interval is defined as the function of manipulative of sample mean subtracted by error enclosed for the population mean of the function Formula for measuring the confidence interval by using the function is given by, confidence interval = $\bar{x} - EBM$ Error bounded for the sample mean is defined as the computation of tscore value for the confidence interval which is multiplied to the standard deviation value divided by the total values given in the data set.
Confidence intervals are preferable to P-values, as they tell us the range of possible effect sizes compatible with the data. The interval estimate gives an indication of how much uncertainty in estimate of the true mean. The confidence intervals should overlap completely with each other if we take two samples from the same population.
Wieslawa Kwiatkowska, Department of Angiology, Regional Specialist Hospital, Research and Development Center, 51-124 Wroclaw, ul. The data collected included evaluation of the infection, ARV treatment, past cardiovascular events, assessment of traditional and nontraditional risk facA­tors for cardiovascular diseases, cIMT measurements and amount of atherosclerotic plaques in the carotid arteries.
The cardiovascular risk profile of the HIV infected patients is siA­gnificantly different from HIV negative people.
Currently, we can rather discuss etiopathogenic areas gathering the risk factors and determining faster development of atheA­rosclerosis.
Moreover, the impact of HIV infection, infection duration, basic parameters of virological and immunological status over the course of infection and imA­pact of the overall antiretroviral treatment duration on the deA­velopment of the subclinical atherosclerosis were evaluated. The inclusion criteria were a diaA­gnosed HIV infection and the patient's informed consent to participate in the study. Exercise ECG had been planned in the case of a medical history suggesting angina, but so far there have been no indications for the exercise test in any of our patients. LDL cholesterol was calculated acA­cording to the Friedewald equation, and non-HDL choleA­sterol by subtracting HDL from TC (total cholesterol).
The effect of drug class on subclinical atherosclerosis was not consiA­dered either, as individual therapy might have changed seA­veral times before the beginning of this study. No differenA­ces were found in the average concentration of lipoproteA­in (a) between the two groups. The proportion of these changes is similar in both groups (Table 4), but there are significant qualitative difA­ferences (Table 5). These three patients are exposed to multiple risk factors, incluA­ding family history and hyperlipoproteinemia.
No present correlation between cIMT and co-infection with HBV, HCV or AIDS history was observed (Table 11). In the geA­neral English population, this percentage for men aged 16 to 64 is 2% and for women 0.9% [27].
There are reports suggesting that cART may be an additional risk factor for the development of cardiovascuA­lar disease [20,29,50]. An analysis of incidence and intensity of risk factors was perA­formed for a separate group aged 18-59 in the NATPOL PLUS study, and this will often be referred to in the discusA­sion. 51%) and are coA­nvergent with NATPOL PLUS epidemiological data for the Polish adult population (50%) [83]. The mean total choA­lesterol concentration in infected patients is significantly lower than in the control group and lower than in Polish population studies for this age group [83]. And thus, in both our groups, the incidence of hypertension was higher than in the epidemiological stuA­dies of Poles of the same age. The percenA­tage of patients with MS was also similar to that found in other studies [7,21,35,54,81].
Configuration changes may indicate chronic consumption of platelets and fibrinogen in an ongoing inflammatory process. Elevated concenA­trations were observed by other authors, especially in HIV infected patients treated with cART [10]. The cIMT is hiA­gher in HIV infected subjects in all locations, both within the common carotid arteries and in the bulbs. Non-HDL cholesterol reA­presents the most atherogenic cholesterol fractions (LDL and remnants).
At this stage, we treat this result as an interesting tendency, which will be given more attention in further stuA­dies. Time of ARV treatment longer than 5 years is associated with greA­ater severity of subclinical atherosclerosis in our cohort.
The atherosclerosis is strongly influenced by a complex set of risk factors such as age, non-HDL cholesterol, hyperA­tension and duration of antiretroviral treatment. Important changes in basic hemostaA­tic parameters were observed, and their causes and signiA­ficance will be investigated in further studies.
The parameters to be estimated depend not only on whether the endpoint is continuous or dichotomous, but also on the number of groups being studied. Recall that sample means and sample proportions are unbiased estimates of the corresponding population parameters. In a sense, one could think of the t distribution as a family of distributions for smaller samples.
The formulas for confidence intervals for the population mean depend on the sample size and are given below. Both of these situations involve comparisons between two independent groups, meaning that there are different people in the groups being compared.
The standard error of the point estimate will incorporate the variability in the outcome of interest in each of the comparison groups.
The men have higher mean values on each of the other characteristics considered (indicated by the positive confidence intervals).
This judgment is based on whether the observed difference is beyond that expected by chance. We compute the sample size (which in this case is the number of distinct participants or distinct pairs), the mean and standard deviation of the difference scores, and we denote these summary statistics as n, d and sd, respectively.
The data below are systolic blood pressures measured at the sixth and seventh examinations in a subsample of n=15 randomly selected participants. This is similar to a one sample problem with a continuous outcome except that we are now using the difference scores. Because the 95% confidence interval for the mean difference does not include zero, we can conclude that there is a statistically significant difference (in this case a significant improvement) in depressive symptom scores after taking the new drug as compared to placebo. Here smoking status defines the comparison groups, and we will call the current smokers group 1 and the non-smokers group 2. Because the 95% confidence interval includes zero, we conclude that the difference in prevalent CVD between smokers and non-smokers is not statistically significant. Patients are randomly assigned to receive either the new pain reliever or the standard pain reliever following surgery. While dealing with a large data, the confidence interval is a very important concept in statistics. A 95% confidence interval does'nt mean that particular interval has 95% chance of capturing the actual value of the parameter. P-values simply provide a cut-off beyond which we assert that the findings are ‘statistically significant’. In this case, the standard deviation is replaced by the estimated standard deviation 's', also known as the standard error. If the confidence intervals overlap, the two estimates are deemed to be not significantly different. An error bar can be represent the standard deviation, but more often than not it shows the 95% confidence interval of the mean. The first of these risk areas is the incidence of well-known typical and non-typical risk factors in HIV inA­fected patients, the existence and development of which, resulting from prolonged survival time, can be observed as in the general population. The following exclusion criteria were adopted: currently diagnosed acute medical condition, currently diagnosed AIDS, serum creatinine concentration higher than 2 mg%, more than 5-fold increase in transamiA­nase levels.
In all patients, a duplex ultrasound of carotid and vertebral arteries was performed, their patency assessed and ultrasound images recorded for further proA­cessing in order to evaluate subclinical atherosclerosis by means of computer-measured cIMT.
The presence of anti-HIV, anti-HBc and anti-HCV antibodies was determined in the control group using the enzyme imA­munoassay (EIA) method with microparticles. Other tests revealed lower hematocrit in the infected group; this difference is at the border of statistical significance. In the study group, dominant disorders involve dyslipidemia or hypertriglyceridemia, and in the control group, the dyslipidemia and hypercholesterolemia incidence is the same. A family history of CVD, assesA­sed according to current guidelines, was positive in 29% of the infected patients and 14.8% of the control group.
Peripheral occlusive arterial disease with symptomatic lower limb ischemia (claudication) and reduced ABI value concomiA­tant with coexistent asymptomatic high-grade stenosis of the carotid artery was found in one patient. The statistiA­cal analysis reveals a more complex relationship between cIMT and CVD risk factors and certain characteristics of the infection and ARV treatment.
Comparison of individual risk factors with the Polish epidemiological data shows an overrepresentation of smoA­kers in the cohort, 63.8% of patients, while the percentage of smokers in the adult (18-59) Polish population is aboA­ut 38%, which is the same as in the matched age and sex control group (37%) in this study [83]. However, the Polish population is dominated by hypercholesterolemia (approA­ximately 55-60%) [62,77,83]. We were somewhat surpriA­sed by the identical percentage of people with MS diagnoA­sed according to various criteria, taking into account low BMI in the cohort and no effect of waist circumference on the WHR. Fibrinogen is an acute phase proA­tein involved in the clotting process in response to infecA­tion. An effect of hoA­mocysteine on cIMT progression in HIV positive people has also been reported [13]. Despite the observations of other authors claiming increased concentration of CRP in HIV infected patients [30,59], our study showed no differences in CRP concentration between the infected and non-infecA­ted group. The incidenA­ce of atherosclerotic plaques in our cohort is significantly higher than in the control group. Although the concentration of non-HDL cholesterol in the study group is significantly lower than in the control group (as for other cholesterol fractions), this parameter seems to be a strong non-traditional risk factor for subclinical atherosclerosis among HIV infected paA­tients. The literature on this subject contains reports on teA­sting the impact of HIV RNA on endothelial function using flow-mediated vasodilatation (FMD) in ARV non-treated patients [61]; yet no correlation was found between HIV RNA and cIMT. When the outcome of interest is dichotomous like this, the record for each member of the sample indicates having the condition or characteristic of interest or not.
If we assume equal variances between groups, we can pool the information on variability (sample variances) to generate an estimate of the population variability. However,we will first check whether the assumption of equality of population variances is reasonable. The appropriate formula for the confidence interval for the mean difference depends on the sample size. Since the data in the two samples (examination 6 and 7) are matched, we compute difference scores by subtracting the blood pressure measured at examination 7 from that measured at examination 6 or vice versa.
The trial was run as a crossover trial in which each patient received both the new drug and a placebo. It is the ratio of the odds or disease in those with a risk factor compared to the odds of disease in those without the risk factor. A confidence interval for the difference in prevalent CVD (or prevalence difference) between smokers and non-smokers is given below. By convention we typically regard the unexposed (or least exposed) group as the comparison group, and the proportion of successes or the risk for the unexposed comparison group is the denominator for the ratio. First, a confidence interval is generated for Ln(RR), and then the antilog of the upper and lower limits of the confidence interval for Ln(RR) are computed to give the upper and lower limits of the confidence interval for the RR.
A confidence interval represents the long term chances of capturing the actual value of the population parameter over many different samples. With the analytic results, we can determining the P value to see whether the result is statistically significant.
Since the standard error is an estimate for the true value of the standard deviation, the distribution of the sample mean $\bar x$ is no longer normal with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$. However, this is a conservative test of significance that is appropriate when reporting multiple comparisons but the rates may still be significantly different at the 0.05 significance level even if the confidence intervals overlap.
The 95% confidence interval is an interval constructed such that in 95% of samples the true value of the population mean will fall within its limits.

The concentration of all cholesteA­rol fractions is lower, whereas the concentration of triglycerides is higher. A statistically higher incidenA­ce of some classical risk factors such as male gender and smoking, or of nonspecific factors - lifestyle, low physical activity and poor diet - is characteristic of the HIV infecA­ted subpopulation [13,19,20,38,57]. Carotid artery stenosis was recognized according to the NASCET (North American Symptomatic Carotid Endarterectomy Trial) and Bluth criA­teria.
Differences in quantitative features between the study and control groA­ups were analyzed by Student's t-test, the Welch test or the Mann-Whitney test, respectively. Fasting glucose, CRP and the homocysteine level did not differ significantly between the two groups. Ischemic heart disease and a previous stroke were discovered in one paA­tient and ischemic heart disease alone in one patient.
At present, these validations are not strong enough due to the low number of smokers in the control group and non-smokers in the cohort.
Comparison of lipid disorA­ders in these two groups demonstrated substantial qualiA­tative differences.
The prevalence of hypertension in individual cohorts varies - from a few percent up to 34% in the slightly older Italian cohort [21]. The percentage of diabetics among infected patients is 6-7.3%, depending on the authors [18,30,51]. In the adult population of Poles aged 18-59, in as many as 47.3%, the BMI was equal to or greater than 25, which is reflected in our control group. The sample should be representative of the population, with participants selected at random from the population. In contrast, when comparing two independent samples in this fashion the confidence interval provides a range of values for the difference. If a 95% confidence interval includes the null value, then there is no statistically meaningful or statistically significant difference between the groups. Based on this interval, we also conclude that there is no statistically significant difference in mean systolic blood pressures between men and women, because the 95% confidence interval includes the null value, zero. When the samples are dependent, we cannot use the techniques in the previous section to compare means. Before receiving the assigned treatment, patients are asked to rate their pain on a scale of 0-10 with high scores indicative of more pain.
The additional information concerning about the point is conventional in the given data set. Confidence interval for the population mean, based on a simple random sample of size n, for population with unknown mean and unknown standard deviation, is$\bar x$ ± t $\frac{s}{\sqrt{n}}$where, t is the upper $\frac{1-C}{2}$ critical value for the t distribution with n - 1 degrees of freedom, t(n - 1).
When comparing two parameter estimates, it is always true that if the confidence intervals do not overlap, then the statistics will be statistically significantly different. Carotid ultrasound was performed using a high-resoA­lution ultrasound GE LOGIQ 7 GE with broadband lineA­ar probe 6-12 MHz and 5x magnification.
Usually, the percentage of smokers is similar to that shown in our study, while in the Warsaw HIV cohort, it is very high at 90% [9,18,30,34,35,37,51,61,70]. In the study group, significantly lower total cholesterol and LDL and HDL cholesterol levels were observed, and hypercholesterolemia was three times less frequent than in the control group (8.3% vs. Considering only abA­normal WHR as an expression of central obesity, abdominal obesity concerns 43.1% of our study cohort.
The relatively high percentage of MS according to IDF criteria was proA­bably due to using a waist circumference consistent with European standards and strong representation of factors other than waist circumference.
Our observation, if confirmed in further studies, may indicate dynamic changes of IMT in this relaA­tively young subpopulation - the possibility of progression but also regression, which is suggested in the Coll study, where both phenomena were reported [9].
Based on the observation of a relationship between cIMT and current HIV RNA, we can claim an impact of the current infection status on the cIMT dynamics in this young subpopulation.
In generating estimates, it is also important to quantify the precision of estimates from different samples. Rather, it reflects the amount of random error in the sample and provides a range of values that are likely to include the unknown parameter. Just as with large samples, the t distribution assumes that the outcome of interest is approximately normally distributed. If the confidence interval does not include the null value, then we conclude that there is a statistically significant difference between the groups. Because the samples are dependent, statistical techniques that account for the dependency must be used. Each patient is then given the assigned treatment and after 30 minutes is again asked to rate their pain on the same scale.
Confidence intervals deliberated for determining the means that are the intervals construct by means of a method that they will enclose to the population mean of a particular segment of the time period, on average is moreover 95% or 99% of the confidence level.
Understanding that relation requires the concept of no effect, that is no difference between the groups being compared.
This is why error bar showing 95% confidence interval are so useful on graphs, because if the bars of any two means do not overlap then we can infer that these mean are from different populations.
A strong statistical correlation between cIMT and age, hypertension, non-high-density lipoprotein (non-HDL) cholesterol and ARV time were found.
Four series of images were collected for each patient: left common caroA­tid artery (LCA), right common carotid artery (RCA), left bulb (LB) and right bulb (RB). Differences in the qualitative features were analyzed using the c2 test or Fisher's exact test (for small groups). WHR is markedly afA­fected not by waist circumference, which is similar in both groups, but by hip circumference, and this is significanA­tly lower among HIV infected people. In Poland, this percentage in the same age group is slightly higher at 45.4% (NATPOL PLUS). MS as a categorical vaA­riable shows no association with cIMT, which had already been reported [37]. Time of treatment longer than 5 years, as well as diagnoA­sed hyperlipoproteinemia, are associated with significantly greater severity of subclinical atherosclerosis. Another way of thinking about a confidence interval is that it is the range of likely values of the parameter (defined as the point estimate + margin of error) with a specified level of confidence (which is similar to a probability). For each of the characteristics in the table above there is a statistically significant difference in means between men and women, because none of the confidence intervals include the null value, zero. Since the interval contains zero (no difference), we do not have sufficient evidence to conclude that there is a difference. When the outcome is continuous, the assessment of a treatment effect in a crossover trial is performed using the techniques described here. The difference in depressive symptoms was measured in each patient by subtracting the depressive symptom score after taking the placebo from the depressive symptom score after taking the new drug. All of these measures (risk difference, risk ratio, odds ratio) are used as measures of association by epidemiologists, and these three measures are considered in more detail in the module on Measures of Association in the core course in epidemiology.
For effect sizes that involve subtraction and for slopes and correlations, no effect is an effect size of zero.
The images were recorded in three projections for each series - anterior, lateral and posterior. The corA­relation between continuous variables was described using Pearson's or Spearman's correlation coefficient (depending on the normality of data). Two surprising facts are lack of difference in cIMT between smoking and non-smoking HIV infected patients, and a significant cIMT difference between infected and non-infected smokers. Dyslipidemia or isolated hypertriglyceridemia prevail in the infected group, and the average triglyceride level in the cohort is statistically higher than in the control group and compared with Polish epidemiological studies, where the average concentration of triglycerides in a comparable age group is lower [83].
The predictive importance of WHR for CVD risk assessment in HIV infected people has not been established yet. This observation is in contrast to other works showing the effect of MS on the cIMT value [2].
Low fibriA­nogen concentrations in HIV-positive individuals were also reported in other papers [1,26]. In our study cohort, approxiA­mately 40% of patients suffer from coexisting HCV infecA­tion, which may lead to lowering CRP levels, as indicated by the observations of other authors [66]. The dynamic nature of the chanA­ges is also confirmed by the results of drug-based studies that demonstrated the regression of subclinical atheroscA­lerosis expressed by IMT [53,71]. Note also that this 95% confidence interval for the difference in mean blood pressures is much wider here than the one based on the full sample derived in the previous example, because the very small sample size produces a very imprecise estimate of the difference in mean systolic blood pressures.
Confidence interval estimates for the risk difference, the relative risk and the odds ratio are described below. This confidence level is referred to as 95% or 99% guarantee of the intervals respectively.When there is a vast population data is available, confidence interval allows to choose correct interval for the research. Far wall images of the distal common carotid arA­teries and bulbs were recorded parallel to the probe surface at the smallest artery diameter and then saved on the hard drive and on DVDs. The effect of clinical features on the cIMT value in the studied group was assessed using uniA­variate or multivariate regression. The MS incidence is higher than in the control group; the difference is on the border of statistiA­cal significance (Table 4).
The probable explanation for both cases, apart from the small number of infected non-smokers and non-infected smokers, may be the complex character of the infection, ARV treatment and the accompanying metabolic disorders that reduce the differences among infected patients and exacerbate the difA­ferences between infected and non-infected participants. Special attention should be paid when asA­sessing central obesity using this index, especially in ARV treated patients, because its value may be higher due to the loss of fat around the hips and buttocks in the course of HIV-associated adipose redistribution syndrome (HARS) [46]. Fibrinogen concenA­tration may differ depending on the type of antiretroviral drugs, as high concentrations were observed while using PI, and low concentrations were observed for drugs from the NNRTI group [48].
Our observation is also practical: many HIV infected patients treated with ARV suffer from hypertriglyceridemia with triglyceride concentration exceeding 400 mg%, making it impossible to calculate LDL cholesterol.
With this in mind, it can be assumed (and treated as a hypothesis) that the adverse period of HIV infection, confirmed by high viral load or a low number of CD4 T-cells, may result in an increased cIMT value. It represents the range of numbers that are supposed to be good estimates for the population parameter.
The multivariate analyA­sis employed the stepwise method, which removed all staA­tistically insignificant features from the model. At the moment, we do not know what the reason for reduced fibrinogen levels in the cohort is and how important its observation is.
Given our strong observaA­tions, we believe that the assessment of lipid disorders in HIV infected patients should include the non-HDL choA­lesterol parameter, which is easy to calculate in a doctor's office. When there are small differences between groups, it may be possible to demonstrate that the differences are statistically significant if the sample size is sufficiently large, as it is in this example. Usually, the induction of these disorders is linked to antiretroviral treatment, as the disorders may be affected by all classes of drugs: protease inhibitors (PIs), nucleoside (NRTIs) and non-nucleoside reverse transcripA­tase inhibitors (NNRTIs) [14,20,24,25,26,58,65]. This situation was also confirmed in our cohort, in which high WHR is signiA­ficantly affected by low hip circumference, and waist cirA­cumference is irrelevant and does not differentiate the two groups.
Is this a sympA­tom of deep pathology in the chain of inflammatory proA­cesses or a symptom of liver dysfunction?
Our observations are in line with studies that show the relationship of subclinical atheroscA­lerosis with HIV infection per se [47,61,78]. It is very important to find confidence interval in order to perform any research or statistical survey on a large population data. Atherosclerotic plaque was assessed using a criteA­rion treating the plaque as focal IMT growth >1.5 mm. This paper does not deal with the symptoms of liA­podystrophy (which occurs in various forms in the majoriA­ty of the cohort). Possible causes may include malnutrition (as indicated by a significantly lower BMI) or the coexistence of other infections - hepaA­titis B or C - which may lead to the weakening of fibriA­nogen synthesis.
The effect of these cholesterol fractions on cIMT progression was reported by others [14,31]. Even in paA­tients treated successfully with antiretroviral therapy, chroA­nic immune activation continues, although at a low level [32].
The measurement results were transferred to a database analyA­zing a number of statistical features for the measurements of each projection and series. D-dimers are higher in the cohort, but this difference is not significant compared to the control group. The relationship between cIMT and hyperA­tension is most often evaluated based on quantitative data - the value of systolic or diastolic blood pressure. It is known that persistent stimulation of the immuA­ne system, characteristic of HIV infection, accelerates the development of atherosclerosis.
The main parameter for each patient was the average IMT value obtained for all the seA­ries, defined as cIMT. Results for the basic hemostatic parameters plus significantly lower hematocrit in the infected group may indirectly indicate that blood rheological properties shoA­uld be more favorable than in the healthy group. The use of a categorical variable allowed us to exclude the impact of incidental blood pressure fluctuations and demonstrate the connection of subclinical atherosclerosis development with long-term hypertension.
An atherogenic effect is observed both in the course of the immune deficit, as well as immune system stimulation related to antiretroviral treA­atment [28,31,32]. The siA­gnificantly lower mean platelet count in the infected groA­up is easily explained by coinfections with HBV and HCV as well as thrombocytopenia, which often accompany the infection and the main pathogenic mechanisms of which are already known [69]. The assumptions of the Bland and Altman plot were met, and the correlation coefficients for the intra- and interobserver reproducibility tests were 0.99.

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