Cause and Effect

Cause and effect refers to a relationship between two phenomena in which one phenomenon is the reason behind the other. For example, eating too much fast food without any physical activity leads to weight gain. Here eating without any physical activity is the “cause” and weight gain is the “effect.” Another popular example in the discussion of cause and effect is that of smoking and lung cancer. A question that has surfaced in cancer research in the past several decades is, What is the effect of smoking on an individual's health? Also asked is the question, Does smoking cause lung cancer? Using data from observational studies, researchers have long established the relationship between smoking and the incidence of lung cancer; however, it took compelling evidence from several studies over several decades to establish smoking as a “cause” of lung cancer.

The term effect has been used frequently in scientific research. Most of the time, it can be seen that a statistically significant result from a linear regression or correlation analysis between two variables X and Y is explained as effect. Does X really cause Y or just relate to Y? The association (correlation) of two variables with each other in the statistical sense does not imply that one is the cause and the other is the effect. There needs to be a mechanism that explains the relationship in order for the association to be a causal one. For example, without the discovery of the substance nicotine in tobacco, it would have been difficult to establish the causal relationship between smoking and lung cancer. Tobacco companies have claimed that since there is not a single randomized controlled trial that establishes the differences in death from lung cancer between smokers and nonsmokers, there was no causal relationship. However, a cause-and-effect relationship is established by observing the same phenomenon in a wide variety of settings while controlling for other suspected mechanisms.

Statistical correlation (e.g., association) describes how the values of variable Y of a specific population are associated with the values of another variable X from the same population. For example, the death rate from lung cancer increases with increased age in the general population. The association or correlation describes the situation that there is a relationship between age and the death rate from lung cancer. Randomized prospective studies are often used as a tool to establish a causal effect. Time is a key element in causality because the cause must happen prior to the effect. Causes are often referred to as treatments or exposures in a study. Suppose a causal relationship between an investigational drug A and response Y needs to be established. Suppose YA represents the [Page 132]response when the participant is treated using A and Y0 is the response when the subject is treated with placebo under the same conditions. The causal effect of the investigational drug is defined as the population average δ = E(YA – Y0). However, a person cannot be treated with both placebo and Treatment A under the same conditions. Each participant in a randomized study will have, usually, equal potential of receiving Treatment A or the placebo. The responses from the treatment group and the placebo group are collected at a specific time after exposure to the treatment or placebo. Since participants are randomized to the two groups, it is expected that the conditions (represented by covariates) are balanced between the two groups. Therefore, randomization controls for other possible causes that can affect the response Y, and hence the difference between the average responses from the two groups, can be thought of an estimated causal effect of treatment A on Y.

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